This package is designed for empirical asset pricing
Project description
Documentation
Module
portfolio_analysis
This module is used for portfolio analysis by 4 steps:
- select breakpoints
- distribute the assets into groups
- calculate the average and difference of groups
- summary the result
class ptf_analysis()
This class is for portfolio analysis containing few functions.
def select_breakpoints(self, character, number, perc=None, percn=None):
This function, corresponding to the step 1, selects the breakpoints of the sample.
**input : **
character (ndarray/Series): The asset characteristics by which the assets are grouped.
number (int): The number of the breakpoints and the number of interval is number+1. Once the number is given, the assets would be grouped into number+1 groups by the average partition of the asset characteristic.
perc (list/ndarray): perc are percentile points of the characteristics. Once it is set, then number is overwritten. eg. perc = [0, 30, 70, 100] represents the percentiles at 0%, 30%, 70%, 100%.
percn (list/ndarray): percn are percentiles of the characteristics. eg. the characteristics are divided by NYSE breakpoints.
output :
breakpoint : The breakpoint is the percentiles of the asset characteristic, ranging from 0% to 100%, whose in length is number+2.
Example
from EAP.portfolio_analysis import Ptf_analysis as ptfa
import matplotlib.pyplot as plt
import numpy as np
# generate characteristics
character = np.random.normal(0, 100, 10000)
# generate breakpoint
breakpoint = ptfa().slect_breakpoint(character=character, number=9)
print('Breakpoint:', breakpoint)
# comapre with the true breakpoint
for i in np.linspace(0, 100, 11):
print('True breakpoint', i, '%:', np.percentile(character,i))
========================================================================
Generated breakpoint: [-418.25352494 -127.85494153 -84.90868131 -53.27163604 -25.2394311 1.74938872 25.93867426 50.87047751 84.42711213 128.52009426 334.42181608]
True breakpoint 0.0 %: -418.25352493659074
True breakpoint 10.0 %: -127.85494153240666
True breakpoint 20.0 %: -84.90868130631613
True breakpoint 30.0 %: -53.271636036097135
True breakpoint 40.0 %: -25.239431099072657
True breakpoint 50.0 %: 1.7493887248228535
True breakpoint 60.0 %: 25.938674261710755
True breakpoint 70.0 %: 50.870477505977846
True breakpoint 80.0 %: 84.42711212754239
True breakpoint 90.0 %: 128.5200942602427
True breakpoint 100.0 %: 334.42181607589504
========================================================================
def distribute(self, character, breakpoint):
This function, corresponding to the step 2, distributes the assets into groups by characteristics grouped by the breakpoint.
input :
character (ndarray/Series): The characteristic by which the assets are grouped.
breakpoint (list/array): The breakpoints of the characteristic.
**output : **
label (ndarray): an array containing the group number of each asset.
Example
# continue the previous code
# generate the groups
print('The Label of unique value:\n', np.sort(np.unique(ptfa().distribute(character, breakpoint))))
# plot the histogram of the label
# each group have the same number of samples
plt.hist(ptfa().distribute(character, breakpoint))
label = ptfa().distribute(character, breakpoint)[:, 0]
# print the label
print('Label:\n', ptfa().distribute(character, breakpoint))
========================================================================
The Label of unique value:
[0. 1. 2. 3. 4. 5. 6. 7. 8. 9.]
Label:
[[2.]
[8.]
[1.]
...
[1.]
[4.]
[8.]]
def average(self, sample_return, label, cond='uni', weight=None):
This function, corresponding to the step 3, calculates the average return for each group.
input :
sample_return (ndarray): The return of each asset.
label (ndarray): The group label of each asset.
cond (str): If univariate analysis, then cond = 'uni'; if bivariate analysis, then cond = 'bi'.
weight (None): The weight to calculate the weighted average group return.
output :
average_return (ndarray): The average return of each group.
Example
# continue the previous code
# generate the future sample return
sample_return = character/100 + np.random.normal()
ave_ret = ptfa().average(sample_return, label)
# print the groups return
print('average return for groups:\n', ave_ret)
========================================================================
average return for groups:
[[-1.47855293]
[-0.75343815]
[-0.39540537]
[-0.0971466 ]
[ 0.17474793]
[ 0.42303036]
[ 0.68905747]
[ 0.95962212]
[ 1.33445632]
[ 2.03728439]]
def statistics(self, variable, label, func, cond='uni'):
This function is for summary statistics of groups.
input :
variable (ndarray): The variables of the groups.
label (ndarray): The label of the groups for each stock.
func (function): The operations to variables in each group, like numpy.mean, numpy.sum, etc.
cond (str): If univariate analysis, then cond = 'uni'; if bivariate analysis, then cond = 'bi'.
output:
average_statistics (ndarray): The statistics of each group.
def create_breakpoint(self, data, number, perc=None):
This function is for creating breakpoints. In many researches, the special breakpoints are needed like NYSE breakpoints in common. This function is designed for this demand.
input :
data (ndarray/DataFrame): The characteristics for partition.
The structure is
first row to last two row: character.
last row : time index.
number (int): The number of breakpoints.
perc (array/list): The percentile points of breakpoints.
output :
breakpoints array (list): The breakpoints of characteristics.
Example :
# generate variables
character=np.random.normal(0,1,20*3000)
# generate future return
ret=character*-0.5+np.random.normal(0,1,20*3000)
# create sample containing future return, character, time
sample=np.array([character,year]).T
breakpoints = ptfa().create_breakpoint(data=sample, number=4)
print(breakpoints)
class Univariate(ptf_analysis):
This class is designed for univariate portfolio analysis.
def _init_ (self, sample):
The initialization function
input :
sample (ndarray or DataFrame) : The samples to be analyzed. Samples usually contain the future return, characteristics, time. The DEFAULT setting is the 1th column is the forecast return, the 2nd column is the characteristic, the 3rd column or the index(if data type is Dataframe) is time label.
def divide_by_time(self, sample):
This function groups the sample by time.
split the sample by time into groups
output :
groups_by_time (list): The samples group by time.
def average_by_time(self):
This function, using the sample group by time from function divide_by_time, groups the sample by the characteristic, and then calculate average return of each group samples at every time point.
output :
average_group_time(matrix: N_T) : The average return of groups by each characteristic-time pair.
Example
import numpy as np
from portfolio_analysis import Univariate as uni
# generate time
year=np.ones((3000,1),dtype=int)*2020
for i in range(19):
year=np.append(year,(2019-i)*np.ones((3000,1),dtype=int))
# generate character
character=np.random.normal(0,1,20*3000)
# generate future return
ret=character*-0.5+np.random.normal(0,1,20*3000)
# create sample containing future return, character, time
sample=np.array([ret,character,year]).T
# initializ the univariate object
exper=uni(sample,9)
#
data=exper.average_by_time()
print(data)
==========================================================================================================================
[[ 0.82812256 0.87549215 0.81043114 0.77480366 0.85232487 0.85599445 0.90860961 0.76600211 0.91360546 0.85921985 0.96717798 0.77677131 0.88669273 0.86895145 0.97832435 0.88494486 0.82571951 0.84777939 0.89373487 0.95906454]
[ 0.51155724 0.4963439 0.6100762 0.47351625 0.46844971 0.53303287 0.52087477 0.43934316 0.51169633 0.61918844 0.56254028 0.50949226 0.39033219 0.49685445 0.5844816 0.48723354 0.49861094 0.43197525 0.40040156 0.57529228]
[ 0.41566251 0.3421546 0.27117215 0.35550346 0.28884636 0.43710998 0.33146264 0.27860032 0.35956881 0.34818479 0.35692361 0.42462374 0.16909231 0.33823117 0.31762348 0.44863438 0.42785283 0.20093775 0.29664738 0.31509963]
[ 0.21972246 0.24685649 0.29933776 0.09880866 0.13564638 0.17673649 0.14251437 0.12188551 0.1567432 0.20428427 0.15009782 0.08488247 0.20489871 0.10598241 0.12591301 0.17287433 0.11180376 0.09941738 0.22635281 0.22828588]
[ 0.01851548 0.05771421 0.0624163 0.05368921 0.15247324 0.05839522 0.05864669 0.01863668 -0.08367879 0.09273579 0.18374921 0.12331214 0.03635538 0.05804576 0.0116589 -0.04158565 0.11655945 0.09727234 0.14038867 0.13594649]
[-0.07910789 -0.04670755 0.08732773 -0.07361966 -0.00232509 -0.08546681 -0.15020487 -0.05302521 -0.07922696 -0.1088824 -0.01700017 -0.06742183 0.00190131 0.00961174 -0.05953252 -0.09504501 -0.0958816 -0.00355493 -0.08553405 -0.05343558]
[-0.13094033 -0.23888179 -0.11046595 -0.11176528 -0.14017103 -0.17184142 -0.26587781 -0.14426219 -0.15687278 -0.15962335 -0.18586504 -0.2367552 -0.26761165 -0.16169935 -0.26608677 -0.16202763 -0.24272797 -0.17049684 -0.21470737 -0.13520545]
[-0.35621842 -0.28111488 -0.42057927 -0.37219582 -0.25449753 -0.36362452 -0.34165952 -0.28564624 -0.29936621 -0.32545156 -0.28208242 -0.36730096 -0.24269836 -0.31584032 -0.34207757 -0.35185102 -0.35515763 -0.32239715 -0.2803911 -0.36334961]
[-0.58529295 -0.54329245 -0.52006031 -0.49856708 -0.44262707 -0.4464171 -0.58846501 -0.56725297 -0.35845646 -0.52923391 -0.42119445 -0.55659388 -0.47716067 -0.4574991 -0.52123094 -0.54767832 -0.50289813 -0.45529132 -0.58429513 -0.48110405]
[-0.81992395 -0.95766159 -0.92069685 -0.92906348 -0.84891875 -0.81670916 -0.90281776 -0.84845902 -0.90479169 -0.86860559 -0.96790821 -0.9464988 -0.88176205 -0.96118242 -0.92402295 -0.81623283 -0.81560442 -0.85841478 -0.87337267 -0.8070857 ]]
def difference(self, average_group):
This functions calculates the difference of group return, which, in detail, is the last group average return minus the first group average return.
input :
average_group (ndarray): The average return of groups by each characteristic-time pair.
output :
result (ndarray): The matrix added with the difference of average group return.
def summary_and_test(self):
This function summarizes the result and take t-test.
**output : **
self.average (ndarray): The average of the portfolio return across time.
self.ttest (ndarray): The t-value of the portfolio return across time.
def fit(self, number, perc=None, percn=None, maxlag=12, weight=False):
This function fit the model
input :
number (int): The breakpoint number.
perc (list or array): The breakpoint percentile points.
percn (list or array): The breakpoint percentiles.
maxlag (int): The maximum lag for Newey-West adjustment.
weight (boolean): If the weighted return is chosen, then weight is True. The DEFAULT is False.
def factor_adjustment(self, factor):
This function calculates the group return adjusted by risk factors.
input :
factor (ndarray or DataFrame): The return table with difference sequence.
output :
alpha (array): The anomaly
ttest (array): The t-value of the anomaly.
def extractor(self, pos):
This function extracts the return series
input :
pos (int): The position of the return series.
output:
series_ex (Series): The extracted Series.
def summary_statistics(self, variables=None, periodic=False):
This function is for summary statistics and outputs the group statistics and variables statistics.
input :
variables (ndarray/DataFrame): variables, except sort variable, that need to be analyzed.
periodic (boolean): whether print periodic results.
def correlation(self, variables, periodic=False, export=False):
This function is for calculating correlation coefficient of variables.
input :
variables (ndarray/DataFrame): The variables to be analyzed.
periodic (boolean): whether prints the periodic result. The DEFAULT is False.
export (boolean): whether exports the summary table. The DEFAULT is False.
output :
df (DataFrame): The summary table if export is True.
def print_summary_by_time(self, export=False):
This function print the summary grouped by time.
input :
export (boolean): Export the table or not. The table is exported in form of Dataframe. The default setting is False.
output :
df (DataFrame): The table exported in form of Dataframe.
def print_summary(self, explicit=False, export=False, percentage=False):
This function print the summary grouped by characteristic and averaged by time.
input :
explicit (boolean): Whether presents the explicit result. The default is False.
export (boolean): Export the table or not. The table is exported in form of Dataframe. The default setting is False.
percentage (boolean): Whether presents the percentage average return. The default is False.
output :
df (DataFrame): The table exported in form of Dataframe.
Example
# continue the previous code
exper.summary_and_test()
exper.print_summary_by_time()
========================================================================================================
+--------+-------+-------+-------+-------+--------+--------+--------+--------+--------+--------+--------+
| Time | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | diff |
+--------+-------+-------+-------+-------+--------+--------+--------+--------+--------+--------+--------+
| 2001.0 | 0.828 | 0.512 | 0.416 | 0.22 | 0.019 | -0.079 | -0.131 | -0.356 | -0.585 | -0.82 | -1.648 |
| 2002.0 | 0.875 | 0.496 | 0.342 | 0.247 | 0.058 | -0.047 | -0.239 | -0.281 | -0.543 | -0.958 | -1.833 |
| 2003.0 | 0.81 | 0.61 | 0.271 | 0.299 | 0.062 | 0.087 | -0.11 | -0.421 | -0.52 | -0.921 | -1.731 |
| 2004.0 | 0.775 | 0.474 | 0.356 | 0.099 | 0.054 | -0.074 | -0.112 | -0.372 | -0.499 | -0.929 | -1.704 |
| 2005.0 | 0.852 | 0.468 | 0.289 | 0.136 | 0.152 | -0.002 | -0.14 | -0.254 | -0.443 | -0.849 | -1.701 |
| 2006.0 | 0.856 | 0.533 | 0.437 | 0.177 | 0.058 | -0.085 | -0.172 | -0.364 | -0.446 | -0.817 | -1.673 |
| 2007.0 | 0.909 | 0.521 | 0.331 | 0.143 | 0.059 | -0.15 | -0.266 | -0.342 | -0.588 | -0.903 | -1.811 |
| 2008.0 | 0.766 | 0.439 | 0.279 | 0.122 | 0.019 | -0.053 | -0.144 | -0.286 | -0.567 | -0.848 | -1.614 |
| 2009.0 | 0.914 | 0.512 | 0.36 | 0.157 | -0.084 | -0.079 | -0.157 | -0.299 | -0.358 | -0.905 | -1.818 |
| 2010.0 | 0.859 | 0.619 | 0.348 | 0.204 | 0.093 | -0.109 | -0.16 | -0.325 | -0.529 | -0.869 | -1.728 |
| 2011.0 | 0.967 | 0.563 | 0.357 | 0.15 | 0.184 | -0.017 | -0.186 | -0.282 | -0.421 | -0.968 | -1.935 |
| 2012.0 | 0.777 | 0.509 | 0.425 | 0.085 | 0.123 | -0.067 | -0.237 | -0.367 | -0.557 | -0.946 | -1.723 |
| 2013.0 | 0.887 | 0.39 | 0.169 | 0.205 | 0.036 | 0.002 | -0.268 | -0.243 | -0.477 | -0.882 | -1.768 |
| 2014.0 | 0.869 | 0.497 | 0.338 | 0.106 | 0.058 | 0.01 | -0.162 | -0.316 | -0.457 | -0.961 | -1.83 |
| 2015.0 | 0.978 | 0.584 | 0.318 | 0.126 | 0.012 | -0.06 | -0.266 | -0.342 | -0.521 | -0.924 | -1.902 |
| 2016.0 | 0.885 | 0.487 | 0.449 | 0.173 | -0.042 | -0.095 | -0.162 | -0.352 | -0.548 | -0.816 | -1.701 |
| 2017.0 | 0.826 | 0.499 | 0.428 | 0.112 | 0.117 | -0.096 | -0.243 | -0.355 | -0.503 | -0.816 | -1.641 |
| 2018.0 | 0.848 | 0.432 | 0.201 | 0.099 | 0.097 | -0.004 | -0.17 | -0.322 | -0.455 | -0.858 | -1.706 |
| 2019.0 | 0.894 | 0.4 | 0.297 | 0.226 | 0.14 | -0.086 | -0.215 | -0.28 | -0.584 | -0.873 | -1.767 |
| 2020.0 | 0.959 | 0.575 | 0.315 | 0.228 | 0.136 | -0.053 | -0.135 | -0.363 | -0.481 | -0.807 | -1.766 |
+--------+-------+-------+-------+-------+--------+--------+--------+--------+--------+--------+--------+
exper.print_summary()
==================================================================================================================
+---------+--------+--------+--------+--------+-------+--------+---------+---------+---------+---------+---------+
| Group | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Diff |
+---------+--------+--------+--------+--------+-------+--------+---------+---------+---------+---------+---------+
| Average | 0.867 | 0.506 | 0.336 | 0.166 | 0.068 | -0.053 | -0.184 | -0.326 | -0.504 | -0.883 | -1.75 |
| T-Test | 63.706 | 35.707 | 20.199 | 12.637 | 4.6 | -4.463 | -15.616 | -32.172 | -36.497 | -73.162 | -92.152 |
+---------+--------+--------+--------+--------+-------+--------+---------+---------+---------+---------+---------+
# generate factor
factor=np.random.normal(0,1.0,(20,1))
exper=uni(sample,9,factor=factor,maxlag=12)
# print(exper.summary_and_test()) # if needed
exper.print_summary()
====================================================================================================================
+---------+--------+--------+--------+--------+-------+---------+---------+---------+---------+---------+----------+
| Group | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Diff |
+---------+--------+--------+--------+--------+-------+---------+---------+---------+---------+---------+----------+
| Average | 0.867 | 0.506 | 0.336 | 0.166 | 0.068 | -0.053 | -0.184 | -0.326 | -0.504 | -0.883 | -1.75 |
| T-Test | 63.706 | 35.707 | 20.199 | 12.637 | 4.6 | -4.463 | -15.616 | -32.172 | -36.497 | -73.162 | -92.152 |
| Alpha | 0.869 | 0.507 | 0.336 | 0.164 | 0.067 | -0.054 | -0.184 | -0.326 | -0.503 | -0.883 | -1.752 |
| Alpha-T | 62.39 | 69.24 | 43.377 | 16.673 | 8.204 | -12.372 | -16.679 | -65.704 | -87.618 | -93.223 | -139.881 |
+---------+--------+--------+--------+--------+-------+---------+---------+---------+---------+---------+----------+
# summary statistics
# summary statstics
exper.summary_statistics()
exper.summary_statistics(periodic=True)
exper.summary_statistics(variables=np.array([variable_1, variable_2]).T, periodic=True)
=============================================================================================================================================
Group Statistics
+---------------+----------+----------+----------+----------+----------+---------+---------+---------+---------+---------+
| Variable | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+---------------+----------+----------+----------+----------+----------+---------+---------+---------+---------+---------+
| Sort Variable | -1.75599 | -1.04855 | -0.68048 | -0.38582 | -0.13043 | 0.12162 | 0.38283 | 0.67123 | 1.04036 | 1.75617 |
+---------------+----------+----------+----------+----------+----------+---------+---------+---------+---------+---------+
Indicator Statistics
+---------------+----------+---------+---------+---------+----------+----------+----------+----------+---------+---------+---------+--------+
| Variable | Mean | SD | Skew | Kurt | Min | P5 | P25 | Median | P75 | P95 | Max | n |
+---------------+----------+---------+---------+---------+----------+----------+----------+----------+---------+---------+---------+--------+
| Sort Variable | -0.00291 | 1.00034 | 0.00655 | 0.00903 | -3.78607 | -1.64983 | -0.67779 | -0.00555 | 0.66878 | 1.64654 | 5.01253 | 3000.0 |
+---------------+----------+---------+---------+---------+----------+----------+----------+----------+---------+---------+---------+--------+
Group Statistics
+--------+----------+----------+----------+----------+----------+---------+---------+---------+---------+---------+
| Time | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+--------+----------+----------+----------+----------+----------+---------+---------+---------+---------+---------+
| 2001.0 | -1.6925 | -1.02089 | -0.66652 | -0.38477 | -0.1233 | 0.11802 | 0.37854 | 0.65636 | 1.01076 | 1.72971 |
| 2002.0 | -1.87762 | -1.11717 | -0.73731 | -0.41848 | -0.13805 | 0.1111 | 0.36679 | 0.66682 | 1.03146 | 1.73504 |
| 2003.0 | -1.78951 | -1.10062 | -0.72741 | -0.43769 | -0.16465 | 0.10609 | 0.38293 | 0.68745 | 1.07672 | 1.81225 |
| 2004.0 | -1.73014 | -1.06276 | -0.71448 | -0.4134 | -0.15013 | 0.11498 | 0.3735 | 0.65222 | 1.04136 | 1.75216 |
| 2005.0 | -1.76065 | -1.03176 | -0.64098 | -0.361 | -0.11605 | 0.1288 | 0.37912 | 0.67395 | 1.05602 | 1.77653 |
| 2006.0 | -1.74401 | -1.0027 | -0.66083 | -0.39449 | -0.14914 | 0.10178 | 0.3742 | 0.67059 | 1.04616 | 1.76814 |
| 2007.0 | -1.80695 | -1.06589 | -0.68808 | -0.38284 | -0.12541 | 0.1307 | 0.3805 | 0.6842 | 1.07225 | 1.79131 |
| 2008.0 | -1.74075 | -1.03649 | -0.66014 | -0.36012 | -0.08308 | 0.16978 | 0.40924 | 0.69059 | 1.07663 | 1.80214 |
| 2009.0 | -1.72743 | -1.02872 | -0.66078 | -0.35962 | -0.10524 | 0.15432 | 0.41381 | 0.70732 | 1.05451 | 1.77899 |
| 2010.0 | -1.78576 | -1.0724 | -0.70536 | -0.4206 | -0.15331 | 0.10784 | 0.36778 | 0.63268 | 0.97913 | 1.70654 |
| 2011.0 | -1.74376 | -1.06618 | -0.66421 | -0.36223 | -0.11708 | 0.11619 | 0.37691 | 0.65584 | 1.04012 | 1.75902 |
| 2012.0 | -1.74187 | -1.02805 | -0.66739 | -0.35736 | -0.11212 | 0.14089 | 0.40391 | 0.67798 | 1.02562 | 1.73806 |
| 2013.0 | -1.76579 | -1.05636 | -0.71253 | -0.40731 | -0.15883 | 0.08952 | 0.34684 | 0.64058 | 1.0596 | 1.76204 |
| 2014.0 | -1.74755 | -1.05756 | -0.66698 | -0.35469 | -0.08209 | 0.15193 | 0.41016 | 0.70804 | 1.05792 | 1.72348 |
| 2015.0 | -1.71824 | -1.02469 | -0.68511 | -0.39623 | -0.12801 | 0.1155 | 0.3805 | 0.67353 | 1.03347 | 1.79041 |
| 2016.0 | -1.76041 | -1.00856 | -0.65567 | -0.38146 | -0.14799 | 0.12255 | 0.39534 | 0.68455 | 1.03506 | 1.74972 |
| 2017.0 | -1.76569 | -1.09121 | -0.6997 | -0.39767 | -0.16277 | 0.08815 | 0.36036 | 0.65853 | 1.02296 | 1.7052 |
| 2018.0 | -1.7382 | -1.04642 | -0.69095 | -0.39814 | -0.14829 | 0.09936 | 0.35899 | 0.63287 | 1.00188 | 1.77708 |
| 2019.0 | -1.79867 | -1.02312 | -0.63218 | -0.35047 | -0.10632 | 0.13742 | 0.38529 | 0.67535 | 1.05045 | 1.73754 |
| 2020.0 | -1.68432 | -1.02939 | -0.6729 | -0.3778 | -0.13669 | 0.12742 | 0.41184 | 0.6951 | 1.03508 | 1.72796 |
+--------+----------+----------+----------+----------+----------+---------+---------+---------+---------+---------+
Indicator Statistics
+--------+----------+---------+----------+----------+----------+----------+----------+----------+---------+---------+---------+--------+
| Time | Mean | SD | Skew | Kurt | Min | P5 | P25 | Median | P75 | P95 | Max | n |
+--------+----------+---------+----------+----------+----------+----------+----------+----------+---------+---------+---------+--------+
| 2001.0 | 0.00054 | 0.97302 | 0.02247 | -0.10708 | -3.42651 | -1.6194 | -0.65605 | -0.00359 | 0.65144 | 1.64108 | 3.03045 | 3000.0 |
| 2002.0 | -0.03774 | 1.02917 | -0.07101 | -0.04394 | -3.34554 | -1.75824 | -0.73412 | -0.00649 | 0.67196 | 1.60588 | 3.24348 | 3000.0 |
| 2003.0 | -0.01544 | 1.031 | 0.08283 | -0.05399 | -3.70265 | -1.68766 | -0.72952 | -0.02717 | 0.67982 | 1.71738 | 5.01253 | 3000.0 |
| 2004.0 | -0.01367 | 0.99949 | 0.05183 | 0.03698 | -3.78607 | -1.6032 | -0.7196 | -0.00878 | 0.64707 | 1.63855 | 3.94993 | 3000.0 |
| 2005.0 | 0.0104 | 1.00123 | -0.00145 | 0.05439 | -3.45686 | -1.65593 | -0.64007 | 0.00818 | 0.66671 | 1.66286 | 3.25955 | 3000.0 |
| 2006.0 | 0.00097 | 0.99657 | 0.0462 | 0.14851 | -3.66269 | -1.63244 | -0.65111 | -0.02304 | 0.66632 | 1.64847 | 3.80687 | 3000.0 |
| 2007.0 | -0.00102 | 1.02414 | -0.02673 | 0.09203 | -3.6959 | -1.67876 | -0.68666 | -0.00039 | 0.68119 | 1.67692 | 3.46859 | 3000.0 |
| 2008.0 | 0.02678 | 1.00841 | -0.01221 | -0.01983 | -3.23867 | -1.60362 | -0.66403 | 0.05001 | 0.68418 | 1.69399 | 3.12197 | 3000.0 |
| 2009.0 | 0.02272 | 0.99936 | 0.00098 | -0.02585 | -3.47649 | -1.6255 | -0.66684 | 0.01566 | 0.70893 | 1.65815 | 3.52246 | 3000.0 |
| 2010.0 | -0.03435 | 0.99275 | -0.00444 | 0.07042 | -3.76678 | -1.68815 | -0.70062 | -0.02015 | 0.62253 | 1.58344 | 4.38276 | 3000.0 |
| 2011.0 | -0.00054 | 0.99636 | 0.02189 | 0.01578 | -3.27961 | -1.65198 | -0.66553 | -0.00789 | 0.64738 | 1.63708 | 3.82473 | 3000.0 |
| 2012.0 | 0.00797 | 0.99176 | -0.02293 | 0.16201 | -3.71695 | -1.62543 | -0.66423 | 0.00611 | 0.67271 | 1.62142 | 4.53518 | 3000.0 |
| 2013.0 | -0.02023 | 1.00519 | 0.06585 | -0.02879 | -2.94317 | -1.6765 | -0.71018 | -0.04464 | 0.63132 | 1.6228 | 3.69209 | 3000.0 |
| 2014.0 | 0.01427 | 0.9944 | -0.06002 | -0.14694 | -3.24666 | -1.65555 | -0.66567 | 0.03211 | 0.70328 | 1.61143 | 3.76138 | 3000.0 |
| 2015.0 | 0.00411 | 0.99681 | 0.05986 | -0.00795 | -3.23554 | -1.62117 | -0.67571 | -0.01158 | 0.67075 | 1.69081 | 3.2803 | 3000.0 |
| 2016.0 | 0.00331 | 0.99567 | -0.01401 | 0.05045 | -3.32744 | -1.6719 | -0.65461 | -0.02452 | 0.68572 | 1.63524 | 3.64654 | 3000.0 |
| 2017.0 | -0.02818 | 0.99394 | 0.03023 | -0.07768 | -2.89247 | -1.66422 | -0.69934 | -0.04211 | 0.6557 | 1.61093 | 4.08491 | 3000.0 |
| 2018.0 | -0.01518 | 0.99426 | 0.06121 | 0.05183 | -3.6031 | -1.61522 | -0.68846 | -0.02645 | 0.63035 | 1.65972 | 3.17931 | 3000.0 |
| 2019.0 | 0.00753 | 0.99978 | -0.09315 | 0.15681 | -3.66891 | -1.66554 | -0.62705 | 0.01924 | 0.67606 | 1.6475 | 3.63029 | 3000.0 |
| 2020.0 | 0.00963 | 0.97843 | 0.00495 | -0.19773 | -3.52657 | -1.57132 | -0.67812 | -0.0006 | 0.69571 | 1.6329 | 2.96727 | 3000.0 |
+--------+----------+---------+----------+----------+----------+----------+----------+----------+---------+---------+---------+--------+
Group Statistics
+-----------+----------+----------+----------+----------+----------+----------+----------+----------+----------+----------+
| Time | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+-----------+----------+----------+----------+----------+----------+----------+----------+----------+----------+----------+
| 2001.0 | -1.6925 | -1.02089 | -0.66652 | -0.38477 | -0.1233 | 0.11802 | 0.37854 | 0.65636 | 1.01076 | 1.72971 |
| 2002.0 | -1.87762 | -1.11717 | -0.73731 | -0.41848 | -0.13805 | 0.1111 | 0.36679 | 0.66682 | 1.03146 | 1.73504 |
| 2003.0 | -1.78951 | -1.10062 | -0.72741 | -0.43769 | -0.16465 | 0.10609 | 0.38293 | 0.68745 | 1.07672 | 1.81225 |
| 2004.0 | -1.73014 | -1.06276 | -0.71448 | -0.4134 | -0.15013 | 0.11498 | 0.3735 | 0.65222 | 1.04136 | 1.75216 |
| 2005.0 | -1.76065 | -1.03176 | -0.64098 | -0.361 | -0.11605 | 0.1288 | 0.37912 | 0.67395 | 1.05602 | 1.77653 |
| 2006.0 | -1.74401 | -1.0027 | -0.66083 | -0.39449 | -0.14914 | 0.10178 | 0.3742 | 0.67059 | 1.04616 | 1.76814 |
| 2007.0 | -1.80695 | -1.06589 | -0.68808 | -0.38284 | -0.12541 | 0.1307 | 0.3805 | 0.6842 | 1.07225 | 1.79131 |
| 2008.0 | -1.74075 | -1.03649 | -0.66014 | -0.36012 | -0.08308 | 0.16978 | 0.40924 | 0.69059 | 1.07663 | 1.80214 |
| 2009.0 | -1.72743 | -1.02872 | -0.66078 | -0.35962 | -0.10524 | 0.15432 | 0.41381 | 0.70732 | 1.05451 | 1.77899 |
| 2010.0 | -1.78576 | -1.0724 | -0.70536 | -0.4206 | -0.15331 | 0.10784 | 0.36778 | 0.63268 | 0.97913 | 1.70654 |
| 2011.0 | -1.74376 | -1.06618 | -0.66421 | -0.36223 | -0.11708 | 0.11619 | 0.37691 | 0.65584 | 1.04012 | 1.75902 |
| 2012.0 | -1.74187 | -1.02805 | -0.66739 | -0.35736 | -0.11212 | 0.14089 | 0.40391 | 0.67798 | 1.02562 | 1.73806 |
| 2013.0 | -1.76579 | -1.05636 | -0.71253 | -0.40731 | -0.15883 | 0.08952 | 0.34684 | 0.64058 | 1.0596 | 1.76204 |
| 2014.0 | -1.74755 | -1.05756 | -0.66698 | -0.35469 | -0.08209 | 0.15193 | 0.41016 | 0.70804 | 1.05792 | 1.72348 |
| 2015.0 | -1.71824 | -1.02469 | -0.68511 | -0.39623 | -0.12801 | 0.1155 | 0.3805 | 0.67353 | 1.03347 | 1.79041 |
| 2016.0 | -1.76041 | -1.00856 | -0.65567 | -0.38146 | -0.14799 | 0.12255 | 0.39534 | 0.68455 | 1.03506 | 1.74972 |
| 2017.0 | -1.76569 | -1.09121 | -0.6997 | -0.39767 | -0.16277 | 0.08815 | 0.36036 | 0.65853 | 1.02296 | 1.7052 |
| 2018.0 | -1.7382 | -1.04642 | -0.69095 | -0.39814 | -0.14829 | 0.09936 | 0.35899 | 0.63287 | 1.00188 | 1.77708 |
| 2019.0 | -1.79867 | -1.02312 | -0.63218 | -0.35047 | -0.10632 | 0.13742 | 0.38529 | 0.67535 | 1.05045 | 1.73754 |
| 2020.0 | -1.68432 | -1.02939 | -0.6729 | -0.3778 | -0.13669 | 0.12742 | 0.41184 | 0.6951 | 1.03508 | 1.72796 |
| Variable1 | | | | | | | | | | |
| 2001.0 | -0.01522 | -0.04716 | -0.00418 | 0.04429 | 0.02995 | -0.03962 | 0.03099 | -0.00748 | -0.01993 | 0.07281 |
| 2002.0 | -0.04164 | 0.04915 | 0.09105 | -0.01251 | 0.01903 | -0.06013 | 0.13446 | 0.00548 | 0.10778 | 0.0321 |
| 2003.0 | -0.05489 | -0.05391 | 0.07348 | 0.01206 | -0.02717 | 0.09487 | 0.02613 | -0.08623 | -0.01783 | 0.03207 |
| 2004.0 | -0.11632 | -0.05173 | 0.00346 | 0.05961 | 0.05607 | 0.0044 | -0.06302 | -0.0196 | 0.02273 | 0.00575 |
| 2005.0 | -0.03024 | 0.07865 | -0.01689 | 0.01001 | 0.03753 | -0.07502 | -0.04625 | -0.03403 | -0.02387 | -0.0277 |
| 2006.0 | -0.00906 | 0.06595 | -0.06769 | 0.04341 | -0.11204 | 0.02921 | -0.09275 | -0.03564 | 0.02151 | -0.01127 |
| 2007.0 | 0.06778 | 0.04576 | 0.0608 | -0.04811 | 0.00333 | 0.00261 | -0.0016 | -0.07013 | -0.03491 | 0.05194 |
| 2008.0 | -0.05786 | -0.15562 | 0.02984 | 0.0357 | -0.05811 | -0.00905 | -0.01723 | 0.01197 | -0.01656 | 0.05303 |
| 2009.0 | 0.07899 | 0.04472 | 0.01793 | -0.01595 | -0.00243 | -0.01357 | -0.05197 | 0.01346 | -0.06112 | 0.01429 |
| 2010.0 | 0.00449 | -0.01249 | 0.06374 | 0.04358 | -0.06673 | -0.03651 | 0.03834 | 0.108 | -0.01276 | -0.08404 |
| 2011.0 | 0.04746 | -0.02221 | 0.03684 | -0.036 | 0.07592 | 0.0378 | -0.07824 | 0.08281 | -0.06111 | -0.01362 |
| 2012.0 | -0.00621 | -0.05096 | -0.1767 | 0.02314 | 0.04629 | -0.01675 | 0.05391 | 0.04671 | 0.11531 | 0.02835 |
| 2013.0 | -0.015 | 0.04923 | -0.06807 | -0.01484 | 0.03847 | 0.01953 | 0.08062 | -0.05869 | 0.03246 | 0.06554 |
| 2014.0 | 0.04659 | -0.04936 | 0.03138 | -0.03342 | 0.05986 | 0.03902 | -0.02342 | 0.07528 | 0.08315 | 0.05208 |
| 2015.0 | -0.05979 | 0.02031 | 0.02758 | -0.01191 | -0.10045 | 0.06854 | 0.0208 | 0.01457 | 0.02852 | -0.00798 |
| 2016.0 | -0.05725 | 0.10226 | 0.01476 | 0.04893 | -0.06243 | 0.01586 | -0.03891 | 0.0497 | -0.06997 | 0.02027 |
| 2017.0 | -0.08491 | -0.0204 | 0.06377 | -0.03237 | 0.04701 | -0.03702 | 0.03355 | 0.01081 | 0.06146 | -0.10583 |
| 2018.0 | 0.17193 | 0.00903 | -0.09272 | -0.03469 | -0.0089 | 0.02757 | 0.1021 | -0.0237 | 0.0248 | 0.06012 |
| 2019.0 | 0.01284 | -0.16395 | -0.02548 | -0.02048 | 0.02623 | -0.07111 | -0.01099 | -0.00777 | -0.08123 | 0.0173 |
| 2020.0 | 0.0235 | 0.05426 | -0.01945 | -0.00294 | 0.00467 | -0.03483 | -0.05022 | -0.10885 | -0.02188 | 0.04856 |
| Variable2 | | | | | | | | | | |
| 2001.0 | -0.06124 | -0.04428 | -0.04644 | -0.01806 | 0.06192 | -0.04294 | 0.01533 | 0.06654 | 0.09389 | 0.10937 |
| 2002.0 | -0.13372 | -0.07595 | -0.06099 | 0.12119 | 0.0084 | -0.03141 | 0.03979 | 0.01794 | -0.00021 | 0.01842 |
| 2003.0 | 0.03537 | -0.00357 | 0.00429 | -0.01691 | 0.04931 | -0.15836 | 0.0193 | -0.0739 | -0.06891 | 0.0953 |
| 2004.0 | 0.06502 | -0.04215 | 0.038 | -0.07539 | -0.02489 | -0.0284 | 0.00056 | -0.03221 | -0.00046 | 0.00694 |
| 2005.0 | -0.08741 | -0.07291 | 0.14488 | 0.05242 | -0.04511 | -0.01714 | 0.0171 | -0.00856 | 0.00803 | -0.01396 |
| 2006.0 | 0.03065 | -0.02519 | 0.07904 | 0.04322 | -0.01684 | 0.10146 | -0.06241 | 0.07308 | -0.04444 | 0.10448 |
| 2007.0 | 0.02148 | -0.01106 | 0.00893 | 0.02162 | -0.00159 | -0.0297 | 0.04191 | 0.05094 | 0.0363 | -0.00436 |
| 2008.0 | 0.0107 | -0.10686 | 0.04827 | 0.03952 | 0.07151 | -0.03169 | 0.03021 | -0.09669 | -0.0482 | -0.06362 |
| 2009.0 | -0.01609 | -0.08597 | -0.03498 | -0.10286 | 0.01119 | 0.0722 | -0.00609 | -0.01957 | 0.05398 | -0.00213 |
| 2010.0 | -0.07676 | 0.04038 | -0.07815 | -0.0874 | 0.01334 | -0.07987 | -0.0038 | -0.05676 | 0.1112 | 0.05337 |
| 2011.0 | 0.10439 | 0.10231 | -0.01716 | 0.07714 | 0.03848 | -0.0531 | 0.00782 | 0.06249 | -0.01327 | -0.0104 |
| 2012.0 | 0.06762 | -0.14694 | -0.0542 | -0.05754 | 0.04338 | -0.05577 | 0.02918 | 0.05796 | -0.01778 | 0.03046 |
| 2013.0 | 0.01455 | 0.08443 | 0.01292 | -0.03034 | -0.02707 | 0.07382 | 0.02197 | 0.03101 | 0.00928 | -0.04489 |
| 2014.0 | 0.02744 | 0.04831 | -0.04699 | -0.00752 | 0.01465 | 0.03622 | 0.06426 | 0.02387 | 0.04653 | 0.03347 |
| 2015.0 | 0.1187 | 0.05819 | -0.11595 | 0.04011 | -0.0611 | 0.05873 | 0.04269 | 0.08874 | -0.02125 | 0.04671 |
| 2016.0 | -0.04301 | 0.12979 | -0.06156 | 0.05615 | 0.07165 | -0.05736 | -0.03592 | 0.01267 | -0.09932 | 0.02544 |
| 2017.0 | 0.03395 | 0.10936 | 0.02666 | -0.02994 | -0.07346 | -0.00728 | 0.03578 | 0.0431 | -0.03173 | -0.11917 |
| 2018.0 | 0.00207 | -0.00248 | 0.10703 | -0.07196 | -0.0273 | -0.06974 | -0.07203 | 0.00266 | 0.02013 | -0.00583 |
| 2019.0 | 0.03897 | -0.05036 | -0.00791 | 0.08408 | -0.02484 | 0.05819 | -0.00277 | -0.00087 | 0.05029 | -0.11294 |
| 2020.0 | -0.03353 | -0.05889 | -0.04434 | -0.00597 | 0.05152 | -0.08162 | -0.01077 | 0.02026 | -0.02127 | 0.05415 |
+-----------+----------+----------+----------+----------+----------+----------+----------+----------+----------+----------+
Indicator Statistics
+-----------+----------+---------+----------+----------+----------+----------+----------+----------+---------+---------+---------+--------+
| Time | Mean | SD | Skew | Kurt | Min | P5 | P25 | Median | P75 | P95 | Max | n |
+-----------+----------+---------+----------+----------+----------+----------+----------+----------+---------+---------+---------+--------+
| 2001.0 | 0.00054 | 0.97302 | 0.02247 | -0.10708 | -3.42651 | -1.6194 | -0.65605 | -0.00359 | 0.65144 | 1.64108 | 3.03045 | 3000.0 |
| 2002.0 | -0.03774 | 1.02917 | -0.07101 | -0.04394 | -3.34554 | -1.75824 | -0.73412 | -0.00649 | 0.67196 | 1.60588 | 3.24348 | 3000.0 |
| 2003.0 | -0.01544 | 1.031 | 0.08283 | -0.05399 | -3.70265 | -1.68766 | -0.72952 | -0.02717 | 0.67982 | 1.71738 | 5.01253 | 3000.0 |
| 2004.0 | -0.01367 | 0.99949 | 0.05183 | 0.03698 | -3.78607 | -1.6032 | -0.7196 | -0.00878 | 0.64707 | 1.63855 | 3.94993 | 3000.0 |
| 2005.0 | 0.0104 | 1.00123 | -0.00145 | 0.05439 | -3.45686 | -1.65593 | -0.64007 | 0.00818 | 0.66671 | 1.66286 | 3.25955 | 3000.0 |
| 2006.0 | 0.00097 | 0.99657 | 0.0462 | 0.14851 | -3.66269 | -1.63244 | -0.65111 | -0.02304 | 0.66632 | 1.64847 | 3.80687 | 3000.0 |
| 2007.0 | -0.00102 | 1.02414 | -0.02673 | 0.09203 | -3.6959 | -1.67876 | -0.68666 | -0.00039 | 0.68119 | 1.67692 | 3.46859 | 3000.0 |
| 2008.0 | 0.02678 | 1.00841 | -0.01221 | -0.01983 | -3.23867 | -1.60362 | -0.66403 | 0.05001 | 0.68418 | 1.69399 | 3.12197 | 3000.0 |
| 2009.0 | 0.02272 | 0.99936 | 0.00098 | -0.02585 | -3.47649 | -1.6255 | -0.66684 | 0.01566 | 0.70893 | 1.65815 | 3.52246 | 3000.0 |
| 2010.0 | -0.03435 | 0.99275 | -0.00444 | 0.07042 | -3.76678 | -1.68815 | -0.70062 | -0.02015 | 0.62253 | 1.58344 | 4.38276 | 3000.0 |
| 2011.0 | -0.00054 | 0.99636 | 0.02189 | 0.01578 | -3.27961 | -1.65198 | -0.66553 | -0.00789 | 0.64738 | 1.63708 | 3.82473 | 3000.0 |
| 2012.0 | 0.00797 | 0.99176 | -0.02293 | 0.16201 | -3.71695 | -1.62543 | -0.66423 | 0.00611 | 0.67271 | 1.62142 | 4.53518 | 3000.0 |
| 2013.0 | -0.02023 | 1.00519 | 0.06585 | -0.02879 | -2.94317 | -1.6765 | -0.71018 | -0.04464 | 0.63132 | 1.6228 | 3.69209 | 3000.0 |
| 2014.0 | 0.01427 | 0.9944 | -0.06002 | -0.14694 | -3.24666 | -1.65555 | -0.66567 | 0.03211 | 0.70328 | 1.61143 | 3.76138 | 3000.0 |
| 2015.0 | 0.00411 | 0.99681 | 0.05986 | -0.00795 | -3.23554 | -1.62117 | -0.67571 | -0.01158 | 0.67075 | 1.69081 | 3.2803 | 3000.0 |
| 2016.0 | 0.00331 | 0.99567 | -0.01401 | 0.05045 | -3.32744 | -1.6719 | -0.65461 | -0.02452 | 0.68572 | 1.63524 | 3.64654 | 3000.0 |
| 2017.0 | -0.02818 | 0.99394 | 0.03023 | -0.07768 | -2.89247 | -1.66422 | -0.69934 | -0.04211 | 0.6557 | 1.61093 | 4.08491 | 3000.0 |
| 2018.0 | -0.01518 | 0.99426 | 0.06121 | 0.05183 | -3.6031 | -1.61522 | -0.68846 | -0.02645 | 0.63035 | 1.65972 | 3.17931 | 3000.0 |
| 2019.0 | 0.00753 | 0.99978 | -0.09315 | 0.15681 | -3.66891 | -1.66554 | -0.62705 | 0.01924 | 0.67606 | 1.6475 | 3.63029 | 3000.0 |
| 2020.0 | 0.00963 | 0.97843 | 0.00495 | -0.19773 | -3.52657 | -1.57132 | -0.67812 | -0.0006 | 0.69571 | 1.6329 | 2.96727 | 3000.0 |
| Variable1 | | | | | | | | | | | | |
| 2001.0 | 0.00444 | 0.99937 | -0.00111 | 0.02784 | -4.01608 | -1.62687 | -0.66101 | 0.00461 | 0.68782 | 1.66745 | 3.74674 | 3000.0 |
| 2002.0 | 0.03248 | 0.98333 | -0.03543 | -0.12 | -2.95129 | -1.59552 | -0.64121 | 0.03724 | 0.71526 | 1.65638 | 2.94975 | 3000.0 |
| 2003.0 | -0.00014 | 1.0129 | -0.01918 | -0.02553 | -3.53621 | -1.70547 | -0.68189 | 0.01289 | 0.66419 | 1.70014 | 3.46892 | 3000.0 |
| 2004.0 | -0.00986 | 0.99839 | -0.04955 | -0.09378 | -3.64843 | -1.68933 | -0.66527 | 0.00177 | 0.67276 | 1.61928 | 3.39946 | 3000.0 |
| 2005.0 | -0.01278 | 1.01301 | 0.04036 | -0.05986 | -3.94393 | -1.66642 | -0.72307 | -0.01037 | 0.66475 | 1.68997 | 4.01455 | 3000.0 |
| 2006.0 | -0.01684 | 1.00801 | -0.02485 | 0.04404 | -3.42747 | -1.69649 | -0.69847 | 0.00137 | 0.64377 | 1.63762 | 3.71065 | 3000.0 |
| 2007.0 | 0.00775 | 0.99226 | 0.02647 | -0.09826 | -3.35856 | -1.63332 | -0.6701 | 0.01552 | 0.68772 | 1.63534 | 3.38473 | 3000.0 |
| 2008.0 | -0.01839 | 1.00207 | 0.07064 | -0.04444 | -3.49316 | -1.62796 | -0.70664 | -0.04696 | 0.67611 | 1.64585 | 3.41926 | 3000.0 |
| 2009.0 | 0.00244 | 1.00653 | 0.00118 | 0.03134 | -3.97288 | -1.62437 | -0.69253 | 0.00254 | 0.69752 | 1.66172 | 3.59204 | 3000.0 |
| 2010.0 | 0.00456 | 0.98586 | 0.00081 | 0.00748 | -3.77567 | -1.65978 | -0.65396 | -0.00024 | 0.66656 | 1.63131 | 4.09801 | 3000.0 |
| 2011.0 | 0.00697 | 1.00025 | 0.03471 | 0.02968 | -3.36289 | -1.63179 | -0.65539 | -0.00692 | 0.67358 | 1.68125 | 3.31398 | 3000.0 |
| 2012.0 | 0.00631 | 1.01953 | 0.08786 | -0.01507 | -3.65272 | -1.66321 | -0.69096 | 0.01699 | 0.69087 | 1.68358 | 4.29577 | 3000.0 |
| 2013.0 | 0.01293 | 1.0022 | 0.03341 | 0.06975 | -3.4732 | -1.6283 | -0.65712 | -0.00773 | 0.6928 | 1.64534 | 3.63433 | 3000.0 |
| 2014.0 | 0.02812 | 1.01169 | 0.00673 | -0.06633 | -3.29828 | -1.6315 | -0.65895 | 0.02223 | 0.7063 | 1.68416 | 3.34373 | 3000.0 |
| 2015.0 | 2e-05 | 1.00701 | -0.04947 | -0.04389 | -3.62209 | -1.66903 | -0.67316 | 0.00995 | 0.6839 | 1.65849 | 3.37435 | 3000.0 |
| 2016.0 | 0.00232 | 0.9964 | 0.00089 | -0.11472 | -3.41436 | -1.60652 | -0.68629 | -0.02141 | 0.6936 | 1.64288 | 3.24371 | 3000.0 |
| 2017.0 | -0.00639 | 0.99143 | -0.09349 | 0.14564 | -3.7956 | -1.67824 | -0.65161 | 0.01273 | 0.64207 | 1.57087 | 3.3055 | 3000.0 |
| 2018.0 | 0.02355 | 1.00525 | 0.0735 | 0.03266 | -3.24816 | -1.59484 | -0.65466 | -0.00647 | 0.67029 | 1.72254 | 4.04177 | 3000.0 |
| 2019.0 | -0.03246 | 1.01253 | -0.08108 | -0.09494 | -3.68037 | -1.75283 | -0.69156 | -0.01116 | 0.65456 | 1.59883 | 2.96434 | 3000.0 |
| 2020.0 | -0.01072 | 1.0106 | 0.02844 | 0.03357 | -3.57483 | -1.66278 | -0.6799 | -0.04445 | 0.6553 | 1.69042 | 3.88206 | 3000.0 |
| Variable2 | | | | | | | | | | | | |
| 2001.0 | 0.01341 | 0.99215 | -0.04582 | -0.06823 | -3.6463 | -1.66845 | -0.64103 | 0.03084 | 0.67477 | 1.61286 | 3.38016 | 3000.0 |
| 2002.0 | -0.00965 | 1.00207 | -0.01972 | -0.0418 | -3.68085 | -1.6906 | -0.68189 | 0.02149 | 0.65511 | 1.60544 | 3.67893 | 3000.0 |
| 2003.0 | -0.01181 | 0.98368 | 0.03 | 0.07221 | -3.52554 | -1.6329 | -0.6623 | -0.01934 | 0.62873 | 1.56947 | 3.29198 | 3000.0 |
| 2004.0 | -0.0093 | 1.01012 | -0.06468 | 0.05186 | -3.82134 | -1.68905 | -0.68096 | -0.01715 | 0.66304 | 1.60242 | 3.43242 | 3000.0 |
| 2005.0 | -0.00226 | 1.00171 | 0.07204 | 0.24676 | -3.90934 | -1.6036 | -0.66317 | -0.03034 | 0.66551 | 1.65203 | 3.29004 | 3000.0 |
| 2006.0 | 0.02831 | 0.98831 | -0.01583 | -0.06904 | -3.49769 | -1.597 | -0.6341 | 0.02602 | 0.70498 | 1.612 | 3.27316 | 3000.0 |
| 2007.0 | 0.01345 | 0.98311 | -0.00127 | -0.03949 | -3.94062 | -1.56016 | -0.64564 | 0.0141 | 0.70418 | 1.62664 | 3.1278 | 3000.0 |
| 2008.0 | -0.01468 | 0.98965 | -0.02328 | -0.13919 | -3.23034 | -1.64276 | -0.69535 | -0.00703 | 0.64543 | 1.67091 | 2.98688 | 3000.0 |
| 2009.0 | -0.01303 | 0.99521 | -0.01693 | -0.11205 | -3.18737 | -1.65024 | -0.69354 | -0.0227 | 0.6594 | 1.62866 | 3.12058 | 3000.0 |
| 2010.0 | -0.01644 | 1.02983 | 0.01627 | 0.09362 | -3.68702 | -1.71173 | -0.70591 | -0.01513 | 0.67615 | 1.65729 | 3.84489 | 3000.0 |
| 2011.0 | 0.02987 | 0.97808 | -0.01661 | -0.00216 | -3.75328 | -1.58039 | -0.63462 | 0.03478 | 0.70848 | 1.61408 | 3.32421 | 3000.0 |
| 2012.0 | -0.01036 | 1.02126 | -0.04517 | -0.06873 | -3.42255 | -1.71536 | -0.69263 | -0.02 | 0.67138 | 1.68837 | 3.21492 | 3000.0 |
| 2013.0 | 0.01457 | 0.99664 | -0.05389 | -0.01116 | -3.8404 | -1.59651 | -0.68504 | 0.0347 | 0.69874 | 1.62143 | 3.18552 | 3000.0 |
| 2014.0 | 0.02402 | 1.00528 | 0.05727 | 0.23415 | -4.52543 | -1.62336 | -0.66718 | 0.0268 | 0.67981 | 1.70991 | 3.85701 | 3000.0 |
| 2015.0 | 0.02556 | 1.04251 | 0.00448 | -0.2219 | -3.77315 | -1.68143 | -0.71505 | 0.03778 | 0.74572 | 1.72891 | 3.11878 | 3000.0 |
| 2016.0 | -0.00015 | 1.01562 | 0.08258 | 0.0474 | -3.26366 | -1.64969 | -0.70016 | -0.01887 | 0.65377 | 1.69586 | 3.84588 | 3000.0 |
| 2017.0 | -0.00127 | 0.97951 | -0.10032 | 0.00475 | -3.23879 | -1.63675 | -0.66305 | 0.02015 | 0.64732 | 1.57432 | 3.13642 | 3000.0 |
| 2018.0 | -0.01174 | 1.01481 | 0.0055 | 0.077 | -4.15834 | -1.67378 | -0.72306 | 0.00013 | 0.6599 | 1.64383 | 3.77525 | 3000.0 |
| 2019.0 | 0.00318 | 1.01367 | -0.04253 | 0.00838 | -3.90455 | -1.68076 | -0.66782 | -0.00943 | 0.70025 | 1.63818 | 3.43779 | 3000.0 |
| 2020.0 | -0.01305 | 1.00361 | 0.00358 | -0.18842 | -3.11144 | -1.66498 | -0.69793 | -0.01765 | 0.69372 | 1.64435 | 3.36513 | 3000.0 |
+-----------+----------+---------+----------+----------+----------+----------+----------+----------+---------+---------+---------+--------+
===========================================================================================================================================
# correlation
variable_3 = np.random.normal(0, 1, 20*3000)
variable_4 = np.random.normal(0, 1, 20*3000)
print('-------------------------------------- Correlation ---------------------------------')
exper.correlation(variables=np.array([variable_1, variable_2, variable_3, variable_4]).T, periodic=True)
exper.correlation(variables=np.array([variable_1, variable_2, variable_3, variable_4]).T)
=======================================================================================================================================================================
Spearman Correlation
+---------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+
| Time | Variable_0 & Variable_1 | Variable_0 & Variable_2 | Variable_0 & Variable_3 | Variable_1 & Variable_2 | Variable_1 & Variable_3 | Variable_2 & Variable_3 |
+---------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+
| 2001.0 | 0.00863 | 0.00926 | -0.00397 | -0.00906 | -0.00307 | -0.0309 |
| 2002.0 | -0.01452 | -0.04919 | -0.01512 | 0.01882 | -0.01007 | -0.01103 |
| 2003.0 | -0.00284 | -0.00438 | 0.02967 | 0.00591 | -0.00215 | -0.02898 |
| 2004.0 | 0.00591 | -0.00211 | 0.0029 | 0.01874 | -0.0006 | -0.01046 |
| 2005.0 | -0.03282 | 0.00415 | 0.0126 | -0.00071 | 0.01993 | -0.01941 |
| 2006.0 | -0.00586 | -0.01359 | 0.03434 | -0.00489 | 0.00569 | 0.00498 |
| 2007.0 | 0.01482 | -0.01671 | -0.01547 | 0.01586 | 0.03723 | 0.00367 |
| 2008.0 | -0.02851 | 0.00128 | 0.00171 | 0.00211 | -0.03949 | -0.00039 |
| 2009.0 | -0.02377 | 0.01281 | 0.02534 | 0.01994 | -0.00389 | 0.02761 |
| 2010.0 | 0.02264 | -0.0402 | 0.01084 | -0.02077 | -0.02531 | -0.00131 |
| 2011.0 | 0.00374 | -0.0273 | 0.01 | 0.00546 | 0.00095 | 0.0209 |
| 2012.0 | -0.00557 | 0.01421 | -0.00734 | -0.02101 | -0.00696 | 0.00732 |
| 2013.0 | -4e-05 | -0.00498 | -0.02152 | 0.01399 | -0.04743 | 0.01188 |
| 2014.0 | -0.00228 | 0.01015 | -0.01893 | 0.00524 | -0.00558 | 0.01606 |
| 2015.0 | -0.00637 | -0.00037 | 0.00886 | 0.01985 | 0.00351 | -0.01251 |
| 2016.0 | 0.0045 | 0.00385 | -0.02201 | -0.01904 | -0.01806 | -0.00567 |
| 2017.0 | 0.0084 | 0.00174 | -0.01042 | 0.03584 | -0.00474 | -0.01022 |
| 2018.0 | 0.029 | 0.01707 | 0.01334 | 0.00304 | -0.00772 | -0.03887 |
| 2019.0 | -0.02843 | 0.04992 | 0.02054 | 0.0179 | -0.00819 | -0.00156 |
| 2020.0 | -0.00428 | 0.0306 | -0.00014 | -0.03424 | 0.00179 | 0.00909 |
+---------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+
Fisher Correlation
+---------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+
| Time | Variable_0 & Variable_1 | Variable_0 & Variable_2 | Variable_0 & Variable_3 | Variable_1 & Variable_2 | Variable_1 & Variable_3 | Variable_2 & Variable_3 |
+---------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+
| 2001.0 | 0.0047 | 0.00928 | -0.00062 | -0.00261 | -0.00212 | -0.02891 |
| 2002.0 | -0.0136 | -0.04798 | -0.00929 | 0.01184 | -0.00402 | -0.02674 |
| 2003.0 | 0.00528 | -0.00703 | 0.03384 | 0.00351 | -0.0062 | -0.02955 |
| 2004.0 | 0.00026 | -0.00738 | -0.00191 | 0.01757 | -0.00905 | -0.0198 |
| 2005.0 | -0.02188 | 0.00508 | 0.01595 | -0.00102 | 0.02017 | -0.02134 |
| 2006.0 | 0.00079 | -0.01184 | 0.04108 | -0.00318 | 0.01416 | 0.00016 |
| 2007.0 | 0.00898 | -0.00828 | -0.02333 | 0.01113 | 0.04626 | -0.00328 |
| 2008.0 | -0.03725 | 0.0059 | -0.00461 | 0.00724 | -0.0367 | -0.00523 |
| 2009.0 | -0.02321 | 0.01845 | 0.02499 | 0.02819 | -0.01009 | 0.02698 |
| 2010.0 | 0.01829 | -0.03991 | 0.00954 | -0.00806 | -0.02117 | -0.00337 |
| 2011.0 | -0.00429 | -0.02689 | 0.00147 | 0.01042 | 0.00555 | 0.02417 |
| 2012.0 | -0.00896 | 0.02461 | -0.00171 | -0.02136 | -0.00776 | 0.0049 |
| 2013.0 | 0.00897 | -0.00313 | -0.01611 | 0.01796 | -0.04195 | 0.01399 |
| 2014.0 | -0.00553 | 0.01175 | -0.02001 | 0.01146 | -0.00138 | 0.02431 |
| 2015.0 | -0.01301 | 0.00142 | 0.00421 | 0.01506 | 0.01047 | -0.00587 |
| 2016.0 | 0.00976 | 0.00267 | -0.01945 | -0.02886 | -0.01569 | -0.00137 |
| 2017.0 | 0.01281 | 0.00114 | -0.0059 | 0.03967 | -0.00231 | -0.02049 |
| 2018.0 | 0.02602 | 0.02507 | 0.01181 | 0.00088 | 0.00019 | -0.03295 |
| 2019.0 | -0.02941 | 0.04476 | 0.02165 | 0.00689 | 0.00426 | -0.00762 |
| 2020.0 | 0.00638 | 0.01985 | -0.00544 | -0.03257 | -0.00213 | 0.00639 |
+---------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+
+----------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+
| Variable | Variable_0 & Variable_1 | Variable_0 & Variable_2 | Variable_0 & Variable_3 | Variable_1 & Variable_2 | Variable_1 & Variable_3 | Variable_2 & Variable_3 |
+----------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+
| Fisher | -0.00274 | 0.00088 | 0.00281 | 0.00421 | -0.00298 | -0.00528 |
| Spearman | -0.00288 | -0.00019 | 0.00276 | 0.00365 | -0.00571 | -0.00349 |
+----------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+
class MultiPeriod_Univariate():
def _init_(self, ret_matrix, sample):
This function initializes the class MultiPeriod_Univariate.
input:
ret_matrix (DataFrame): The ret_matrix contains future returns series from 1 to n period.
sample (DataFrame): The samples to be analyzed. Samples contains sort variables and time.
def fit(self, number:int, perc:list=None, percn: ndarray=None, maxlag: int=12, weight:bool =False):
The inputs of the function are the same with the Univariate.fit()
def factor_adjustment(self, factor:DataFrame):
The inputs are the same with the Univariate.factor_adjustment()
def summary(self, explicit:bool=False, export:bool=False, percentage:bool=False):
The inputs are the same with the Univariate.print_summary()
Example
# %% test class multiperiod univariate
def test_MultiPeriod_Univariate():
'''
TEST UNIVARIATE
construct sample:
1. 20 Periods
2. 3000 Observations for each Period
3. Divided into 10 groups with 9 breakpoints
4. Character negative with return following the return=character*-0.5+sigma where sigma~N(0,1)
'''
import numpy as np
import pandas as pd
from portfolio_analysis import MultiPeriod_Univariate as muluni
from portfolio_analysis import ptf_analysis as ptfa
from util import plot
# generate time
year=np.ones((3000,1),dtype=int)*2020
for i in range(19):
year=np.append(year,(2019-i)*np.ones((3000,1),dtype=int))
year = pd.DataFrame(year, columns=['year'])
# generate character
character=pd.DataFrame(np.random.normal(0,1,20*3000))
# generate future return
ret1=character + np.random.normal(loc=0, scale=1, size=(20*3000,1))
ret2=character + np.random.normal(loc=0, scale=1, size=(20*3000,1))
# create sample containing future return, character, time
ret_matrix = pd.merge(ret1, ret2, left_index=True, right_index=True)
ret_matrix.columns = ['ret1', 'ret2']
sample=pd.merge(character, year, left_index=True, right_index=True)
sample.columns = ['character', 'year']
# generate the Univiriate Class
exper=muluni(ret_matrix, sample)
# print(exper.ret_matrix)
data = exper.fit(number=4, maxlag=0)
print(exper.average_result)
print(exper.ttest)
print(np.shape(exper.ttest))
# print(exper.params)
# print(np.shape(data))
exper.summary()
print(exper.number)
return data
test_MultiPeriod_Univariate()
class Bivariate(ptf_analysis):
def _init_(self, sample):
This function initializes the class Bivariate
input :
sample (ndarray or DataFrame): The samples to be analyzed. Samples usually contain the future return, characteristics, time. The DEFAULT setting is the 1th column is the forecast return, the 2nd column is the first characteristic, the 3rd column is the second characteristic, the 4th column or the index(if data type is Dataframe) is time label.
def divide_by_time(self):
This function groups the sample by time.
output :
groups_by_time (list): The samples group by time.
def average_by_time(self, conditional=False):
This function, using the sample group by time from function divide_by_time, groups the sample by the characteristic, and then calculate average return of each group samples at every time point.
input :
conditional (boolean): The way of sorting. If true, it is dependent-sort analysis; if false, it is independent sort analysis. The Default setting is False.
output :
average_group_time(matrix: N_N_T) : The average return of groups by each characteristic pair indexed by time.
Example
import numpy as np
from portfolio_analysis import Bivariate as bi
# generate time
year = np.ones((3000,1), dtype=int)*2020
for i in range(19):
year = np.append(year, (2019-i)*np.ones((3000,1), dtype=int))
# generate character
character_1 = np.random.normal(0, 1, 20*3000)
character_2 = np.random.normal(0, 1, 20*3000)
# generate future return
ret=character_1*-0.5 + character_2*0.5 + np.random.normal(0,1,20*3000)
# create sample containing future return, character, time
sample=np.array([ret,character_1, character_2, year]).T
print(sample)
# generate the Univiriate Class
exper=bi(sample,9)
# test function divide_by_time
group_by_time = exper.divide_by_time()
print(group_by_time)
# test function average_by_time
average_group_time = exper.average_by_time()
print(average_group_time)
print(np.shape(average_group_time))
========================================================================
[[-1.248 -0.723 -0.526 2020.000]
[0.739 0.058 1.388 2020.000]
[1.711 -1.081 0.348 2020.000]
...
[-0.906 1.128 -2.996 2001.000]
[-1.240 0.781 -0.451 2001.000]
[-0.216 0.907 -1.086 2001.000]]
group by time:
[array([[0.522, 0.420, -1.185, 2001.000],
[0.381, -0.954, -2.045, 2001.000],
[1.086, -1.116, 1.017, 2001.000],
...,
[-0.906, 1.128, -2.996, 2001.000],
[-1.240, 0.781, -0.451, 2001.000],
[-0.216, 0.907, -1.086, 2001.000]]), array([[-1.170, 1.635, 0.001, 2002.000],
[0.852, -1.479, 0.878, 2002.000],
[-0.080, 0.403, 0.547, 2002.000],
...,
[0.308, -0.107, 0.261, 2002.000],
[0.301, -2.221, 1.165, 2002.000],
[-2.017, 0.576, 0.726, 2002.000]]), array([[-0.371, 1.792, 1.310, 2003.000],
[0.815, -1.668, 0.022, 2003.000],
[2.301, 0.324, 0.586, 2003.000],
...,
[1.337, -1.082, -0.890, 2003.000],
[-0.447, 1.330, 0.707, 2003.000],
[2.666, -1.206, 0.232, 2003.000]]), array([[-0.430, 0.654, 0.543, 2004.000],
[1.787, 0.772, 1.571, 2004.000],
[2.241, -0.778, 1.403, 2004.000],
...,
[0.290, -0.513, 0.026, 2004.000],
[1.303, -0.173, 2.936, 2004.000],
[-0.064, 0.986, 0.777, 2004.000]]), array([[-0.966, -0.162, -0.747, 2005.000],
[1.395, 1.247, 0.257, 2005.000],
[0.850, -2.563, -1.314, 2005.000],
...,
[-1.148, -0.395, -1.396, 2005.000],
[-2.013, 1.442, -2.360, 2005.000],
[0.753, -0.533, -0.829, 2005.000]]), array([[-0.351, 0.771, 0.764, 2006.000],
[-0.338, 0.545, 0.719, 2006.000],
[-0.853, -0.271, 0.107, 2006.000],
...,
[-1.302, 1.416, -0.656, 2006.000],
[1.233, 0.318, 0.925, 2006.000],
[0.169, 0.571, 0.703, 2006.000]]), array([[-1.335, 0.054, -1.674, 2007.000],
[-1.760, -0.648, -1.320, 2007.000],
[-0.783, -0.507, -0.527, 2007.000],
...,
[0.703, -0.111, -0.153, 2007.000],
[-1.252, 0.056, 1.051, 2007.000],
[-1.914, 1.627, -2.030, 2007.000]]), array([[1.767, -0.743, 1.614, 2008.000],
[0.364, -0.737, 0.141, 2008.000],
[-0.691, -0.299, -1.860, 2008.000],
...,
[-0.490, -0.202, -0.279, 2008.000],
[0.982, -0.508, -0.415, 2008.000],
[0.380, -0.796, -0.756, 2008.000]]), array([[-1.207, 1.881, -1.727, 2009.000],
[0.848, -0.094, 0.782, 2009.000],
[-1.822, 1.992, 0.239, 2009.000],
...,
[1.484, -2.619, 0.840, 2009.000],
[0.530, 0.929, 0.644, 2009.000],
[-1.095, 2.209, -0.606, 2009.000]]), array([[-1.747, 0.447, -1.597, 2010.000],
[-1.092, 0.321, 1.201, 2010.000],
[-0.398, 0.282, 0.574, 2010.000],
...,
[3.040, -0.083, 1.477, 2010.000],
[1.221, 0.182, 2.531, 2010.000],
[0.722, -0.342, -0.096, 2010.000]]), array([[0.134, 0.632, -0.437, 2011.000],
[0.679, 0.649, 0.097, 2011.000],
[-0.440, -0.798, -1.114, 2011.000],
...,
[-2.137, 2.317, -1.015, 2011.000],
[0.792, 0.309, 0.440, 2011.000],
[1.685, -0.949, -0.092, 2011.000]]), array([[-0.727, 0.941, 1.412, 2012.000],
[-0.052, 0.951, -1.023, 2012.000],
[0.781, 0.434, 0.105, 2012.000],
...,
[1.158, 1.810, 0.118, 2012.000],
[1.382, -0.029, 0.234, 2012.000],
[0.297, -1.016, -0.231, 2012.000]]), array([[-1.071, 0.400, 1.490, 2013.000],
[-0.559, 1.989, 0.298, 2013.000],
[0.324, -0.078, 0.512, 2013.000],
...,
[-1.160, 0.799, -0.191, 2013.000],
[1.542, -1.006, 0.835, 2013.000],
[-0.160, -0.608, 1.218, 2013.000]]), array([[1.760, 1.303, 0.584, 2014.000],
[0.308, 1.184, 0.710, 2014.000],
[-0.916, -1.485, 0.717, 2014.000],
...,
[-0.839, -1.420, -0.786, 2014.000],
[0.625, -0.289, 0.914, 2014.000],
[-1.393, -0.144, 0.389, 2014.000]]), array([[-0.371, 2.836, 1.156, 2015.000],
[0.625, -0.812, 0.517, 2015.000],
[1.683, -0.697, 0.316, 2015.000],
...,
[-1.519, -0.195, -1.427, 2015.000],
[1.141, -0.541, 1.434, 2015.000],
[1.491, -0.605, 0.456, 2015.000]]), array([[0.396, 1.153, 1.451, 2016.000],
[1.124, -0.064, -1.265, 2016.000],
[0.047, 0.038, 1.536, 2016.000],
...,
[-1.715, 1.981, 0.622, 2016.000],
[-0.997, -0.048, -0.100, 2016.000],
[4.086, -0.561, 1.430, 2016.000]]), array([[-2.620, 1.302, -0.624, 2017.000],
[-3.629, 0.548, -0.361, 2017.000],
[-1.450, 0.024, -1.406, 2017.000],
...,
[0.035, -0.252, -1.975, 2017.000],
[1.145, -1.471, -0.003, 2017.000],
[-1.875, -0.794, -0.484, 2017.000]]), array([[-0.199, 0.571, -1.849, 2018.000],
[-0.535, 0.408, -1.257, 2018.000],
[-1.629, -0.315, 0.223, 2018.000],
...,
[1.010, -0.382, 0.335, 2018.000],
[-2.577, 0.425, -1.771, 2018.000],
[0.316, -0.722, -1.370, 2018.000]]), array([[-0.323, -0.139, -0.376, 2019.000],
[0.105, 0.439, -0.103, 2019.000],
[0.394, 0.929, -1.189, 2019.000],
...,
[0.617, 0.686, -0.222, 2019.000],
[-2.545, 0.752, -1.271, 2019.000],
[2.016, -0.663, 2.025, 2019.000]]), array([[-1.248, -0.723, -0.526, 2020.000],
[0.739, 0.058, 1.388, 2020.000],
[1.711, -1.081, 0.348, 2020.000],
...,
[-2.098, -0.131, -1.182, 2020.000],
[2.356, 0.722, -0.356, 2020.000],
[0.703, -0.360, -0.386, 2020.000]])]
average_group_time:
[[[-0.006 0.056 -0.214 ... 0.008 -0.440 0.230]
[-0.025 0.134 0.298 ... 0.432 0.475 0.022]
[0.416 0.685 0.884 ... 0.384 0.925 0.614]
...
[1.206 1.389 1.050 ... 1.180 1.053 1.124]
[1.458 1.319 1.620 ... 1.101 1.226 1.273]
[1.558 1.582 1.733 ... 1.392 1.841 1.867]]
[[-0.294 -0.542 -0.319 ... -0.468 -0.204 -0.196]
[0.120 -0.160 0.077 ... 0.012 0.260 -0.132]
[0.305 0.077 0.027 ... 0.307 0.102 0.246]
...
[0.971 0.836 1.196 ... 0.867 0.775 0.851]
[0.988 0.800 1.467 ... 0.985 1.328 1.197]
[1.713 1.087 1.665 ... 1.551 1.262 1.628]]
[[-0.686 -0.606 -0.273 ... -0.361 -0.532 -0.435]
[-0.449 -0.263 -0.432 ... -0.168 -0.638 -0.397]
[0.169 -0.096 0.029 ... -0.177 -0.119 -0.089]
...
[0.568 0.623 0.594 ... 0.664 0.517 0.740]
[0.671 0.831 1.049 ... 0.963 0.850 1.072]
[1.214 1.414 1.283 ... 1.040 1.187 1.295]]
...
[[-1.160 -1.274 -1.352 ... -1.244 -1.537 -0.719]
[-0.918 -0.634 -0.714 ... -0.855 -0.798 -1.014]
[-0.732 -0.565 -0.556 ... -0.769 -0.790 -1.063]
...
[0.186 0.032 -0.331 ... 0.512 0.143 0.205]
[0.029 0.107 0.098 ... 0.116 0.275 0.223]
[0.927 0.506 0.767 ... 0.444 0.667 0.860]]
[[-1.694 -1.812 -1.452 ... -1.498 -1.312 -1.729]
[-0.973 -1.123 -0.965 ... -1.175 -1.003 -1.054]
[-0.928 -0.770 -0.845 ... -0.727 -0.961 -0.891]
...
[-0.051 0.025 -0.158 ... 0.210 0.221 0.048]
[0.223 0.166 0.475 ... 0.266 -0.050 -0.149]
[0.218 0.157 -0.182 ... 0.416 0.225 0.479]]
[[-1.693 -1.962 -1.773 ... -1.600 -1.497 -1.749]
[-1.580 -1.482 -1.580 ... -1.337 -1.629 -1.711]
[-1.384 -0.927 -1.158 ... -1.390 -1.010 -1.213]
...
[-0.747 -0.601 -0.499 ... -0.831 -0.348 -0.404]
[-0.238 -0.269 -0.472 ... -0.031 -0.502 -0.356]
[-0.322 0.136 0.020 ... -0.202 -0.066 -0.342]]]
shape of average_group_time:
(10, 10, 20)
def difference(self, average_group):
This functions calculates the difference of group return, which, in detail, is the last group average return minus the first group average return.
input :
average_group (ndarray): The average return of groups by each characteristic-time pair.
output :
result (ndarray): The matrix added with the difference of average group return.
def factor_adjustment(self, factor):
This function calculates the group return adjusted by risk factors.
input :
factor (ndarray or DataFrame): The return table with difference sequence.
output :
alpha (ndarray): The anomaly
ttest (ndarray): The t-value of the anomaly.
def summary_and_test(self, **kwargs):
This function summarizes the result and take t-test.
input :
export (boolean): Export the table or not. The table is exported in form of Dataframe. The default setting is False.
**output : **
self.average (array): The average of the portfolio return across time.
self.ttest (array): The t-value of the portfolio return across time.
def extractor(self, r_pos, c_pos):
This function extracts the return series.
input :
r_pos (int): The row position of the return matrix.
c_pos (int): The column position of the return matrix.
output :
series_ex (Series): The extracted Series.
def fit(self, number, perc_row=None, perc_col=None, percn_row=None, percn_col=None, weight=False, maxlag=12, **kwargs):
This function run the function summary_and_test().
input :
number (int): The breakpoint number.
perc_row (list or array): The breakpoint percentile points of row characteristics.
perc_col (list or array): The breakpoint percentile points of column characteristics.
percn_row (list or array): The breakpoints percentiles of row characteristics.
percn_col (list or array): The breakpoints percentiles of column characteristics.
weight (boolean): Whether calculate the weighted average return.
maxlag (int): The maximum lag for Newey-West adjustment.
kwargs : kwargs include settings like conditional, etc.
def print_summary_by_time(self, export=False):
This function print the summary grouped by time.
input :
export (boolean): Export the table or not. The table is exported in form of Dataframe. The default setting is False.
output :
df (DataFrame): The table exported in form of DataFrame.
def print_summary(self, explicit=False, export=False, percentage=False):
This function print the summary grouped by characteristic and averaged by time.
input :
explicit (boolean): Whether presents the explicit result. The default is False.
export (boolean): Export the table or not. The table is exported in form of Dataframe. The default setting is False.
percentage (boolean): Whether presents the percentage return. The default is False.
output :
df (DataFrame): The table exported in form of Dataframe.
Example
# Continue the above code
# test function difference
result = exper.difference(average_group_time)
print('result :\n', result)
print('difference matrix :\n', np.shape(result))
# test function summary_and_test
average, ttest = exper.summary_and_test()
print('average :\n', average)
print(' shape of average :', np.shape(average))
print('ttest :\n', ttest)
print('shape of ttest :', np.shape(ttest))
# test function print_summary_by_time()
exper.print_summary_by_time()
# test function print_summary
exper.print_summary()
# generate factor
factor=np.random.normal(0,1.0,(20,1))
exper=bi(sample,9,factor=factor,maxlag=12)
exper.fit()
exper.print_summary()
========================================================================
result :
[[[-0.006 0.056 -0.214 ... 0.008 -0.440 0.230]
[-0.025 0.134 0.298 ... 0.432 0.475 0.022]
[0.416 0.685 0.884 ... 0.384 0.925 0.614]
...
[1.458 1.319 1.620 ... 1.101 1.226 1.273]
[1.558 1.582 1.733 ... 1.392 1.841 1.867]
[1.564 1.526 1.947 ... 1.384 2.281 1.637]]
[[-0.294 -0.542 -0.319 ... -0.468 -0.204 -0.196]
[0.120 -0.160 0.077 ... 0.012 0.260 -0.132]
[0.305 0.077 0.027 ... 0.307 0.102 0.246]
...
[0.988 0.800 1.467 ... 0.985 1.328 1.197]
[1.713 1.087 1.665 ... 1.551 1.262 1.628]
[2.007 1.629 1.983 ... 2.019 1.466 1.824]]
[[-0.686 -0.606 -0.273 ... -0.361 -0.532 -0.435]
[-0.449 -0.263 -0.432 ... -0.168 -0.638 -0.397]
[0.169 -0.096 0.029 ... -0.177 -0.119 -0.089]
...
[0.671 0.831 1.049 ... 0.963 0.850 1.072]
[1.214 1.414 1.283 ... 1.040 1.187 1.295]
[1.900 2.020 1.556 ... 1.401 1.720 1.730]]
...
[[-1.694 -1.812 -1.452 ... -1.498 -1.312 -1.729]
[-0.973 -1.123 -0.965 ... -1.175 -1.003 -1.054]
[-0.928 -0.770 -0.845 ... -0.727 -0.961 -0.891]
...
[0.223 0.166 0.475 ... 0.266 -0.050 -0.149]
[0.218 0.157 -0.182 ... 0.416 0.225 0.479]
[1.912 1.969 1.270 ... 1.914 1.536 2.208]]
[[-1.693 -1.962 -1.773 ... -1.600 -1.497 -1.749]
[-1.580 -1.482 -1.580 ... -1.337 -1.629 -1.711]
[-1.384 -0.927 -1.158 ... -1.390 -1.010 -1.213]
...
[-0.238 -0.269 -0.472 ... -0.031 -0.502 -0.356]
[-0.322 0.136 0.020 ... -0.202 -0.066 -0.342]
[1.372 2.098 1.793 ... 1.398 1.431 1.407]]
[[-1.687 -2.018 -1.559 ... -1.608 -1.057 -1.979]
[-1.554 -1.615 -1.879 ... -1.769 -2.103 -1.733]
[-1.799 -1.612 -2.043 ... -1.773 -1.934 -1.827]
...
[-1.696 -1.588 -2.092 ... -1.132 -1.727 -1.629]
[-1.879 -1.446 -1.713 ... -1.594 -1.907 -2.209]
[-0.192 0.572 -0.153 ... 0.014 -0.850 -0.230]]]
difference matrix :
(11, 11, 20)
average :
[[-0.009 0.307 0.487 0.670 0.808 0.870 1.121 1.170 1.395 1.763 1.771]
[-0.348 0.025 0.155 0.353 0.500 0.556 0.791 0.923 1.013 1.426 1.774]
[-0.492 -0.264 -0.008 0.144 0.248 0.429 0.543 0.663 0.854 1.249 1.741]
[-0.712 -0.379 -0.135 -0.027 0.132 0.207 0.361 0.552 0.753 1.011 1.723]
[-0.864 -0.470 -0.229 -0.095 0.010 0.096 0.225 0.395 0.562 0.876 1.740]
[-0.936 -0.588 -0.369 -0.266 -0.109 -0.043 0.104 0.292 0.524 0.769 1.706]
[-1.166 -0.700 -0.531 -0.455 -0.250 -0.162 0.061 0.113 0.331 0.596 1.762]
[-1.206 -0.863 -0.702 -0.530 -0.408 -0.195 -0.072 -0.033 0.139 0.587
1.794]
[-1.418 -1.080 -0.907 -0.827 -0.537 -0.401 -0.280 -0.108 0.087 0.384
1.803]
[-1.740 -1.428 -1.208 -1.037 -0.882 -0.800 -0.722 -0.563 -0.264 -0.020
1.720]
[-1.732 -1.735 -1.695 -1.707 -1.689 -1.670 -1.843 -1.733 -1.659 -1.782
-0.051]]
shape of average : (11, 11)
ttest :
Ttest_1sampResult(statistic=array([[-0.210, 9.363, 10.040, 14.328, 19.642, 19.275, 32.422, 31.651,
32.548, 36.339, 30.879],
[-8.735, 0.554, 4.106, 9.711, 15.652, 17.688, 18.663, 21.424,
24.727, 25.303, 27.968],
[-14.510, -5.950, -0.196, 3.603, 4.279, 10.713, 11.675, 15.120,
28.222, 30.641, 33.960],
[-13.954, -12.731, -3.512, -0.734, 4.065, 3.896, 10.159, 11.573,
19.965, 33.017, 27.068],
[-22.685, -10.826, -5.787, -2.676, 0.240, 3.617, 4.984, 8.858,
12.281, 22.043, 35.963],
[-17.923, -13.135, -7.587, -8.412, -3.183, -1.094, 2.233, 6.425,
14.503, 19.564, 22.897],
[-23.358, -18.494, -11.156, -12.058, -6.798, -3.088, 1.608, 2.929,
9.236, 12.340, 25.862],
[-29.779, -21.416, -16.812, -12.196, -9.915, -4.330, -1.904,
-0.730, 4.491, 14.137, 32.595],
[-28.227, -28.724, -24.521, -19.015, -10.798, -8.905, -6.847,
-2.320, 2.612, 8.876, 32.366],
[-58.707, -35.555, -33.894, -25.661, -22.006, -19.782, -17.041,
-13.409, -6.740, -0.442, 30.899],
[-29.798, -36.048, -35.280, -26.596, -33.752, -24.635, -42.514,
-31.417, -26.573, -25.966, -0.585]]), pvalue=array([[0.836, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000,
0.000, 0.000],
[0.000, 0.586, 0.001, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000,
0.000, 0.000],
[0.000, 0.000, 0.847, 0.002, 0.000, 0.000, 0.000, 0.000, 0.000,
0.000, 0.000],
[0.000, 0.000, 0.002, 0.472, 0.001, 0.001, 0.000, 0.000, 0.000,
0.000, 0.000],
[0.000, 0.000, 0.000, 0.015, 0.813, 0.002, 0.000, 0.000, 0.000,
0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.005, 0.288, 0.038, 0.000, 0.000,
0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.006, 0.124, 0.009, 0.000,
0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.072, 0.474, 0.000,
0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.032, 0.017,
0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000,
0.664, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000,
0.000, 0.565]]))
shape of ttest : (2, 11, 11)
+--------+-------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+
| Time | Group | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Diff |
+--------+-------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+
| 2001.0 | 1 | -0.006 | -0.025 | 0.416 | 0.536 | 0.896 | 0.852 | 1.127 | 1.206 | 1.458 | 1.558 | 1.564 |
| | 2 | -0.294 | 0.12 | 0.305 | 0.324 | 0.419 | 0.637 | 0.349 | 0.971 | 0.988 | 1.713 | 2.007 |
| | 3 | -0.686 | -0.449 | 0.169 | -0.136 | -0.057 | 0.23 | 0.503 | 0.568 | 0.671 | 1.214 | 1.9 |
| | 4 | -1.005 | -0.287 | -0.135 | 0.05 | 0.196 | 0.587 | 0.36 | 0.707 | 0.68 | 1.066 | 2.071 |
| | 5 | -0.669 | -0.713 | -0.364 | 0.075 | -0.345 | 0.085 | 0.265 | 0.364 | 0.569 | 0.922 | 1.591 |
| | 6 | -1.136 | -0.535 | -0.669 | -0.325 | -0.265 | -0.137 | 0.041 | 0.571 | 0.444 | 1.052 | 2.188 |
| | 7 | -1.34 | -0.766 | -0.515 | -0.439 | -0.201 | -0.342 | 0.211 | -0.107 | 0.369 | 0.231 | 1.571 |
| | 8 | -1.16 | -0.918 | -0.732 | -0.563 | -0.625 | -0.182 | -0.06 | 0.186 | 0.029 | 0.927 | 2.086 |
| | 9 | -1.694 | -0.973 | -0.928 | -0.63 | -0.557 | -0.391 | -0.531 | -0.051 | 0.223 | 0.218 | 1.912 |
| | 10 | -1.693 | -1.58 | -1.384 | -0.712 | -0.67 | -0.707 | -0.803 | -0.747 | -0.238 | -0.322 | 1.372 |
| | Diff | -1.687 | -1.554 | -1.799 | -1.248 | -1.566 | -1.559 | -1.93 | -1.953 | -1.696 | -1.879 | -0.192 |
| 2002.0 | 1 | 0.056 | 0.134 | 0.685 | 0.891 | 1.142 | 0.668 | 1.173 | 1.389 | 1.319 | 1.582 | 1.526 |
| | 2 | -0.542 | -0.16 | 0.077 | 0.046 | 0.603 | 0.746 | 0.779 | 0.836 | 0.8 | 1.087 | 1.629 |
| | 3 | -0.606 | -0.263 | -0.096 | 0.235 | -0.006 | 0.273 | 0.79 | 0.623 | 0.831 | 1.414 | 2.02 |
| | 4 | -0.634 | -0.419 | 0.107 | -0.265 | 0.193 | 0.035 | 0.15 | 0.514 | 0.694 | 0.999 | 1.633 |
| | 5 | -1.139 | -0.555 | -0.269 | 0.015 | -0.198 | 0.13 | -0.018 | 0.496 | 0.657 | 0.763 | 1.902 |
| | 6 | -0.587 | -0.192 | -0.27 | -0.348 | 0.291 | -0.125 | -0.091 | 0.103 | 0.489 | 0.949 | 1.536 |
| | 7 | -0.916 | -0.847 | -0.781 | -0.223 | -0.065 | -0.498 | -0.066 | 0.277 | 0.37 | 0.383 | 1.299 |
| | 8 | -1.274 | -0.634 | -0.565 | -0.773 | -0.335 | -0.161 | -0.002 | 0.032 | 0.107 | 0.506 | 1.779 |
| | 9 | -1.812 | -1.123 | -0.77 | -0.67 | -0.922 | -0.32 | -0.569 | 0.025 | 0.166 | 0.157 | 1.969 |
| | 10 | -1.962 | -1.482 | -0.927 | -1.269 | -0.649 | -0.576 | -0.869 | -0.601 | -0.269 | 0.136 | 2.098 |
| | Diff | -2.018 | -1.615 | -1.612 | -2.16 | -1.791 | -1.243 | -2.042 | -1.99 | -1.588 | -1.446 | 0.572 |
| 2003.0 | 1 | -0.214 | 0.298 | 0.884 | 0.701 | 0.773 | 0.705 | 1.12 | 1.05 | 1.62 | 1.733 | 1.947 |
| | 2 | -0.319 | 0.077 | 0.027 | 0.399 | 0.495 | 0.534 | 0.922 | 1.196 | 1.467 | 1.665 | 1.983 |
| | 3 | -0.273 | -0.432 | 0.029 | 0.3 | 0.726 | 0.243 | 0.655 | 0.594 | 1.049 | 1.283 | 1.556 |
| | 4 | -0.643 | -0.531 | -0.149 | 0.124 | 0.086 | -0.055 | 0.186 | 0.563 | 0.696 | 1.047 | 1.69 |
| | 5 | -0.922 | -0.1 | -0.214 | -0.203 | 0.229 | 0.024 | -0.049 | 0.283 | 0.895 | 0.965 | 1.888 |
| | 6 | -0.492 | -0.802 | -0.234 | -0.392 | -0.198 | -0.148 | 0.083 | 0.348 | 0.61 | 0.702 | 1.194 |
| | 7 | -1.483 | -0.691 | -0.522 | -0.633 | -0.409 | -0.008 | 0.193 | 0.292 | -0.001 | 0.835 | 2.317 |
| | 8 | -1.352 | -0.714 | -0.556 | -0.788 | -0.063 | -0.393 | -0.047 | -0.331 | 0.098 | 0.767 | 2.119 |
| | 9 | -1.452 | -0.965 | -0.845 | -0.935 | -0.38 | -0.281 | -0.293 | -0.158 | 0.475 | -0.182 | 1.27 |
| | 10 | -1.773 | -1.58 | -1.158 | -1.133 | -0.702 | -1.006 | -0.465 | -0.499 | -0.472 | 0.02 | 1.793 |
| | Diff | -1.559 | -1.879 | -2.043 | -1.833 | -1.475 | -1.711 | -1.585 | -1.548 | -2.092 | -1.713 | -0.153 |
| 2004.0 | 1 | -0.176 | 0.258 | 0.289 | 0.622 | 0.792 | 1.224 | 1.096 | 1.166 | 1.604 | 1.758 | 1.934 |
| | 2 | -0.342 | 0.185 | 0.181 | 0.413 | 0.552 | 0.689 | 1.024 | 1.149 | 0.971 | 1.626 | 1.967 |
| | 3 | -0.363 | 0.12 | -0.258 | 0.258 | -0.219 | 0.244 | 0.817 | 0.795 | 0.942 | 1.121 | 1.485 |
| | 4 | -0.956 | -0.466 | -0.361 | -0.046 | 0.217 | 0.052 | 0.652 | 0.6 | 0.776 | 0.872 | 1.829 |
| | 5 | -1.072 | -0.247 | -0.348 | 0.101 | 0.185 | 0.061 | 0.476 | 0.288 | 0.292 | 0.871 | 1.943 |
| | 6 | -0.782 | -0.744 | -0.451 | -0.449 | -0.116 | -0.059 | 0.442 | 0.26 | 0.297 | 0.406 | 1.188 |
| | 7 | -1.011 | -0.523 | -0.174 | -0.264 | -0.209 | 0.018 | -0.09 | -0.152 | 0.406 | 0.771 | 1.782 |
| | 8 | -1.064 | -1.185 | -0.958 | -0.314 | -0.714 | -0.096 | -0.343 | -0.017 | 0.205 | 0.427 | 1.491 |
| | 9 | -1.272 | -1.341 | -0.932 | -0.839 | -0.425 | -0.452 | -0.498 | -0.107 | 0.153 | 0.259 | 1.532 |
| | 10 | -1.551 | -1.152 | -1.257 | -1.175 | -0.789 | -0.613 | -0.566 | -0.606 | 0.003 | 0.16 | 1.712 |
| | Diff | -1.376 | -1.41 | -1.547 | -1.797 | -1.581 | -1.837 | -1.662 | -1.772 | -1.6 | -1.598 | -0.222 |
| 2005.0 | 1 | 0.292 | 0.185 | 0.793 | 0.676 | 0.866 | 0.658 | 0.898 | 1.312 | 1.711 | 1.957 | 1.664 |
| | 2 | -0.351 | -0.267 | 0.235 | 0.484 | 0.402 | 0.517 | 0.938 | 0.5 | 1.084 | 1.604 | 1.955 |
| | 3 | -0.492 | -0.213 | 0.28 | 0.022 | 0.338 | 0.221 | 0.903 | 0.862 | 0.848 | 1.144 | 1.635 |
| | 4 | -0.425 | -0.268 | -0.228 | 0.014 | 0.252 | 0.27 | 0.453 | 0.612 | 0.911 | 0.999 | 1.424 |
| | 5 | -0.673 | -0.538 | -0.462 | -0.144 | -0.027 | 0.154 | 0.409 | -0.003 | 0.414 | 0.774 | 1.447 |
| | 6 | -1.109 | -0.604 | -0.465 | -0.06 | -0.048 | 0.104 | -0.058 | 0.212 | 0.749 | 1.172 | 2.282 |
| | 7 | -1.106 | -0.633 | -0.221 | -0.54 | -0.558 | -0.036 | 0.076 | -0.037 | 0.14 | 0.895 | 2.001 |
| | 8 | -1.485 | -1.188 | -0.414 | -0.21 | -0.223 | -0.556 | 0.016 | 0.029 | 0.234 | 0.521 | 2.006 |
| | 9 | -1.199 | -1.172 | -1.14 | -0.85 | -0.706 | -0.571 | -0.217 | -0.066 | 0.055 | 0.49 | 1.689 |
| | 10 | -1.876 | -1.479 | -1.317 | -1.205 | -1.136 | -0.596 | -1.07 | -0.469 | -0.376 | 0.321 | 2.197 |
| | Diff | -2.168 | -1.664 | -2.11 | -1.881 | -2.002 | -1.254 | -1.968 | -1.781 | -2.087 | -1.635 | 0.533 |
| 2006.0 | 1 | -0.006 | 0.369 | 0.611 | 0.916 | 0.818 | 0.894 | 1.053 | 1.307 | 1.403 | 1.791 | 1.797 |
| | 2 | -0.597 | -0.006 | 0.287 | 0.339 | 0.519 | 0.422 | 0.971 | 0.978 | 0.995 | 1.383 | 1.98 |
| | 3 | -0.662 | -0.362 | -0.057 | 0.17 | 0.198 | 0.369 | 0.781 | 1.019 | 0.817 | 1.337 | 1.999 |
| | 4 | -1.05 | -0.16 | 0.006 | 0.179 | -0.003 | -0.07 | 0.039 | 0.602 | 0.701 | 1.133 | 2.184 |
| | 5 | -0.966 | -0.898 | 0.001 | 0.046 | 0.031 | 0.178 | 0.454 | 0.281 | 0.479 | 0.663 | 1.629 |
| | 6 | -0.757 | -0.6 | -0.35 | -0.201 | -0.069 | -0.236 | 0.408 | 0.476 | 0.838 | 0.652 | 1.409 |
| | 7 | -1.058 | -0.532 | -0.504 | -0.384 | -0.417 | -0.004 | -0.082 | -0.06 | 0.311 | 0.522 | 1.58 |
| | 8 | -1.148 | -0.962 | -0.734 | -0.498 | -0.527 | 0.101 | -0.373 | -0.033 | 0.389 | 0.735 | 1.884 |
| | 9 | -1.473 | -0.956 | -0.508 | -0.85 | -0.689 | -0.417 | -0.198 | -0.285 | 0.005 | 0.284 | 1.757 |
| | 10 | -1.494 | -1.458 | -1.18 | -1.087 | -0.525 | -1.031 | -0.547 | -0.41 | -0.092 | 0.256 | 1.75 |
| | Diff | -1.488 | -1.827 | -1.792 | -2.003 | -1.344 | -1.924 | -1.601 | -1.716 | -1.495 | -1.535 | -0.047 |
| 2007.0 | 1 | -0.123 | 0.481 | 0.258 | 0.852 | 1.025 | 0.964 | 1.239 | 0.922 | 1.271 | 1.566 | 1.689 |
| | 2 | -0.425 | 0.048 | -0.015 | 0.031 | 0.277 | 0.5 | 0.746 | 0.831 | 1.023 | 1.435 | 1.861 |
| | 3 | -0.495 | 0.105 | 0.106 | -0.066 | 0.553 | 0.421 | 0.491 | 0.851 | 0.83 | 0.951 | 1.446 |
| | 4 | -0.595 | -0.274 | -0.412 | 0.034 | -0.059 | 0.189 | 0.594 | 0.278 | 1.072 | 0.971 | 1.566 |
| | 5 | -0.888 | -0.202 | -0.076 | 0.01 | -0.195 | 0.265 | 0.346 | 0.696 | 0.097 | 1.018 | 1.906 |
| | 6 | -1.027 | -0.787 | -0.022 | -0.213 | -0.181 | -0.109 | 0.147 | 0.205 | 0.118 | 0.798 | 1.825 |
| | 7 | -1.302 | -1.056 | -0.662 | -0.689 | -0.457 | 0.04 | 0.059 | 0.069 | 0.3 | 0.425 | 1.727 |
| | 8 | -1.333 | -0.748 | -0.862 | -0.387 | -0.526 | -0.571 | -0.221 | -0.04 | 0.0 | 0.551 | 1.884 |
| | 9 | -0.981 | -0.873 | -1.158 | -0.487 | -0.287 | -0.094 | -0.132 | -0.17 | 0.071 | 0.416 | 1.397 |
| | 10 | -1.842 | -1.518 | -1.186 | -0.903 | -0.762 | -0.558 | -0.743 | -0.43 | -0.455 | 0.242 | 2.084 |
| | Diff | -1.719 | -1.999 | -1.444 | -1.754 | -1.787 | -1.521 | -1.982 | -1.351 | -1.726 | -1.325 | 0.395 |
| 2008.0 | 1 | -0.098 | 0.303 | 0.088 | 0.747 | 0.614 | 0.964 | 1.201 | 1.296 | 1.374 | 1.807 | 1.905 |
| | 2 | -0.602 | -0.213 | 0.199 | 0.435 | 0.603 | 0.781 | 0.739 | 1.198 | 0.876 | 0.948 | 1.55 |
| | 3 | -0.607 | -0.182 | 0.041 | 0.394 | 0.28 | 0.617 | 0.472 | 0.661 | 1.057 | 1.099 | 1.706 |
| | 4 | -0.394 | -0.623 | 0.087 | -0.195 | 0.018 | -0.299 | 0.508 | 0.65 | 0.721 | 0.878 | 1.272 |
| | 5 | -0.837 | -0.421 | -0.008 | -0.168 | -0.132 | -0.049 | 0.384 | 0.486 | 0.573 | 0.728 | 1.565 |
| | 6 | -0.996 | -0.694 | -0.157 | -0.295 | 0.108 | 0.004 | 0.307 | 0.11 | 0.604 | 0.8 | 1.796 |
| | 7 | -0.842 | -0.59 | -0.517 | -0.619 | -0.429 | -0.233 | 0.302 | 0.106 | 0.414 | 0.541 | 1.383 |
| | 8 | -1.337 | -1.116 | -0.813 | -0.695 | -0.061 | -0.409 | -0.136 | -0.352 | 0.222 | 0.71 | 2.047 |
| | 9 | -1.193 | -1.169 | -0.754 | -0.77 | -0.284 | -0.354 | -0.131 | -0.069 | 0.118 | 0.631 | 1.825 |
| | 10 | -1.847 | -1.415 | -1.344 | -0.984 | -0.846 | -0.686 | -0.583 | -0.694 | -0.077 | 0.003 | 1.85 |
| | Diff | -1.749 | -1.718 | -1.432 | -1.731 | -1.459 | -1.649 | -1.784 | -1.99 | -1.451 | -1.804 | -0.055 |
| 2009.0 | 1 | 0.004 | 0.41 | 0.595 | 0.964 | 0.871 | 0.773 | 0.991 | 1.168 | 1.108 | 1.644 | 1.64 |
| | 2 | 0.028 | -0.482 | 0.104 | 0.088 | 0.597 | 0.706 | 0.974 | 0.825 | 0.79 | 1.275 | 1.247 |
| | 3 | -0.386 | -0.29 | -0.234 | 0.33 | 0.229 | 0.582 | 0.577 | 0.727 | 0.614 | 1.094 | 1.481 |
| | 4 | -0.637 | -0.508 | -0.199 | -0.332 | -0.074 | 0.255 | 0.284 | 0.096 | 0.439 | 1.158 | 1.794 |
| | 5 | -0.723 | -0.472 | 0.157 | -0.091 | 0.04 | 0.133 | 0.102 | 0.35 | 0.496 | 0.852 | 1.575 |
| | 6 | -1.057 | -0.643 | -0.585 | -0.612 | -0.204 | 0.115 | 0.32 | 0.33 | 0.603 | 0.667 | 1.723 |
| | 7 | -0.863 | -0.911 | -0.952 | -0.353 | -0.174 | -0.03 | -0.055 | 0.114 | 0.405 | 0.857 | 1.719 |
| | 8 | -1.121 | -0.646 | -0.564 | -0.685 | -0.477 | -0.235 | 0.039 | 0.048 | 0.211 | 0.168 | 1.29 |
| | 9 | -1.336 | -1.282 | -1.043 | -0.84 | -0.532 | -0.551 | -0.331 | -0.215 | 0.067 | 0.438 | 1.774 |
| | 10 | -1.727 | -1.131 | -1.202 | -0.873 | -1.011 | -0.627 | -0.7 | -0.537 | -0.467 | 0.101 | 1.828 |
| | Diff | -1.731 | -1.541 | -1.797 | -1.837 | -1.882 | -1.4 | -1.691 | -1.705 | -1.575 | -1.543 | 0.188 |
| 2010.0 | 1 | 0.398 | 0.232 | 0.344 | 0.271 | 0.476 | 0.836 | 1.238 | 1.36 | 1.652 | 1.797 | 1.399 |
| | 2 | -0.324 | 0.262 | 0.119 | 0.492 | 0.53 | 0.695 | 0.681 | 0.693 | 0.927 | 1.509 | 1.833 |
| | 3 | -0.438 | -0.564 | -0.147 | 0.335 | 0.688 | 0.283 | 0.359 | 0.804 | 0.797 | 1.339 | 1.777 |
| | 4 | -0.582 | -0.318 | -0.246 | -0.045 | 0.266 | 0.529 | 0.367 | 0.539 | 0.559 | 1.126 | 1.708 |
| | 5 | -1.221 | -0.754 | -0.498 | 0.03 | -0.185 | -0.02 | 0.324 | 0.695 | 0.711 | 0.862 | 2.084 |
| | 6 | -1.001 | -0.697 | -0.32 | -0.427 | -0.047 | 0.352 | 0.018 | 0.329 | 0.554 | 0.62 | 1.621 |
| | 7 | -0.948 | -0.484 | -0.402 | -0.555 | -0.1 | -0.253 | -0.326 | 0.218 | 0.242 | 0.401 | 1.349 |
| | 8 | -1.214 | -0.57 | -0.531 | -0.58 | -0.383 | -0.304 | -0.024 | -0.187 | -0.011 | 0.663 | 1.877 |
| | 9 | -1.187 | -0.866 | -0.827 | -1.277 | -0.418 | -0.583 | -0.491 | 0.196 | -0.153 | 0.566 | 1.753 |
| | 10 | -1.815 | -1.309 | -1.377 | -1.038 | -0.939 | -0.781 | -0.335 | -0.757 | -0.224 | -0.121 | 1.694 |
| | Diff | -2.213 | -1.541 | -1.721 | -1.309 | -1.415 | -1.617 | -1.573 | -2.117 | -1.876 | -1.919 | 0.295 |
| 2011.0 | 1 | 0.118 | 0.372 | 0.283 | 0.764 | 0.693 | 0.581 | 1.095 | 1.004 | 1.381 | 2.34 | 2.222 |
| | 2 | -0.12 | -0.056 | 0.197 | 0.623 | 0.528 | 0.429 | 1.032 | 0.995 | 0.792 | 1.525 | 1.645 |
| | 3 | -0.727 | -0.498 | 0.392 | -0.075 | 0.101 | 0.42 | 0.886 | 0.547 | 0.744 | 1.446 | 2.172 |
| | 4 | -0.743 | -0.357 | -0.019 | -0.137 | 0.228 | 0.258 | 0.283 | 0.824 | 0.982 | 0.807 | 1.55 |
| | 5 | -0.762 | -0.51 | -0.224 | 0.031 | 0.244 | 0.032 | 0.252 | 0.406 | 0.877 | 1.207 | 1.969 |
| | 6 | -1.281 | -0.633 | -0.157 | -0.182 | 0.031 | -0.15 | -0.177 | 0.459 | 0.495 | 0.794 | 2.075 |
| | 7 | -1.463 | -0.75 | -0.557 | -0.396 | -0.311 | 0.082 | -0.033 | 0.155 | 0.569 | 0.505 | 1.968 |
| | 8 | -1.224 | -0.942 | -1.001 | -0.362 | -0.396 | -0.274 | -0.03 | -0.247 | 0.136 | 0.574 | 1.798 |
| | 9 | -1.545 | -0.878 | -0.998 | -0.706 | -0.379 | -0.32 | -0.212 | 0.023 | 0.162 | 0.527 | 2.072 |
| | 10 | -1.606 | -1.534 | -1.321 | -0.935 | -1.014 | -0.947 | -0.52 | -0.564 | -0.12 | -0.016 | 1.59 |
| | Diff | -1.725 | -1.907 | -1.604 | -1.699 | -1.707 | -1.528 | -1.614 | -1.568 | -1.501 | -2.356 | -0.631 |
| 2012.0 | 1 | 0.007 | 0.437 | 0.364 | 0.65 | 0.744 | 0.871 | 0.846 | 1.401 | 1.454 | 1.942 | 1.935 |
| | 2 | -0.211 | 0.347 | 0.334 | 0.474 | 0.388 | 0.553 | 0.609 | 1.23 | 1.096 | 1.132 | 1.344 |
| | 3 | -0.593 | -0.204 | 0.255 | 0.025 | 0.188 | 0.467 | 0.501 | 0.876 | 1.01 | 1.093 | 1.686 |
| | 4 | -0.8 | -0.355 | -0.228 | -0.071 | 0.162 | 0.032 | 0.527 | 0.331 | 0.865 | 0.778 | 1.578 |
| | 5 | -0.686 | -0.649 | -0.231 | -0.307 | 0.045 | 0.356 | 0.535 | 0.464 | 0.571 | 1.283 | 1.969 |
| | 6 | -0.937 | -0.828 | -0.39 | -0.22 | -0.177 | 0.17 | 0.229 | 0.407 | 0.525 | 0.794 | 1.732 |
| | 7 | -1.389 | -0.866 | -0.569 | -0.473 | -0.265 | -0.039 | 0.233 | 0.029 | 0.113 | 0.725 | 2.114 |
| | 8 | -0.986 | -0.783 | -0.699 | -0.509 | -0.592 | -0.219 | 0.232 | -0.225 | 0.145 | 0.466 | 1.453 |
| | 9 | -1.321 | -1.27 | -0.977 | -0.913 | -0.673 | -0.394 | -0.46 | -0.266 | -0.082 | 0.417 | 1.738 |
| | 10 | -1.775 | -1.274 | -1.423 | -1.141 | -1.174 | -0.84 | -0.887 | -0.78 | -0.291 | -0.13 | 1.645 |
| | Diff | -1.782 | -1.711 | -1.787 | -1.79 | -1.917 | -1.711 | -1.732 | -2.181 | -1.745 | -2.072 | -0.29 |
| 2013.0 | 1 | -0.048 | 0.324 | 0.48 | 0.571 | 0.748 | 0.703 | 1.18 | 1.111 | 1.442 | 1.638 | 1.686 |
| | 2 | -0.562 | 0.103 | -0.179 | 0.233 | 0.691 | 0.473 | 0.932 | 1.174 | 0.961 | 1.348 | 1.91 |
| | 3 | -0.398 | -0.175 | -0.166 | 0.234 | 0.4 | 0.682 | 0.489 | 0.469 | 0.74 | 1.726 | 2.124 |
| | 4 | -0.738 | -0.619 | -0.418 | -0.073 | -0.108 | 0.24 | 0.276 | 0.373 | 0.468 | 1.071 | 1.809 |
| | 5 | -0.863 | -0.377 | -0.39 | -0.113 | -0.033 | 0.235 | 0.186 | 0.682 | 0.684 | 0.81 | 1.673 |
| | 6 | -1.077 | -0.916 | -0.246 | -0.251 | -0.21 | -0.143 | 0.18 | 0.216 | 0.254 | 0.814 | 1.891 |
| | 7 | -1.058 | -0.795 | -0.693 | -0.696 | -0.014 | -0.276 | 0.019 | 0.193 | 0.325 | 0.614 | 1.672 |
| | 8 | -1.311 | -1.051 | -0.623 | -0.405 | -0.395 | -0.427 | -0.012 | -0.002 | 0.087 | 0.423 | 1.734 |
| | 9 | -1.397 | -1.082 | -0.901 | -0.708 | -0.414 | -0.726 | -0.495 | -0.321 | 0.057 | 0.26 | 1.657 |
| | 10 | -1.667 | -1.489 | -1.047 | -1.229 | -1.01 | -0.663 | -0.617 | -0.362 | -0.299 | -0.169 | 1.498 |
| | Diff | -1.619 | -1.813 | -1.527 | -1.799 | -1.758 | -1.366 | -1.796 | -1.473 | -1.741 | -1.807 | -0.187 |
| 2014.0 | 1 | -0.034 | 0.241 | 0.419 | 0.757 | 0.858 | 0.525 | 1.198 | 1.045 | 1.02 | 1.699 | 1.733 |
| | 2 | -0.408 | 0.19 | -0.119 | 0.337 | 0.591 | 0.377 | 0.904 | 0.903 | 0.883 | 1.41 | 1.818 |
| | 3 | -0.409 | -0.099 | 0.102 | -0.019 | -0.073 | 0.459 | 0.414 | 0.252 | 0.845 | 1.126 | 1.535 |
| | 4 | -0.512 | -0.355 | 0.119 | 0.074 | 0.43 | 0.225 | 0.139 | 0.802 | 0.797 | 0.88 | 1.392 |
| | 5 | -1.035 | -0.427 | -0.468 | -0.243 | 0.106 | -0.02 | -0.197 | 0.573 | 0.423 | 0.553 | 1.588 |
| | 6 | -0.499 | -0.515 | -0.074 | -0.169 | -0.163 | -0.3 | -0.116 | 0.761 | 0.447 | 0.751 | 1.249 |
| | 7 | -1.057 | -0.442 | -0.697 | -0.293 | -0.076 | -0.288 | -0.158 | -0.161 | 0.508 | 0.707 | 1.764 |
| | 8 | -0.999 | -0.741 | -0.487 | -0.661 | -0.527 | 0.079 | 0.098 | -0.015 | 0.3 | 0.619 | 1.618 |
| | 9 | -1.416 | -0.84 | -0.994 | -0.848 | -0.619 | -0.711 | -0.267 | 0.02 | -0.047 | 0.582 | 1.998 |
| | 10 | -1.844 | -1.085 | -1.056 | -0.792 | -1.005 | -0.656 | -0.896 | -0.854 | 0.081 | 0.034 | 1.878 |
| | Diff | -1.81 | -1.326 | -1.475 | -1.549 | -1.863 | -1.181 | -2.094 | -1.899 | -0.939 | -1.665 | 0.145 |
| 2015.0 | 1 | -0.102 | 0.472 | 0.353 | 0.39 | 0.892 | 1.007 | 0.944 | 1.42 | 1.429 | 1.755 | 1.857 |
| | 2 | -0.089 | 0.226 | 0.475 | 0.355 | 0.74 | 0.802 | 0.882 | 0.944 | 1.093 | 1.243 | 1.331 |
| | 3 | -0.556 | -0.277 | 0.071 | -0.042 | 0.272 | 0.659 | 0.171 | 0.743 | 0.942 | 1.302 | 1.858 |
| | 4 | -0.575 | -0.359 | -0.347 | 0.069 | 0.077 | 0.37 | 0.366 | 0.779 | 0.873 | 0.916 | 1.491 |
| | 5 | -0.694 | -0.451 | -0.051 | -0.235 | -0.243 | 0.179 | 0.247 | 0.142 | 0.391 | 0.725 | 1.418 |
| | 6 | -1.202 | -0.162 | -0.674 | -0.078 | -0.235 | -0.062 | 0.205 | 0.275 | 0.616 | 0.691 | 1.893 |
| | 7 | -1.446 | -0.757 | -0.59 | -0.406 | -0.359 | 0.124 | 0.106 | 0.449 | 0.247 | 0.399 | 1.845 |
| | 8 | -1.208 | -0.749 | -0.583 | -0.524 | -0.355 | -0.074 | -0.097 | -0.111 | -0.251 | 0.833 | 2.041 |
| | 9 | -1.29 | -1.283 | -0.671 | -0.799 | -0.689 | 0.015 | 0.018 | -0.311 | 0.217 | 0.559 | 1.849 |
| | 10 | -1.864 | -1.381 | -1.103 | -0.893 | -0.727 | -1.004 | -0.913 | -0.132 | -0.472 | 0.081 | 1.944 |
| | Diff | -1.762 | -1.853 | -1.457 | -1.283 | -1.619 | -2.01 | -1.857 | -1.552 | -1.9 | -1.674 | 0.087 |
| 2016.0 | 1 | -0.049 | 0.267 | 0.437 | 0.574 | 1.052 | 0.797 | 1.475 | 1.057 | 1.621 | 2.096 | 2.144 |
| | 2 | -0.385 | -0.062 | -0.086 | 0.358 | 0.585 | 0.521 | 0.623 | 0.743 | 0.793 | 2.004 | 2.389 |
| | 3 | -0.141 | -0.174 | -0.067 | 0.258 | 0.383 | 0.591 | 0.5 | 0.695 | 0.816 | 1.503 | 1.644 |
| | 4 | -1.209 | -0.191 | -0.135 | -0.375 | 0.25 | 0.226 | 0.472 | 0.19 | 0.625 | 1.256 | 2.466 |
| | 5 | -0.779 | -0.3 | -0.227 | -0.264 | 0.101 | 0.066 | 0.08 | 0.286 | 0.469 | 0.917 | 1.696 |
| | 6 | -0.917 | -0.6 | -0.65 | -0.345 | -0.301 | 0.188 | 0.083 | -0.182 | 0.615 | 0.608 | 1.526 |
| | 7 | -1.478 | -0.925 | -0.501 | -0.582 | -0.114 | -0.603 | -0.066 | -0.055 | 0.614 | 0.535 | 2.013 |
| | 8 | -1.171 | -0.774 | -0.448 | -0.626 | -0.555 | -0.03 | -0.336 | -0.17 | 0.222 | 0.496 | 1.666 |
| | 9 | -1.861 | -0.947 | -0.966 | -0.679 | -0.868 | -0.535 | -0.165 | -0.605 | 0.078 | 0.37 | 2.232 |
| | 10 | -1.829 | -1.318 | -0.905 | -1.276 | -0.799 | -0.802 | -0.785 | -0.527 | -0.28 | -0.392 | 1.437 |
| | Diff | -1.78 | -1.584 | -1.342 | -1.85 | -1.851 | -1.599 | -2.261 | -1.583 | -1.901 | -2.488 | -0.707 |
| 2017.0 | 1 | 0.011 | 0.448 | 0.522 | 0.26 | 0.508 | 1.239 | 1.196 | 0.836 | 1.442 | 1.491 | 1.479 |
| | 2 | -0.55 | 0.057 | 0.314 | 0.301 | 0.169 | 0.32 | 0.844 | 0.798 | 1.21 | 1.167 | 1.716 |
| | 3 | -0.68 | -0.113 | -0.196 | -0.14 | 0.102 | 0.14 | 0.175 | 0.248 | 0.639 | 1.27 | 1.95 |
| | 4 | -0.374 | -0.539 | -0.147 | 0.189 | 0.187 | 0.574 | 0.384 | 0.713 | 0.945 | 1.278 | 1.652 |
| | 5 | -0.881 | -0.352 | -0.322 | -0.16 | 0.276 | -0.108 | 0.277 | 0.097 | 0.836 | 0.817 | 1.699 |
| | 6 | -0.874 | -0.436 | -0.232 | -0.06 | -0.278 | 0.051 | 0.179 | 0.216 | 0.568 | 0.901 | 1.775 |
| | 7 | -1.164 | -0.722 | -0.315 | -0.685 | -0.425 | -0.446 | 0.235 | 0.311 | 0.389 | 0.842 | 2.006 |
| | 8 | -1.241 | -0.877 | -0.857 | -0.97 | -0.498 | -0.112 | 0.059 | -0.083 | 0.05 | 0.389 | 1.63 |
| | 9 | -1.399 | -1.35 | -1.142 | -0.936 | -0.252 | -0.369 | -0.156 | -0.276 | 0.114 | 0.575 | 1.974 |
| | 10 | -1.788 | -1.7 | -1.365 | -0.75 | -0.811 | -0.979 | -0.596 | -0.708 | -0.339 | 0.011 | 1.799 |
| | Diff | -1.799 | -2.148 | -1.886 | -1.01 | -1.319 | -2.218 | -1.792 | -1.544 | -1.781 | -1.48 | 0.32 |
| 2018.0 | 1 | 0.008 | 0.432 | 0.384 | 0.844 | 0.812 | 0.936 | 1.029 | 1.18 | 1.101 | 1.392 | 1.384 |
| | 2 | -0.468 | 0.012 | 0.307 | 0.623 | 0.365 | 0.51 | 0.678 | 0.867 | 0.985 | 1.551 | 2.019 |
| | 3 | -0.361 | -0.168 | -0.177 | 0.34 | 0.501 | 0.448 | 0.516 | 0.664 | 0.963 | 1.04 | 1.401 |
| | 4 | -0.615 | -0.416 | -0.068 | -0.069 | 0.191 | -0.086 | 0.502 | 0.559 | 0.686 | 0.978 | 1.593 |
| | 5 | -0.837 | -0.41 | -0.226 | -0.388 | 0.277 | 0.209 | -0.095 | 0.29 | 0.83 | 1.08 | 1.917 |
| | 6 | -1.293 | -0.31 | -0.482 | -0.24 | 0.118 | 0.133 | 0.139 | 0.027 | 0.563 | 0.959 | 2.252 |
| | 7 | -1.1 | -0.543 | -0.849 | -0.144 | -0.267 | 0.051 | 0.122 | 0.21 | 0.074 | 0.187 | 1.286 |
| | 8 | -1.244 | -0.855 | -0.769 | -0.346 | -0.521 | 0.072 | -0.271 | 0.512 | 0.116 | 0.444 | 1.688 |
| | 9 | -1.498 | -1.175 | -0.727 | -1.168 | -0.162 | -0.464 | 0.05 | 0.21 | 0.266 | 0.416 | 1.914 |
| | 10 | -1.6 | -1.337 | -1.39 | -0.975 | -1.115 | -0.983 | -0.877 | -0.831 | -0.031 | -0.202 | 1.398 |
| | Diff | -1.608 | -1.769 | -1.773 | -1.819 | -1.927 | -1.92 | -1.906 | -2.011 | -1.132 | -1.594 | 0.014 |
| 2019.0 | 1 | -0.44 | 0.475 | 0.925 | 0.48 | 1.048 | 1.155 | 1.371 | 1.053 | 1.226 | 1.841 | 2.281 |
| | 2 | -0.204 | 0.26 | 0.102 | 0.299 | 0.613 | 0.416 | 0.424 | 0.775 | 1.328 | 1.262 | 1.466 |
| | 3 | -0.532 | -0.638 | -0.119 | 0.308 | 0.423 | 0.775 | 0.427 | 0.517 | 0.85 | 1.187 | 1.72 |
| | 4 | -0.93 | -0.281 | 0.02 | 0.134 | 0.224 | 0.44 | 0.321 | 0.863 | 0.927 | 1.049 | 1.979 |
| | 5 | -1.019 | -0.393 | -0.3 | 0.244 | 0.094 | -0.029 | 0.351 | 0.646 | 0.458 | 0.969 | 1.988 |
| | 6 | -0.765 | -0.487 | -0.181 | -0.323 | -0.04 | -0.275 | -0.429 | 0.413 | 0.534 | 0.63 | 1.395 |
| | 7 | -0.918 | -0.659 | -0.149 | -0.239 | -0.002 | 0.076 | 0.273 | 0.309 | 0.355 | 0.676 | 1.594 |
| | 8 | -1.537 | -0.798 | -0.79 | -0.386 | -0.164 | -0.058 | -0.127 | 0.143 | 0.275 | 0.667 | 2.205 |
| | 9 | -1.312 | -1.003 | -0.961 | -0.559 | -0.569 | -0.486 | -0.378 | 0.221 | -0.05 | 0.225 | 1.536 |
| | 10 | -1.497 | -1.629 | -1.01 | -1.305 | -0.99 | -0.801 | -0.715 | -0.348 | -0.502 | -0.066 | 1.431 |
| | Diff | -1.057 | -2.103 | -1.934 | -1.785 | -2.038 | -1.957 | -2.086 | -1.401 | -1.727 | -1.907 | -0.85 |
| 2020.0 | 1 | 0.23 | 0.022 | 0.614 | 0.927 | 0.523 | 1.044 | 0.959 | 1.124 | 1.273 | 1.867 | 1.637 |
| | 2 | -0.196 | -0.132 | 0.246 | 0.41 | 0.343 | 0.486 | 0.765 | 0.851 | 1.197 | 1.628 | 1.824 |
| | 3 | -0.435 | -0.397 | -0.089 | 0.152 | -0.056 | 0.45 | 0.429 | 0.74 | 1.072 | 1.295 | 1.73 |
| | 4 | -0.823 | -0.261 | 0.059 | 0.19 | -0.096 | 0.364 | 0.348 | 0.438 | 0.645 | 0.952 | 1.775 |
| | 5 | -0.614 | -0.623 | -0.055 | -0.146 | -0.07 | 0.04 | 0.166 | 0.375 | 0.511 | 0.746 | 1.36 |
| | 6 | -0.933 | -0.574 | -0.774 | -0.133 | -0.194 | -0.236 | 0.176 | 0.301 | 0.547 | 0.627 | 1.56 |
| | 7 | -1.388 | -0.506 | -0.445 | -0.479 | -0.142 | -0.575 | 0.27 | 0.09 | 0.466 | 0.863 | 2.251 |
| | 8 | -0.719 | -1.014 | -1.063 | -0.313 | -0.218 | -0.042 | 0.194 | 0.205 | 0.223 | 0.86 | 1.578 |
| | 9 | -1.729 | -1.054 | -0.891 | -1.075 | -0.912 | -0.011 | -0.14 | 0.048 | -0.149 | 0.479 | 2.208 |
| | 10 | -1.749 | -1.711 | -1.213 | -1.071 | -0.96 | -1.143 | -0.949 | -0.404 | -0.356 | -0.342 | 1.407 |
| | Diff | -1.979 | -1.733 | -1.827 | -1.998 | -1.483 | -2.187 | -1.909 | -1.528 | -1.629 | -2.209 | -0.23 |
+--------+-------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+
+-------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+--------+
| Group | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Diff |
+-------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+--------+
| 1 | 0.001 | 0.404 | 0.582 | 0.692 | 0.813 | 0.926 | 0.991 | 1.186 | 1.436 | 1.735 | 1.734 |
| | 0.023 | 10.409 | 12.521 | 12.719 | 21.586 | 28.711 | 25.342 | 30.539 | 40.084 | 50.195 | 31.306 |
| 2 | -0.329 | -0.065 | 0.156 | 0.261 | 0.429 | 0.51 | 0.709 | 0.908 | 1.065 | 1.39 | 1.719 |
| | -5.829 | -1.779 | 3.245 | 5.842 | 10.537 | 11.431 | 14.92 | 21.006 | 24.647 | 33.373 | 23.585 |
| 3 | -0.538 | -0.193 | -0.021 | 0.183 | 0.3 | 0.453 | 0.533 | 0.646 | 0.851 | 1.242 | 1.78 |
| | -13.214 | -5.684 | -0.454 | 6.47 | 12.997 | 11.485 | 13.978 | 17.107 | 27.073 | 25.137 | 21.695 |
| 4 | -0.691 | -0.332 | -0.065 | 0.055 | 0.142 | 0.313 | 0.369 | 0.503 | 0.736 | 1.034 | 1.725 |
| | -20.494 | -10.105 | -1.874 | 1.247 | 3.242 | 9.129 | 9.121 | 12.057 | 15.833 | 24.654 | 26.702 |
| 5 | -0.824 | -0.439 | -0.292 | -0.184 | 0.028 | 0.137 | 0.242 | 0.407 | 0.639 | 0.93 | 1.755 |
| | -19.074 | -8.937 | -8.189 | -3.622 | 0.598 | 3.632 | 5.026 | 9.74 | 14.213 | 19.002 | 29.906 |
| 6 | -0.999 | -0.557 | -0.383 | -0.256 | -0.102 | 0.019 | 0.078 | 0.255 | 0.506 | 0.711 | 1.71 |
| | -24.83 | -12.412 | -9.966 | -8.078 | -2.96 | 0.627 | 1.588 | 4.753 | 13.01 | 16.397 | 24.858 |
| 7 | -1.043 | -0.701 | -0.57 | -0.472 | -0.349 | -0.163 | -0.009 | 0.234 | 0.408 | 0.674 | 1.717 |
| | -22.39 | -18.651 | -15.173 | -7.718 | -8.648 | -4.423 | -0.261 | 5.529 | 12.285 | 13.125 | 28.054 |
| 8 | -1.168 | -0.845 | -0.703 | -0.513 | -0.445 | -0.338 | -0.19 | -0.023 | 0.114 | 0.617 | 1.786 |
| | -37.234 | -18.681 | -14.622 | -11.528 | -11.526 | -7.705 | -4.063 | -0.463 | 3.978 | 19.966 | 35.299 |
| 9 | -1.419 | -1.109 | -0.998 | -0.789 | -0.593 | -0.429 | -0.291 | -0.197 | 0.015 | 0.423 | 1.843 |
| | -36.366 | -29.646 | -17.698 | -23.854 | -18.852 | -11.099 | -7.294 | -4.962 | 0.321 | 10.342 | 43.131 |
| 10 | -1.796 | -1.401 | -1.233 | -1.072 | -0.943 | -0.807 | -0.669 | -0.51 | -0.271 | -0.083 | 1.714 |
| | -42.272 | -33.192 | -30.341 | -35.35 | -22.034 | -17.648 | -14.833 | -10.624 | -6.58 | -1.658 | 26.054 |
| Diff | -1.798 | -1.804 | -1.815 | -1.764 | -1.756 | -1.734 | -1.66 | -1.696 | -1.707 | -1.818 | -0.02 |
| | -24.606 | -25.698 | -37.732 | -26.27 | -33.109 | -28.342 | -30.244 | -24.987 | -26.689 | -30.782 | -0.234 |
+-------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+--------+
+-------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+--------+
| Group | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Diff |
+-------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+--------+
| 1 | 0.001 | 0.404 | 0.582 | 0.692 | 0.813 | 0.926 | 0.991 | 1.186 | 1.436 | 1.735 | 1.734 |
| | 0.023 | 10.409 | 12.521 | 12.719 | 21.586 | 28.711 | 25.342 | 30.539 | 40.084 | 50.195 | 31.306 |
| alpha | 0.001 | 0.393 | 0.588 | 0.695 | 0.814 | 0.928 | 0.994 | 1.182 | 1.431 | 1.73 | 1.73 |
| | 0.023 | 15.172 | 16.757 | 18.333 | 25.684 | 52.337 | 53.463 | 33.971 | 32.144 | 120.675 | 64.353 |
| 2 | -0.329 | -0.065 | 0.156 | 0.261 | 0.429 | 0.51 | 0.709 | 0.908 | 1.065 | 1.39 | 1.719 |
| | -5.829 | -1.779 | 3.245 | 5.842 | 10.537 | 11.431 | 14.92 | 21.006 | 24.647 | 33.373 | 23.585 |
| alpha | -0.328 | -0.067 | 0.168 | 0.257 | 0.433 | 0.526 | 0.708 | 0.9 | 1.064 | 1.385 | 1.712 |
| | -6.882 | -4.699 | 5.144 | 5.719 | 9.258 | 16.709 | 46.722 | 30.124 | 48.315 | 54.9 | 33.901 |
| 3 | -0.538 | -0.193 | -0.021 | 0.183 | 0.3 | 0.453 | 0.533 | 0.646 | 0.851 | 1.242 | 1.78 |
| | -13.214 | -5.684 | -0.454 | 6.47 | 12.997 | 11.485 | 13.978 | 17.107 | 27.073 | 25.137 | 21.695 |
| alpha | -0.532 | -0.187 | -0.021 | 0.179 | 0.299 | 0.45 | 0.523 | 0.654 | 0.847 | 1.227 | 1.76 |
| | -15.226 | -10.095 | -0.443 | 12.856 | 25.329 | 18.972 | 12.407 | 18.425 | 31.055 | 24.734 | 21.164 |
| 4 | -0.691 | -0.332 | -0.065 | 0.055 | 0.142 | 0.313 | 0.369 | 0.503 | 0.736 | 1.034 | 1.725 |
| | -20.494 | -10.105 | -1.874 | 1.247 | 3.242 | 9.129 | 9.121 | 12.057 | 15.833 | 24.654 | 26.702 |
| alpha | -0.695 | -0.335 | -0.063 | 0.049 | 0.146 | 0.317 | 0.365 | 0.508 | 0.749 | 1.039 | 1.735 |
| | -34.692 | -8.032 | -2.253 | 1.587 | 4.982 | 8.723 | 19.073 | 18.714 | 10.766 | 59.53 | 53.763 |
| 5 | -0.824 | -0.439 | -0.292 | -0.184 | 0.028 | 0.137 | 0.242 | 0.407 | 0.639 | 0.93 | 1.755 |
| | -19.074 | -8.937 | -8.189 | -3.622 | 0.598 | 3.632 | 5.026 | 9.74 | 14.213 | 19.002 | 29.906 |
| alpha | -0.828 | -0.441 | -0.289 | -0.196 | 0.034 | 0.141 | 0.242 | 0.402 | 0.633 | 0.924 | 1.752 |
| | -50.38 | -17.93 | -14.905 | -6.066 | 1.608 | 5.277 | 6.61 | 16.518 | 12.557 | 21.612 | 44.153 |
| 6 | -0.999 | -0.557 | -0.383 | -0.256 | -0.102 | 0.019 | 0.078 | 0.255 | 0.506 | 0.711 | 1.71 |
| | -24.83 | -12.412 | -9.966 | -8.078 | -2.96 | 0.627 | 1.588 | 4.753 | 13.01 | 16.397 | 24.858 |
| alpha | -1.001 | -0.553 | -0.385 | -0.264 | -0.106 | 0.026 | 0.094 | 0.266 | 0.507 | 0.717 | 1.718 |
| | -69.664 | -17.632 | -7.841 | -11.507 | -4.864 | 1.416 | 2.265 | 8.531 | 13.376 | 32.65 | 60.333 |
| 7 | -1.043 | -0.701 | -0.57 | -0.472 | -0.349 | -0.163 | -0.009 | 0.234 | 0.408 | 0.674 | 1.717 |
| | -22.39 | -18.651 | -15.173 | -7.718 | -8.648 | -4.423 | -0.261 | 5.529 | 12.285 | 13.125 | 28.054 |
| alpha | -1.036 | -0.695 | -0.58 | -0.467 | -0.348 | -0.161 | -0.013 | 0.236 | 0.413 | 0.68 | 1.716 |
| | -15.761 | -26.285 | -30.789 | -9.662 | -21.064 | -10.49 | -0.54 | 11.513 | 13.003 | 16.793 | 26.971 |
| 8 | -1.168 | -0.845 | -0.703 | -0.513 | -0.445 | -0.338 | -0.19 | -0.023 | 0.114 | 0.617 | 1.786 |
| | -37.234 | -18.681 | -14.622 | -11.528 | -11.526 | -7.705 | -4.063 | -0.463 | 3.978 | 19.966 | 35.299 |
| alpha | -1.165 | -0.866 | -0.695 | -0.521 | -0.441 | -0.334 | -0.192 | -0.014 | 0.117 | 0.612 | 1.777 |
| | -68.442 | -47.472 | -16.293 | -18.214 | -13.313 | -20.344 | -6.396 | -0.495 | 8.054 | 37.427 | 74.827 |
| 9 | -1.419 | -1.109 | -0.998 | -0.789 | -0.593 | -0.429 | -0.291 | -0.197 | 0.015 | 0.423 | 1.843 |
| | -36.366 | -29.646 | -17.698 | -23.854 | -18.852 | -11.099 | -7.294 | -4.962 | 0.321 | 10.342 | 43.131 |
| alpha | -1.421 | -1.101 | -0.999 | -0.796 | -0.586 | -0.43 | -0.297 | -0.208 | 0.008 | 0.422 | 1.843 |
| | -58.572 | -36.794 | -24.981 | -57.723 | -40.075 | -22.395 | -11.038 | -8.076 | 0.188 | 12.12 | 79.95 |
| 10 | -1.796 | -1.401 | -1.233 | -1.072 | -0.943 | -0.807 | -0.669 | -0.51 | -0.271 | -0.083 | 1.714 |
| | -42.272 | -33.192 | -30.341 | -35.35 | -22.034 | -17.648 | -14.833 | -10.624 | -6.58 | -1.658 | 26.054 |
| alpha | -1.792 | -1.396 | -1.235 | -1.075 | -0.934 | -0.802 | -0.676 | -0.504 | -0.27 | -0.078 | 1.714 |
| | -94.079 | -29.367 | -24.322 | -49.929 | -18.363 | -22.423 | -17.282 | -12.055 | -6.679 | -2.087 | 64.666 |
| Diff | -1.798 | -1.804 | -1.815 | -1.764 | -1.756 | -1.734 | -1.66 | -1.696 | -1.707 | -1.818 | -0.02 |
| | -24.606 | -25.698 | -37.732 | -26.27 | -33.109 | -28.342 | -30.244 | -24.987 | -26.689 | -30.782 | -0.234 |
| alpha | -1.792 | -1.789 | -1.823 | -1.77 | -1.749 | -1.73 | -1.671 | -1.686 | -1.7 | -1.808 | -0.016 |
| | -68.889 | -25.304 | -35.662 | -49.993 | -23.566 | -35.304 | -39.998 | -48.493 | -20.813 | -57.675 | -0.471 |
+-------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+--------+
========================================================================
# conditional portfolio
# test function average_by_time
exper_con = bi(sample, 9, maxlag=12)
average_group_time = exper_con.average_by_time(conditional=True)
print('average_group_time: \n', average_group_time)
print('shape of average_group_time: \n', np.shape(average_group_time))
# test function difference
result = exper_con.difference(average_group_time)
print('result :\n', result)
print('difference matrix :\n', np.shape(result))
# test function summary_and_test
average, ttest = exper_con.summary_and_test(conditional=True)
print('average :\n', average)
print(' shape of average :', np.shape(average))
print('ttest :\n', ttest)
print('shape of ttest :', np.shape(ttest))
# test function print_summary_by_time()
exper_con.print_summary_by_time()
# test function print_summary
exper_con.print_summary()
=========================================================================
average_group_time:
[[[-0.038 -0.166 -0.106 ... 0.159 -0.269 -0.153]
[0.646 0.607 0.207 ... 0.646 0.522 -0.120]
[0.562 0.595 0.529 ... 0.522 0.629 0.842]
...
[1.532 1.257 1.386 ... 1.063 1.323 1.445]
[1.433 1.618 1.642 ... 1.232 1.724 1.240]
[1.646 1.492 1.715 ... 2.065 1.609 1.576]]
[[-0.433 -0.127 -0.365 ... -0.312 -0.494 -0.538]
[0.192 0.154 -0.039 ... -0.105 -0.220 -0.270]
[0.429 0.335 -0.084 ... -0.161 0.102 0.251]
...
[1.122 0.987 0.814 ... 0.751 0.682 0.701]
[0.960 0.856 1.060 ... 0.965 0.826 1.156]
[1.539 1.672 1.229 ... 1.255 1.344 1.735]]
[[-0.557 -0.607 -1.008 ... -0.587 -0.488 -0.685]
[0.035 -0.231 0.071 ... -0.228 -0.036 -0.438]
[-0.087 0.027 -0.119 ... 0.156 -0.255 -0.007]
...
[0.653 0.694 0.489 ... 0.783 0.667 0.883]
[0.840 0.749 0.810 ... 0.521 0.976 0.843]
[1.274 1.040 1.282 ... 1.386 0.971 1.234]]
...
[[-1.452 -1.150 -1.096 ... -1.098 -1.268 -1.428]
[-0.720 -0.787 -0.790 ... -1.104 -1.268 -0.895]
[-0.509 -0.782 -1.040 ... -0.461 -0.857 -0.520]
...
[0.020 -0.202 -0.355 ... 0.117 0.083 -0.006]
[0.088 0.343 0.038 ... 0.158 0.171 0.327]
[0.339 0.452 0.345 ... 0.401 0.555 0.581]]
[[-1.216 -1.196 -1.604 ... -1.820 -1.136 -1.514]
[-1.210 -1.053 -0.910 ... -1.118 -0.663 -1.092]
[-0.780 -0.610 -0.867 ... -0.967 -0.940 -1.062]
...
[-0.344 -0.105 -0.444 ... -0.542 -0.119 -0.295]
[0.138 0.346 -0.113 ... 0.010 -0.221 0.080]
[0.415 0.361 0.335 ... 0.362 0.132 0.715]]
[[-1.876 -1.826 -1.527 ... -1.676 -2.018 -1.795]
[-1.439 -1.495 -1.771 ... -1.645 -1.366 -1.513]
[-1.214 -1.419 -0.954 ... -1.269 -1.173 -1.191]
...
[-0.186 -0.994 -0.262 ... -0.384 -0.375 -0.574]
[-0.496 -0.515 -0.625 ... -0.037 -0.381 -0.155]
[-0.384 -0.406 -0.220 ... -0.068 0.175 -0.261]]]
shape of average_group_time:
(10, 10, 20)
result :
[[[-0.038 -0.166 -0.106 ... 0.159 -0.269 -0.153]
[0.646 0.607 0.207 ... 0.646 0.522 -0.120]
[0.562 0.595 0.529 ... 0.522 0.629 0.842]
...
[1.433 1.618 1.642 ... 1.232 1.724 1.240]
[1.646 1.492 1.715 ... 2.065 1.609 1.576]
[1.685 1.658 1.821 ... 1.906 1.878 1.730]]
[[-0.433 -0.127 -0.365 ... -0.312 -0.494 -0.538]
[0.192 0.154 -0.039 ... -0.105 -0.220 -0.270]
[0.429 0.335 -0.084 ... -0.161 0.102 0.251]
...
[0.960 0.856 1.060 ... 0.965 0.826 1.156]
[1.539 1.672 1.229 ... 1.255 1.344 1.735]
[1.972 1.799 1.594 ... 1.567 1.838 2.273]]
[[-0.557 -0.607 -1.008 ... -0.587 -0.488 -0.685]
[0.035 -0.231 0.071 ... -0.228 -0.036 -0.438]
[-0.087 0.027 -0.119 ... 0.156 -0.255 -0.007]
...
[0.840 0.749 0.810 ... 0.521 0.976 0.843]
[1.274 1.040 1.282 ... 1.386 0.971 1.234]
[1.831 1.647 2.291 ... 1.973 1.458 1.919]]
...
[[-1.216 -1.196 -1.604 ... -1.820 -1.136 -1.514]
[-1.210 -1.053 -0.910 ... -1.118 -0.663 -1.092]
[-0.780 -0.610 -0.867 ... -0.967 -0.940 -1.062]
...
[0.138 0.346 -0.113 ... 0.010 -0.221 0.080]
[0.415 0.361 0.335 ... 0.362 0.132 0.715]
[1.631 1.557 1.938 ... 2.182 1.268 2.229]]
[[-1.876 -1.826 -1.527 ... -1.676 -2.018 -1.795]
[-1.439 -1.495 -1.771 ... -1.645 -1.366 -1.513]
[-1.214 -1.419 -0.954 ... -1.269 -1.173 -1.191]
...
[-0.496 -0.515 -0.625 ... -0.037 -0.381 -0.155]
[-0.384 -0.406 -0.220 ... -0.068 0.175 -0.261]
[1.493 1.420 1.307 ... 1.609 2.194 1.534]]
[[-1.838 -1.660 -1.421 ... -1.835 -1.749 -1.642]
[-2.085 -2.102 -1.978 ... -2.291 -1.888 -1.393]
[-1.776 -2.014 -1.483 ... -1.791 -1.801 -2.033]
...
[-1.929 -2.133 -2.268 ... -1.268 -2.105 -1.395]
[-2.030 -1.898 -1.934 ... -2.133 -1.433 -1.837]
[-0.192 -0.239 -0.514 ... -0.298 0.316 -0.196]]]
difference matrix :
(11, 11, 20)
average :
[[-0.038 0.370 0.505 0.619 0.796 0.939 1.107 1.248 1.409 1.706 1.744]
[-0.350 -0.051 0.196 0.240 0.400 0.583 0.697 0.858 0.994 1.397 1.746]
[-0.569 -0.187 -0.004 0.144 0.285 0.358 0.533 0.688 0.807 1.214 1.782]
[-0.711 -0.364 -0.128 -0.024 0.173 0.294 0.403 0.515 0.741 1.070 1.782]
[-0.792 -0.508 -0.339 -0.126 0.020 0.102 0.254 0.383 0.643 0.941 1.733]
[-0.974 -0.573 -0.388 -0.224 -0.131 0.039 0.147 0.216 0.495 0.798 1.772]
[-1.058 -0.738 -0.517 -0.375 -0.299 -0.152 0.071 0.168 0.293 0.728 1.786]
[-1.190 -0.868 -0.695 -0.507 -0.386 -0.265 -0.122 0.044 0.177 0.541
1.731]
[-1.377 -1.038 -0.951 -0.718 -0.540 -0.506 -0.383 -0.218 -0.016 0.337
1.714]
[-1.776 -1.409 -1.193 -1.103 -0.996 -0.872 -0.639 -0.468 -0.369 -0.067
1.709]
[-1.738 -1.779 -1.698 -1.722 -1.791 -1.811 -1.747 -1.716 -1.778 -1.773
-0.035]]
shape of average : (11, 11)
ttest :
Ttest_1sampResult(statistic=array([[-0.766, 8.116, 11.277, 10.899, 22.006, 18.667, 24.400, 24.478,
35.421, 30.592, 23.568],
[-10.661, -1.511, 5.209, 5.210, 7.975, 12.688, 17.417, 20.672,
27.177, 33.248, 31.875],
[-12.848, -6.098, -0.127, 2.526, 7.683, 9.839, 11.904, 21.529,
24.455, 28.413, 28.988],
[-17.377, -8.674, -2.496, -0.586, 5.316, 7.416, 9.065, 10.686,
15.126, 19.900, 25.131],
[-14.475, -14.309, -8.058, -3.938, 0.536, 2.572, 6.850, 8.335,
18.277, 21.266, 25.570],
[-19.275, -11.824, -8.954, -4.821, -3.072, 0.851, 2.700, 6.193,
9.897, 18.036, 27.111],
[-24.154, -18.151, -10.755, -10.206, -6.406, -2.871, 1.819, 3.415,
8.517, 15.138, 30.275],
[-27.714, -20.058, -16.177, -11.078, -9.717, -8.066, -4.597,
1.273, 4.322, 12.620, 28.072],
[-25.313, -22.253, -27.550, -23.118, -12.510, -11.787, -9.905,
-6.951, -0.301, 7.280, 20.847],
[-38.837, -37.726, -28.888, -25.884, -23.686, -21.055, -13.418,
-9.744, -6.285, -1.344, 25.915],
[-26.896, -28.445, -25.380, -22.034, -32.129, -24.922, -26.006,
-24.258, -21.094, -25.287, -0.396]]), pvalue=array([[0.453, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000,
0.000, 0.000],
[0.000, 0.147, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000,
0.000, 0.000],
[0.000, 0.000, 0.900, 0.021, 0.000, 0.000, 0.000, 0.000, 0.000,
0.000, 0.000],
[0.000, 0.000, 0.022, 0.565, 0.000, 0.000, 0.000, 0.000, 0.000,
0.000, 0.000],
[0.000, 0.000, 0.000, 0.001, 0.598, 0.019, 0.000, 0.000, 0.000,
0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.006, 0.405, 0.014, 0.000, 0.000,
0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.010, 0.085, 0.003, 0.000,
0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.218, 0.000,
0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.767,
0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000,
0.195, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000,
0.000, 0.697]]))
shape of ttest : (2, 11, 11)
+--------+-------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+
| Time | Group | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Diff |
+--------+-------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+
| 2001.0 | 1 | -0.038 | 0.646 | 0.562 | 0.805 | 0.737 | 0.861 | 0.813 | 1.532 | 1.433 | 1.646 | 1.685 |
| | 2 | -0.433 | 0.192 | 0.429 | 0.363 | 0.545 | 0.76 | 0.735 | 1.122 | 0.96 | 1.539 | 1.972 |
| | 3 | -0.557 | 0.035 | -0.087 | 0.471 | 0.255 | 0.258 | 0.488 | 0.653 | 0.84 | 1.274 | 1.831 |
| | 4 | -0.773 | -0.504 | -0.37 | -0.107 | 0.381 | 0.296 | 0.252 | 0.391 | 0.331 | 1.199 | 1.972 |
| | 5 | -0.94 | -0.509 | -0.54 | -0.373 | -0.106 | 0.187 | 0.312 | 0.408 | 0.886 | 0.532 | 1.472 |
| | 6 | -1.166 | -0.593 | -0.435 | -0.41 | -0.297 | 0.119 | 0.174 | 0.384 | 0.908 | 0.862 | 2.028 |
| | 7 | -0.953 | -0.845 | -0.453 | -0.259 | -0.11 | 0.26 | 0.097 | 0.217 | 0.404 | 0.926 | 1.878 |
| | 8 | -1.452 | -0.72 | -0.509 | -0.6 | -0.241 | -0.574 | 0.099 | 0.02 | 0.088 | 0.339 | 1.791 |
| | 9 | -1.216 | -1.21 | -0.78 | -0.765 | -0.574 | -0.683 | -0.192 | -0.344 | 0.138 | 0.415 | 1.631 |
| | 10 | -1.876 | -1.439 | -1.214 | -1.096 | -0.982 | -0.982 | -0.296 | -0.186 | -0.496 | -0.384 | 1.493 |
| | Diff | -1.838 | -2.085 | -1.776 | -1.902 | -1.719 | -1.843 | -1.109 | -1.718 | -1.929 | -2.03 | -0.192 |
| 2002.0 | 1 | -0.166 | 0.607 | 0.595 | 0.488 | 0.649 | 0.945 | 1.309 | 1.257 | 1.618 | 1.492 | 1.658 |
| | 2 | -0.127 | 0.154 | 0.335 | 0.274 | 0.444 | 0.536 | 0.887 | 0.987 | 0.856 | 1.672 | 1.799 |
| | 3 | -0.607 | -0.231 | 0.027 | -0.037 | 0.085 | 0.279 | 0.542 | 0.694 | 0.749 | 1.04 | 1.647 |
| | 4 | -0.583 | -0.323 | -0.351 | -0.073 | 0.325 | 0.441 | 0.627 | 0.539 | 0.799 | 1.103 | 1.686 |
| | 5 | -1.041 | -0.315 | -0.363 | -0.144 | 0.081 | -0.229 | -0.014 | -0.076 | 0.66 | 0.937 | 1.978 |
| | 6 | -1.179 | -0.545 | -0.258 | -0.622 | -0.436 | -0.147 | -0.092 | -0.067 | 0.511 | 0.857 | 2.036 |
| | 7 | -1.222 | -0.731 | -0.132 | -0.202 | -0.371 | 0.163 | -0.1 | 0.172 | 0.172 | 0.779 | 2.001 |
| | 8 | -1.15 | -0.787 | -0.782 | -0.896 | -0.568 | -0.294 | -0.142 | -0.202 | 0.343 | 0.452 | 1.602 |
| | 9 | -1.196 | -1.053 | -0.61 | -0.898 | -0.76 | -0.351 | -0.138 | -0.105 | 0.346 | 0.361 | 1.557 |
| | 10 | -1.826 | -1.495 | -1.419 | -0.918 | -1.364 | -1.13 | -0.63 | -0.994 | -0.515 | -0.406 | 1.42 |
| | Diff | -1.66 | -2.102 | -2.014 | -1.406 | -2.013 | -2.075 | -1.938 | -2.251 | -2.133 | -1.898 | -0.239 |
| 2003.0 | 1 | -0.106 | 0.207 | 0.529 | 0.773 | 1.071 | 0.91 | 0.965 | 1.386 | 1.642 | 1.715 | 1.821 |
| | 2 | -0.365 | -0.039 | -0.084 | 0.438 | 0.084 | 0.837 | 0.75 | 0.814 | 1.06 | 1.229 | 1.594 |
| | 3 | -1.008 | 0.071 | -0.119 | 0.252 | 0.303 | 0.281 | 0.573 | 0.489 | 0.81 | 1.282 | 2.291 |
| | 4 | -0.908 | -0.547 | -0.297 | 0.107 | -0.01 | 0.362 | 0.63 | 0.133 | 0.675 | 1.423 | 2.332 |
| | 5 | -0.97 | -0.449 | -0.429 | -0.218 | -0.068 | 0.12 | 0.243 | 0.913 | 0.63 | 1.232 | 2.202 |
| | 6 | -0.947 | -0.529 | -0.589 | -0.075 | 0.061 | 0.0 | 0.534 | 0.405 | 0.301 | 0.987 | 1.934 |
| | 7 | -0.775 | -0.748 | -0.774 | -0.287 | 0.016 | -0.052 | 0.027 | 0.079 | 0.243 | 1.103 | 1.878 |
| | 8 | -1.096 | -0.79 | -1.04 | -0.376 | -0.392 | -0.151 | -0.048 | -0.355 | 0.038 | 0.345 | 1.44 |
| | 9 | -1.604 | -0.91 | -0.867 | -0.737 | -0.581 | -0.591 | -0.542 | -0.444 | -0.113 | 0.335 | 1.938 |
| | 10 | -1.527 | -1.771 | -0.954 | -1.305 | -1.352 | -1.052 | -0.693 | -0.262 | -0.625 | -0.22 | 1.307 |
| | Diff | -1.421 | -1.978 | -1.483 | -2.079 | -2.423 | -1.962 | -1.658 | -1.648 | -2.268 | -1.934 | -0.514 |
| 2004.0 | 1 | 0.181 | 0.325 | 0.266 | 0.885 | 0.838 | 0.695 | 1.184 | 1.553 | 1.317 | 1.913 | 1.732 |
| | 2 | -0.358 | -0.084 | 0.3 | 0.131 | 0.308 | 0.57 | 0.482 | 1.076 | 1.12 | 1.353 | 1.711 |
| | 3 | 0.018 | -0.177 | -0.033 | 0.195 | 0.195 | 0.307 | 0.33 | 0.651 | 0.92 | 1.266 | 1.249 |
| | 4 | -0.812 | -0.404 | -0.241 | 0.108 | 0.117 | 0.131 | 0.473 | 0.473 | 0.518 | 0.922 | 1.735 |
| | 5 | -0.702 | -0.413 | -0.283 | -0.142 | -0.011 | 0.146 | 0.254 | 0.377 | 0.796 | 1.189 | 1.891 |
| | 6 | -1.346 | -0.701 | -0.624 | 0.007 | -0.154 | 0.239 | 0.081 | 0.124 | 0.707 | 0.94 | 2.286 |
| | 7 | -1.105 | -0.888 | -0.324 | -0.554 | -0.286 | -0.105 | 0.094 | 0.134 | 0.363 | 0.496 | 1.601 |
| | 8 | -0.931 | -0.699 | -0.618 | -0.652 | -0.367 | -0.198 | -0.18 | 0.033 | -0.101 | 0.491 | 1.423 |
| | 9 | -0.853 | -1.157 | -0.916 | -0.823 | -0.481 | -0.457 | -0.566 | -0.298 | -0.16 | 0.08 | 0.933 |
| | 10 | -1.848 | -1.408 | -1.374 | -0.981 | -1.179 | -0.896 | -0.592 | -0.292 | -0.893 | -0.066 | 1.782 |
| | Diff | -2.029 | -1.733 | -1.64 | -1.866 | -2.017 | -1.59 | -1.776 | -1.845 | -2.21 | -1.979 | 0.05 |
| 2005.0 | 1 | 0.032 | 0.351 | 0.768 | 0.645 | 0.713 | 1.293 | 0.852 | 1.347 | 1.181 | 2.057 | 2.025 |
| | 2 | -0.504 | -0.064 | 0.462 | 0.064 | 0.514 | 0.422 | 0.922 | 0.621 | 0.827 | 1.471 | 1.975 |
| | 3 | -0.695 | -0.345 | 0.102 | -0.47 | -0.048 | 0.346 | 1.086 | 0.962 | 0.728 | 1.008 | 1.703 |
| | 4 | -0.739 | -0.257 | -0.078 | 0.15 | 0.026 | 0.098 | 0.079 | 0.214 | 0.662 | 1.12 | 1.858 |
| | 5 | -1.097 | -0.662 | -0.328 | -0.317 | 0.128 | 0.046 | 0.06 | 0.565 | 0.489 | 0.872 | 1.969 |
| | 6 | -0.977 | -0.693 | -0.68 | -0.002 | -0.103 | 0.106 | 0.092 | 0.192 | 0.34 | 0.682 | 1.66 |
| | 7 | -1.131 | -0.801 | -0.572 | -0.308 | -0.544 | -0.424 | 0.48 | 0.39 | 0.353 | 0.807 | 1.939 |
| | 8 | -1.239 | -0.631 | -0.835 | -0.218 | -0.708 | -0.426 | 0.036 | 0.124 | 0.278 | 0.728 | 1.967 |
| | 9 | -1.277 | -0.663 | -1.324 | -0.661 | -0.654 | -0.492 | -0.312 | -0.129 | -0.195 | 0.039 | 1.317 |
| | 10 | -1.646 | -1.199 | -1.326 | -0.89 | -0.902 | -0.982 | -0.745 | -0.401 | -0.051 | -0.114 | 1.532 |
| | Diff | -1.678 | -1.55 | -2.094 | -1.535 | -1.615 | -2.275 | -1.596 | -1.748 | -1.232 | -2.171 | -0.493 |
| 2006.0 | 1 | -0.134 | 0.377 | 0.07 | -0.093 | 0.606 | 0.689 | 0.923 | 1.025 | 1.334 | 2.048 | 2.182 |
| | 2 | -0.446 | -0.266 | 0.416 | 0.393 | 0.344 | 0.845 | 0.815 | 0.992 | 1.043 | 1.233 | 1.678 |
| | 3 | -0.611 | -0.323 | -0.094 | 0.31 | 0.399 | 0.249 | 0.263 | 0.596 | 0.959 | 1.317 | 1.929 |
| | 4 | -0.343 | -0.164 | 0.273 | 0.349 | 0.235 | 0.354 | 0.554 | 0.729 | 0.84 | 1.253 | 1.596 |
| | 5 | -0.868 | -0.333 | -0.533 | -0.061 | -0.084 | 0.049 | 0.155 | 0.313 | 0.708 | 1.205 | 2.073 |
| | 6 | -0.749 | -0.973 | -0.488 | -0.017 | -0.125 | -0.251 | 0.389 | 0.057 | 0.495 | 0.795 | 1.544 |
| | 7 | -0.947 | -0.846 | -0.559 | -0.168 | -0.291 | -0.522 | 0.079 | -0.31 | -0.002 | 0.446 | 1.393 |
| | 8 | -1.106 | -0.511 | -1.046 | -0.61 | -0.74 | -0.262 | -0.024 | 0.095 | -0.172 | 0.78 | 1.885 |
| | 9 | -1.605 | -1.381 | -0.907 | -0.943 | -0.206 | -0.585 | -0.281 | -0.156 | -0.068 | 0.29 | 1.895 |
| | 10 | -1.671 | -1.654 | -0.997 | -0.92 | -0.926 | -0.628 | -0.205 | -0.321 | -0.003 | 0.159 | 1.83 |
| | Diff | -1.537 | -2.031 | -1.067 | -0.827 | -1.532 | -1.317 | -1.127 | -1.346 | -1.337 | -1.889 | -0.352 |
| 2007.0 | 1 | -0.495 | 0.213 | 0.431 | 0.626 | 0.795 | 1.297 | 1.212 | 1.878 | 1.193 | 1.457 | 1.951 |
| | 2 | -0.356 | 0.053 | 0.13 | 0.327 | 0.377 | 0.542 | 0.566 | 0.784 | 0.993 | 1.336 | 1.692 |
| | 3 | -0.642 | -0.001 | 0.023 | 0.463 | 0.311 | 0.417 | 0.442 | 0.875 | 0.964 | 1.272 | 1.915 |
| | 4 | -0.51 | -0.271 | 0.064 | 0.196 | 0.343 | 0.29 | 0.19 | 0.545 | 0.814 | 0.929 | 1.439 |
| | 5 | -0.224 | -0.285 | -0.297 | -0.202 | -0.112 | 0.093 | 0.11 | 0.344 | 0.551 | 1.305 | 1.529 |
| | 6 | -1.104 | -0.488 | -0.523 | 0.019 | -0.342 | -0.141 | -0.291 | 0.105 | 0.235 | 0.184 | 1.288 |
| | 7 | -1.498 | -0.797 | -0.566 | -0.41 | -0.297 | 0.154 | 0.359 | 0.356 | 0.213 | 0.619 | 2.117 |
| | 8 | -1.16 | -1.045 | -0.428 | -0.242 | -0.286 | -0.107 | -0.001 | -0.116 | 0.355 | 0.847 | 2.007 |
| | 9 | -1.576 | -1.093 | -0.816 | -0.651 | -0.613 | -0.2 | -0.097 | -0.304 | -0.125 | 0.48 | 2.055 |
| | 10 | -1.85 | -1.367 | -1.071 | -1.091 | -1.125 | -0.881 | -0.743 | -0.648 | 0.096 | -0.003 | 1.847 |
| | Diff | -1.355 | -1.58 | -1.502 | -1.718 | -1.919 | -2.178 | -1.956 | -2.525 | -1.097 | -1.46 | -0.105 |
| 2008.0 | 1 | -0.21 | 0.363 | 0.48 | 0.448 | 1.041 | 0.943 | 1.225 | 1.136 | 1.361 | 1.439 | 1.649 |
| | 2 | -0.224 | 0.209 | 0.133 | 0.57 | 0.456 | 0.803 | 0.852 | 0.808 | 1.366 | 1.571 | 1.795 |
| | 3 | -0.502 | -0.273 | -0.121 | 0.285 | 0.621 | 0.776 | 0.667 | 0.567 | 0.709 | 1.102 | 1.604 |
| | 4 | -0.813 | -0.665 | -0.066 | -0.257 | 0.073 | 0.313 | 0.58 | 0.851 | 0.829 | 1.078 | 1.891 |
| | 5 | -1.0 | -0.37 | -0.261 | 0.031 | -0.28 | 0.14 | 0.13 | 0.174 | 0.523 | 0.833 | 1.833 |
| | 6 | -1.027 | -0.327 | -0.604 | -0.342 | -0.276 | -0.088 | 0.119 | 0.433 | 0.584 | 0.711 | 1.739 |
| | 7 | -0.72 | -0.711 | -0.378 | -0.511 | -0.597 | -0.164 | -0.11 | -0.087 | 0.102 | 0.512 | 1.231 |
| | 8 | -1.166 | -1.171 | -0.748 | -0.33 | -0.236 | -0.381 | -0.295 | 0.03 | 0.25 | 0.156 | 1.322 |
| | 9 | -1.768 | -1.064 | -1.086 | -0.894 | -0.434 | -0.112 | -0.657 | -0.159 | -0.311 | 0.36 | 2.128 |
| | 10 | -1.617 | -1.483 | -1.621 | -1.202 | -0.853 | -1.125 | -0.631 | -0.713 | -0.501 | 0.062 | 1.679 |
| | Diff | -1.407 | -1.846 | -2.101 | -1.65 | -1.894 | -2.068 | -1.856 | -1.849 | -1.862 | -1.377 | 0.03 |
| 2009.0 | 1 | -0.111 | 0.707 | 0.599 | 1.12 | 0.873 | 0.937 | 1.342 | 1.123 | 1.284 | 2.031 | 2.141 |
| | 2 | -0.592 | -0.082 | 0.15 | 0.161 | 0.049 | 0.326 | 0.758 | 1.114 | 0.969 | 1.592 | 2.185 |
| | 3 | -0.563 | -0.046 | 0.278 | 0.248 | 0.387 | 0.391 | 0.365 | 0.624 | 0.646 | 1.112 | 1.675 |
| | 4 | -0.996 | -0.383 | -0.586 | -0.109 | -0.013 | 0.22 | 0.172 | 0.708 | 0.792 | 1.143 | 2.139 |
| | 5 | -0.529 | -0.604 | -0.623 | -0.256 | 0.164 | -0.305 | 0.083 | 0.361 | 0.374 | 0.964 | 1.493 |
| | 6 | -0.875 | -0.351 | -0.57 | -0.257 | 0.067 | 0.111 | 0.277 | 0.136 | 0.388 | 0.824 | 1.699 |
| | 7 | -0.881 | -0.789 | -0.42 | -0.351 | -0.26 | -0.413 | 0.084 | 0.054 | 0.426 | 0.392 | 1.272 |
| | 8 | -0.91 | -0.8 | -0.609 | -0.403 | -0.485 | -0.247 | -0.072 | 0.129 | 0.274 | 0.46 | 1.37 |
| | 9 | -1.107 | -1.13 | -1.032 | -0.551 | -0.553 | -0.323 | -0.213 | -0.054 | 0.326 | 0.711 | 1.818 |
| | 10 | -1.767 | -1.507 | -1.239 | -1.17 | -0.757 | -0.78 | -0.64 | -0.117 | -0.225 | 0.323 | 2.091 |
| | Diff | -1.657 | -2.214 | -1.838 | -2.29 | -1.63 | -1.716 | -1.983 | -1.239 | -1.508 | -1.707 | -0.051 |
| 2010.0 | 1 | -0.287 | 0.288 | 0.459 | 0.678 | 0.721 | 1.091 | 1.118 | 1.305 | 1.602 | 1.755 | 2.042 |
| | 2 | -0.274 | -0.082 | 0.23 | 0.045 | 0.821 | 0.435 | 0.578 | 1.064 | 1.204 | 1.665 | 1.939 |
| | 3 | -0.357 | -0.211 | -0.068 | -0.017 | 0.071 | 0.257 | 0.773 | 1.022 | 0.806 | 1.679 | 2.036 |
| | 4 | -0.693 | -0.069 | -0.266 | 0.084 | 0.29 | 0.164 | 0.393 | 0.402 | 0.729 | 0.536 | 1.229 |
| | 5 | -0.665 | -0.552 | -0.51 | 0.137 | -0.072 | 0.147 | 0.497 | 0.172 | 0.398 | 0.754 | 1.419 |
| | 6 | -0.844 | -0.569 | -0.068 | -0.586 | -0.24 | 0.305 | 0.372 | 0.315 | 0.225 | 0.874 | 1.719 |
| | 7 | -1.212 | -0.704 | -0.61 | -0.235 | -0.402 | -0.185 | 0.014 | 0.33 | 0.108 | 0.818 | 2.03 |
| | 8 | -1.018 | -0.706 | -0.717 | -0.999 | -0.414 | -0.463 | -0.096 | 0.066 | 0.021 | 0.656 | 1.674 |
| | 9 | -1.255 | -1.237 | -0.964 | -0.802 | -0.615 | -0.807 | -0.498 | -0.067 | 0.365 | 0.169 | 1.424 |
| | 10 | -1.85 | -1.389 | -1.081 | -1.109 | -0.865 | -0.738 | -0.608 | -0.459 | -0.261 | 0.215 | 2.065 |
| | Diff | -1.563 | -1.677 | -1.54 | -1.786 | -1.587 | -1.829 | -1.726 | -1.764 | -1.863 | -1.54 | 0.023 |
| 2011.0 | 1 | 0.169 | 0.438 | 0.218 | 0.275 | 0.676 | 0.923 | 0.878 | 1.186 | 1.132 | 1.475 | 1.305 |
| | 2 | -0.004 | -0.139 | 0.209 | 0.025 | 0.077 | 0.322 | 0.608 | 1.004 | 0.836 | 1.172 | 1.176 |
| | 3 | -0.568 | -0.327 | 0.012 | 0.499 | 0.414 | 0.282 | 0.396 | 0.571 | 1.102 | 1.131 | 1.7 |
| | 4 | -0.401 | 0.069 | -0.17 | -0.238 | 0.452 | 0.459 | 0.74 | 0.379 | 0.564 | 1.212 | 1.613 |
| | 5 | -0.604 | -0.313 | -0.367 | -0.21 | 0.213 | 0.095 | 0.297 | 0.456 | 0.843 | 0.799 | 1.403 |
| | 6 | -0.918 | -0.356 | -0.231 | -0.253 | -0.046 | 0.161 | 0.094 | 0.195 | 0.429 | 0.872 | 1.79 |
| | 7 | -1.323 | -0.612 | -1.067 | -0.479 | -0.403 | -0.344 | 0.117 | 0.182 | 0.486 | 0.597 | 1.921 |
| | 8 | -1.21 | -0.912 | -0.727 | -0.577 | -0.211 | -0.288 | -0.204 | -0.101 | 0.279 | 0.515 | 1.724 |
| | 9 | -1.526 | -1.13 | -0.857 | -0.898 | -0.619 | -0.409 | -0.703 | -0.27 | -0.444 | 0.39 | 1.916 |
| | 10 | -1.494 | -1.23 | -1.183 | -0.995 | -0.76 | -0.512 | -0.939 | -0.465 | -0.414 | 0.022 | 1.516 |
| | Diff | -1.664 | -1.667 | -1.401 | -1.27 | -1.436 | -1.434 | -1.817 | -1.652 | -1.547 | -1.453 | 0.211 |
| 2012.0 | 1 | 0.355 | 0.543 | 0.323 | 0.426 | 0.847 | 1.066 | 1.189 | 1.121 | 1.505 | 1.638 | 1.283 |
| | 2 | -0.463 | -0.002 | 0.173 | 0.558 | 0.259 | 0.773 | 0.613 | 0.583 | 0.821 | 1.137 | 1.601 |
| | 3 | -0.644 | -0.167 | -0.133 | -0.187 | 0.321 | 0.271 | 0.368 | 0.596 | 0.759 | 0.944 | 1.589 |
| | 4 | -0.513 | -0.345 | -0.163 | -0.318 | 0.175 | 0.123 | 0.474 | 0.572 | 0.767 | 1.217 | 1.73 |
| | 5 | -1.035 | -0.422 | -0.36 | 0.083 | -0.025 | 0.11 | 0.547 | 0.281 | 0.768 | 1.138 | 2.174 |
| | 6 | -1.151 | -1.138 | -0.028 | -0.234 | -0.407 | -0.02 | 0.337 | 0.157 | 0.133 | 1.024 | 2.175 |
| | 7 | -1.09 | -0.713 | -0.77 | -0.417 | -0.104 | -0.28 | -0.095 | -0.007 | 0.187 | 0.96 | 2.05 |
| | 8 | -1.284 | -0.778 | -0.875 | -0.532 | -0.216 | -0.157 | -0.153 | 0.223 | -0.082 | 0.395 | 1.679 |
| | 9 | -1.172 | -1.218 | -1.136 | -0.595 | -0.552 | -0.689 | -0.272 | -0.076 | -0.095 | 0.16 | 1.332 |
| | 10 | -1.855 | -1.282 | -0.878 | -1.277 | -0.92 | -0.561 | -0.258 | -0.569 | -0.608 | -0.357 | 1.498 |
| | Diff | -2.21 | -1.826 | -1.2 | -1.702 | -1.767 | -1.627 | -1.447 | -1.69 | -2.113 | -1.995 | 0.215 |
| 2013.0 | 1 | 0.054 | 0.156 | 0.472 | 0.67 | 0.935 | 1.303 | 1.078 | 1.027 | 1.346 | 1.666 | 1.612 |
| | 2 | -0.462 | -0.084 | 0.156 | 0.184 | 0.089 | 0.825 | 0.211 | 0.815 | 1.177 | 1.115 | 1.577 |
| | 3 | -0.764 | -0.211 | -0.227 | -0.244 | 0.1 | 0.18 | 0.639 | 0.573 | 0.599 | 1.508 | 2.272 |
| | 4 | -0.76 | -0.582 | 0.163 | -0.183 | 0.098 | 0.348 | 0.479 | 0.177 | 0.826 | 1.184 | 1.944 |
| | 5 | -0.668 | -0.585 | -0.516 | 0.034 | 0.285 | -0.056 | 0.153 | 0.284 | 0.714 | 0.881 | 1.549 |
| | 6 | -0.672 | -0.426 | -0.322 | -0.306 | -0.337 | -0.117 | -0.384 | 0.128 | 0.474 | 0.782 | 1.455 |
| | 7 | -0.841 | -0.843 | -0.311 | -0.6 | -0.675 | 0.014 | 0.073 | 0.102 | 0.466 | 0.795 | 1.635 |
| | 8 | -1.15 | -0.983 | -0.668 | -0.618 | -0.635 | -0.179 | -0.051 | 0.159 | 0.379 | 0.498 | 1.648 |
| | 9 | -1.261 | -1.046 | -1.009 | -0.75 | -0.799 | -0.685 | -0.386 | -0.202 | 0.33 | 0.259 | 1.519 |
| | 10 | -1.298 | -1.397 | -1.262 | -1.227 | -1.006 | -1.037 | -0.523 | -0.412 | -0.285 | -0.081 | 1.218 |
| | Diff | -1.352 | -1.554 | -1.733 | -1.897 | -1.942 | -2.341 | -1.601 | -1.439 | -1.632 | -1.747 | -0.394 |
| 2014.0 | 1 | 0.016 | 0.383 | 0.626 | 0.505 | 0.887 | 0.958 | 1.023 | 0.982 | 1.511 | 1.943 | 1.927 |
| | 2 | -0.291 | 0.181 | 0.061 | 0.299 | 0.518 | 0.548 | 0.868 | 0.911 | 0.754 | 1.463 | 1.754 |
| | 3 | -0.575 | -0.307 | 0.263 | 0.156 | 0.548 | 0.436 | 0.767 | 0.639 | 0.921 | 1.429 | 2.004 |
| | 4 | -0.621 | -0.382 | -0.244 | -0.112 | 0.19 | -0.121 | 0.205 | 0.872 | 0.934 | 0.82 | 1.442 |
| | 5 | -0.406 | -0.827 | 0.036 | -0.188 | 0.002 | 0.256 | 0.158 | 0.456 | 0.783 | 0.808 | 1.213 |
| | 6 | -0.407 | -0.516 | -0.294 | -0.361 | -0.231 | 0.267 | 0.032 | 0.355 | 0.419 | 1.04 | 1.446 |
| | 7 | -1.024 | -0.946 | -0.377 | -0.628 | -0.147 | -0.325 | 0.358 | 0.408 | 0.368 | 0.522 | 1.546 |
| | 8 | -1.069 | -0.909 | -0.882 | -0.282 | -0.32 | -0.296 | -0.218 | 0.101 | 0.151 | 0.831 | 1.9 |
| | 9 | -1.538 | -0.649 | -0.772 | -0.715 | -0.642 | -0.785 | -0.307 | 0.029 | -0.277 | 0.615 | 2.153 |
| | 10 | -2.103 | -1.438 | -0.928 | -1.108 | -1.004 | -0.691 | -0.857 | -0.283 | -0.819 | -0.427 | 1.676 |
| | Diff | -2.119 | -1.82 | -1.555 | -1.613 | -1.891 | -1.649 | -1.88 | -1.266 | -2.33 | -2.37 | -0.251 |
| 2015.0 | 1 | 0.39 | 0.143 | 0.267 | 0.742 | 0.841 | 0.992 | 1.043 | 1.02 | 1.634 | 1.141 | 0.751 |
| | 2 | -0.241 | -0.1 | 0.003 | 0.123 | 0.481 | 0.551 | 0.563 | 0.491 | 1.024 | 1.3 | 1.542 |
| | 3 | -0.704 | -0.15 | -0.104 | 0.181 | 0.401 | 0.428 | 0.706 | 0.675 | 0.691 | 1.222 | 1.925 |
| | 4 | -0.995 | -0.283 | -0.148 | 0.022 | 0.281 | 0.12 | 0.627 | 0.663 | 0.874 | 1.606 | 2.601 |
| | 5 | -0.69 | -0.723 | 0.021 | -0.153 | -0.106 | 0.127 | 0.255 | 0.522 | 0.395 | 0.737 | 1.427 |
| | 6 | -0.931 | -0.666 | -0.443 | -0.241 | 0.035 | 0.115 | -0.022 | 0.021 | 0.541 | 0.672 | 1.603 |
| | 7 | -1.016 | -0.378 | -0.301 | -0.303 | -0.179 | 0.215 | -0.099 | 0.247 | 0.235 | 0.664 | 1.68 |
| | 8 | -1.768 | -1.027 | -0.635 | -0.421 | -0.454 | -0.263 | -0.282 | 0.239 | 0.032 | 0.646 | 2.414 |
| | 9 | -1.373 | -1.221 | -0.891 | -0.612 | -0.131 | -0.57 | -0.448 | -0.27 | -0.217 | 0.605 | 1.978 |
| | 10 | -2.049 | -1.09 | -1.228 | -0.896 | -0.662 | -0.876 | -0.907 | -0.507 | -0.358 | -0.057 | 1.992 |
| | Diff | -2.439 | -1.233 | -1.496 | -1.639 | -1.503 | -1.867 | -1.95 | -1.526 | -1.992 | -1.198 | 1.241 |
| 2016.0 | 1 | -0.195 | 0.343 | 0.774 | 0.671 | 0.829 | 1.082 | 0.755 | 1.169 | 1.342 | 1.639 | 1.833 |
| | 2 | -0.289 | -0.275 | 0.411 | 0.35 | 0.304 | 0.351 | 0.775 | 1.015 | 1.124 | 1.28 | 1.569 |
| | 3 | -0.458 | -0.253 | 0.198 | 0.232 | 0.257 | 0.176 | 0.548 | 0.593 | 0.66 | 1.04 | 1.498 |
| | 4 | -0.644 | -0.597 | -0.059 | 0.028 | -0.117 | 0.485 | 0.275 | 0.448 | 0.278 | 1.175 | 1.819 |
| | 5 | -0.846 | -0.632 | -0.195 | -0.071 | 0.201 | 0.338 | 0.448 | 0.376 | 0.698 | 0.807 | 1.653 |
| | 6 | -1.086 | -0.536 | -0.521 | -0.098 | -0.024 | 0.231 | -0.119 | 0.015 | 0.493 | 0.827 | 1.913 |
| | 7 | -0.995 | -0.601 | -0.363 | -0.179 | -0.258 | 0.047 | 0.175 | 0.197 | 0.511 | 0.99 | 1.986 |
| | 8 | -1.181 | -0.676 | -0.362 | -0.401 | -0.272 | -0.503 | -0.291 | 0.28 | 0.547 | 0.814 | 1.995 |
| | 9 | -1.269 | -0.765 | -0.995 | -0.507 | -0.523 | -0.395 | -0.462 | -0.305 | 0.046 | 0.081 | 1.35 |
| | 10 | -2.056 | -1.221 | -1.385 | -1.244 | -0.968 | -1.02 | -0.73 | -0.804 | -0.448 | 0.224 | 2.281 |
| | Diff | -1.862 | -1.564 | -2.159 | -1.915 | -1.798 | -2.103 | -1.485 | -1.973 | -1.79 | -1.414 | 0.447 |
| 2017.0 | 1 | 0.055 | 0.262 | 0.674 | 0.776 | 0.993 | 1.017 | 1.248 | 1.074 | 1.551 | 1.822 | 1.766 |
| | 2 | -0.219 | 0.008 | 0.209 | 0.479 | 0.637 | 0.712 | 0.599 | 0.827 | 0.806 | 1.47 | 1.689 |
| | 3 | -0.372 | -0.12 | 0.103 | 0.068 | 0.118 | 0.221 | 0.429 | 0.641 | 0.928 | 1.056 | 1.429 |
| | 4 | -0.741 | -0.525 | -0.302 | 0.249 | 0.16 | 0.452 | 0.081 | 0.844 | 1.107 | 0.955 | 1.696 |
| | 5 | -1.111 | -0.398 | -0.461 | -0.19 | 0.07 | 0.107 | 0.138 | 0.182 | 0.606 | 1.09 | 2.202 |
| | 6 | -1.016 | -0.812 | -0.264 | -0.154 | -0.107 | -0.261 | 0.286 | 0.315 | 0.691 | 0.964 | 1.98 |
| | 7 | -1.359 | -1.114 | -0.564 | -0.049 | -0.065 | -0.473 | -0.178 | 0.459 | 0.366 | 0.528 | 1.887 |
| | 8 | -1.117 | -0.955 | -0.577 | -0.658 | -0.047 | 0.035 | -0.206 | -0.049 | 0.195 | 0.34 | 1.456 |
| | 9 | -1.478 | -0.961 | -1.086 | -0.654 | -0.576 | -0.488 | -0.571 | -0.255 | 0.257 | 0.185 | 1.663 |
| | 10 | -1.691 | -1.288 | -1.057 | -1.037 | -1.187 | -1.082 | -0.992 | -0.597 | -0.407 | -0.08 | 1.61 |
| | Diff | -1.746 | -1.55 | -1.731 | -1.814 | -2.18 | -2.099 | -2.239 | -1.671 | -1.958 | -1.902 | -0.156 |
| 2018.0 | 1 | 0.159 | 0.646 | 0.522 | 0.586 | 0.452 | 0.658 | 1.525 | 1.063 | 1.232 | 2.065 | 1.906 |
| | 2 | -0.312 | -0.105 | -0.161 | 0.218 | 0.442 | 0.525 | 0.649 | 0.751 | 0.965 | 1.255 | 1.567 |
| | 3 | -0.587 | -0.228 | 0.156 | 0.055 | 0.231 | 0.673 | 0.583 | 0.783 | 0.521 | 1.386 | 1.973 |
| | 4 | -0.777 | -0.222 | 0.347 | -0.119 | 0.119 | 0.586 | 0.407 | 0.473 | 0.559 | 0.898 | 1.675 |
| | 5 | -0.675 | -0.63 | -0.45 | -0.164 | 0.34 | -0.08 | 0.501 | 0.672 | 0.632 | 0.877 | 1.552 |
| | 6 | -0.744 | -0.468 | -0.214 | -0.166 | -0.06 | 0.293 | 0.408 | 0.501 | 0.761 | 0.464 | 1.208 |
| | 7 | -1.09 | -0.811 | -0.777 | -0.528 | 0.051 | -0.11 | -0.111 | -0.054 | 0.519 | 0.637 | 1.727 |
| | 8 | -1.098 | -1.104 | -0.461 | -0.483 | -0.293 | -0.121 | -0.265 | 0.117 | 0.158 | 0.401 | 1.499 |
| | 9 | -1.82 | -1.118 | -0.967 | -0.78 | -0.115 | -0.431 | -0.391 | -0.542 | 0.01 | 0.362 | 2.182 |
| | 10 | -1.676 | -1.645 | -1.269 | -0.707 | -1.179 | -0.882 | -0.713 | -0.384 | -0.037 | -0.068 | 1.609 |
| | Diff | -1.835 | -2.291 | -1.791 | -1.293 | -1.631 | -1.54 | -2.238 | -1.447 | -1.268 | -2.133 | -0.298 |
| 2019.0 | 1 | -0.269 | 0.522 | 0.629 | 0.862 | 0.873 | 0.643 | 1.114 | 1.323 | 1.724 | 1.609 | 1.878 |
| | 2 | -0.494 | -0.22 | 0.102 | -0.258 | 0.415 | 0.16 | 0.982 | 0.682 | 0.826 | 1.344 | 1.838 |
| | 3 | -0.488 | -0.036 | -0.255 | 0.443 | 0.346 | 0.62 | 0.333 | 0.667 | 0.976 | 0.971 | 1.458 |
| | 4 | -0.955 | -0.298 | 0.098 | -0.072 | 0.208 | 0.546 | 0.529 | 0.383 | 0.754 | 0.801 | 1.756 |
| | 5 | -1.059 | -0.722 | -0.322 | 0.119 | -0.228 | 0.464 | 0.264 | 0.418 | 0.549 | 0.857 | 1.916 |
| | 6 | -0.988 | -0.521 | -0.472 | 0.128 | 0.272 | 0.223 | 0.274 | 0.264 | 0.298 | 0.852 | 1.839 |
| | 7 | -0.995 | -0.554 | -0.444 | -0.549 | -0.447 | -0.223 | 0.005 | -0.104 | 0.249 | 0.951 | 1.946 |
| | 8 | -1.268 | -1.268 | -0.857 | -0.312 | -0.375 | -0.225 | 0.001 | 0.083 | 0.171 | 0.555 | 1.822 |
| | 9 | -1.136 | -0.663 | -0.94 | -0.428 | -0.562 | -0.331 | -0.209 | -0.119 | -0.221 | 0.132 | 1.268 |
| | 10 | -2.018 | -1.366 | -1.173 | -1.45 | -0.915 | -0.876 | -0.574 | -0.375 | -0.381 | 0.175 | 2.194 |
| | Diff | -1.749 | -1.888 | -1.801 | -2.312 | -1.788 | -1.518 | -1.688 | -1.698 | -2.105 | -1.433 | 0.316 |
| 2020.0 | 1 | -0.153 | -0.12 | 0.842 | 0.497 | 0.534 | 0.48 | 1.354 | 1.445 | 1.24 | 1.576 | 1.73 |
| | 2 | -0.538 | -0.27 | 0.251 | 0.05 | 0.845 | 0.814 | 0.734 | 0.701 | 1.156 | 1.735 | 2.273 |
| | 3 | -0.685 | -0.438 | -0.007 | -0.016 | 0.384 | 0.316 | 0.357 | 0.883 | 0.843 | 1.234 | 1.919 |
| | 4 | -0.65 | -0.537 | -0.157 | -0.175 | 0.125 | 0.212 | 0.292 | 0.502 | 1.163 | 0.83 | 1.479 |
| | 5 | -0.716 | -0.422 | -0.0 | -0.229 | 0.004 | 0.275 | 0.494 | 0.455 | 0.866 | 0.995 | 1.711 |
| | 6 | -1.345 | -0.243 | -0.137 | -0.502 | 0.134 | -0.371 | 0.372 | 0.285 | 0.966 | 0.751 | 2.096 |
| | 7 | -0.98 | -0.325 | -0.587 | -0.484 | -0.615 | -0.268 | 0.149 | 0.598 | 0.098 | 1.026 | 2.006 |
| | 8 | -1.428 | -0.895 | -0.52 | -0.526 | -0.461 | -0.205 | -0.041 | -0.006 | 0.327 | 0.581 | 2.009 |
| | 9 | -1.514 | -1.092 | -1.062 | -0.705 | -0.81 | -0.727 | -0.405 | -0.295 | 0.08 | 0.715 | 2.229 |
| | 10 | -1.795 | -1.513 | -1.191 | -1.427 | -1.005 | -0.712 | -0.507 | -0.574 | -0.155 | -0.261 | 1.534 |
| | Diff | -1.642 | -1.393 | -2.033 | -1.924 | -1.539 | -1.192 | -1.861 | -2.019 | -1.395 | -1.837 | -0.196 |
+--------+-------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+
+-------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+--------+
| Group | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Diff |
+-------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+--------+
| 1 | -0.038 | 0.37 | 0.505 | 0.619 | 0.796 | 0.939 | 1.107 | 1.248 | 1.409 | 1.706 | 1.744 |
| | -0.766 | 8.116 | 11.277 | 10.899 | 22.006 | 18.667 | 24.4 | 24.478 | 35.421 | 30.592 | 23.568 |
| 2 | -0.35 | -0.051 | 0.196 | 0.24 | 0.4 | 0.583 | 0.697 | 0.858 | 0.994 | 1.397 | 1.746 |
| | -10.661 | -1.511 | 5.209 | 5.21 | 7.975 | 12.688 | 17.417 | 20.672 | 27.177 | 33.248 | 31.875 |
| 3 | -0.569 | -0.187 | -0.004 | 0.144 | 0.285 | 0.358 | 0.533 | 0.688 | 0.807 | 1.214 | 1.782 |
| | -12.848 | -6.098 | -0.127 | 2.526 | 7.683 | 9.839 | 11.904 | 21.529 | 24.455 | 28.413 | 28.988 |
| 4 | -0.711 | -0.364 | -0.128 | -0.024 | 0.173 | 0.294 | 0.403 | 0.515 | 0.741 | 1.07 | 1.782 |
| | -17.377 | -8.674 | -2.496 | -0.586 | 5.316 | 7.416 | 9.065 | 10.686 | 15.126 | 19.9 | 25.131 |
| 5 | -0.792 | -0.508 | -0.339 | -0.126 | 0.02 | 0.102 | 0.254 | 0.383 | 0.643 | 0.941 | 1.733 |
| | -14.475 | -14.309 | -8.058 | -3.938 | 0.536 | 2.572 | 6.85 | 8.335 | 18.277 | 21.266 | 25.57 |
| 6 | -0.974 | -0.573 | -0.388 | -0.224 | -0.131 | 0.039 | 0.147 | 0.216 | 0.495 | 0.798 | 1.772 |
| | -19.275 | -11.824 | -8.954 | -4.821 | -3.072 | 0.851 | 2.7 | 6.193 | 9.897 | 18.036 | 27.111 |
| 7 | -1.058 | -0.738 | -0.517 | -0.375 | -0.299 | -0.152 | 0.071 | 0.168 | 0.293 | 0.728 | 1.786 |
| | -24.154 | -18.151 | -10.755 | -10.206 | -6.406 | -2.871 | 1.819 | 3.415 | 8.517 | 15.138 | 30.275 |
| 8 | -1.19 | -0.868 | -0.695 | -0.507 | -0.386 | -0.265 | -0.122 | 0.044 | 0.177 | 0.541 | 1.731 |
| | -27.714 | -20.058 | -16.177 | -11.078 | -9.717 | -8.066 | -4.597 | 1.273 | 4.322 | 12.62 | 28.072 |
| 9 | -1.377 | -1.038 | -0.951 | -0.718 | -0.54 | -0.506 | -0.383 | -0.218 | -0.016 | 0.337 | 1.714 |
| | -25.313 | -22.253 | -27.55 | -23.118 | -12.51 | -11.787 | -9.905 | -6.951 | -0.301 | 7.28 | 20.847 |
| 10 | -1.776 | -1.409 | -1.193 | -1.103 | -0.996 | -0.872 | -0.639 | -0.468 | -0.369 | -0.067 | 1.709 |
| | -38.837 | -37.726 | -28.888 | -25.884 | -23.686 | -21.055 | -13.418 | -9.744 | -6.285 | -1.344 | 25.915 |
| Diff | -1.738 | -1.779 | -1.698 | -1.722 | -1.791 | -1.811 | -1.747 | -1.716 | -1.778 | -1.773 | -0.035 |
| | -26.896 | -28.445 | -25.38 | -22.034 | -32.129 | -24.922 | -26.006 | -24.258 | -21.094 | -25.287 | -0.396 |
+-------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+--------+
class MultiPeriod_Bivariate():
def _init_(self, ret_matrix, sample):
This function initializes the class MultiPeriod_Univariate.
input:
ret_matrix (DataFrame): The ret_matrix contains future returns series from 1 to n period.
sample (DataFrame): The samples to be analyzed. Samples contains sort variables and time.
def fit(self, number:int, perc_row:list=None, perc_col:list=None, percn_row: ndarray=None, percn_col:ndarray=None, maxlag: int=12, weight:bool =False):
The inputs of the function are the same with the Bivariate.fit()
def factor_adjustment(self, factor:DataFrame):
The inputs are the same with the Bivariate.factor_adjustment()
def summary(self, explicit:bool=False, export:bool=False, percentage:bool=False):
The inputs are the same with the Bivariate.print_summary()
Example
def test_multiperiod_bivariate():
'''
TEST UNIVARIATE
construct sample:
1. 20 Periods
2. 3000 Observations for each Period
3. Divided into 10 groups with 9 breakpoints
4. Character negative with return following the return=character*-0.5+sigma where sigma~N(0,1)
'''
import numpy as np
import pandas as pd
from portfolio_analysis import MultiPeriod_Bivariate as mulbi
from portfolio_analysis import ptf_analysis as ptfa
from util import plot
# generate time
year=np.ones((3000,1),dtype=int)*2020
for i in range(19):
year=np.append(year,(2019-i)*np.ones((3000,1),dtype=int))
year = pd.DataFrame(year, columns=['year'])
# generate character
character_1 = pd.DataFrame(np.random.normal(0, 1, 20*3000))
character_2 = pd.DataFrame(np.random.normal(0, 1, 20*3000))
# generate future return
ret1= 0.5 * character_1 - 0.5 * character_2 + np.random.normal(loc=0, scale=1, size=(20*3000,1))
ret2= - 0.5 * character_1 + 0.5 * character_2 + np.random.normal(loc=0, scale=1, size=(20*3000,1))
# create sample containing future return, character, time
ret_matrix = pd.merge(ret1, ret2, left_index=True, right_index=True)
ret_matrix.columns = ['ret1', 'ret2']
sample=pd.merge(character_2, year, left_index=True, right_index=True)
sample=pd.merge(character_1, sample, left_index=True, right_index=True)
sample.columns = ['character_1', 'character_2', 'year']
# generate the Univiriate Class
exper=mulbi(ret_matrix, sample)
# print(exper.ret_matrix)
data = exper.fit(number=4, maxlag=12)
print(exper.average_result)
print(exper.ttest)
print(np.shape(exper.ttest))
# print(exper.params)
# print(np.shape(data))
exper.summary()
# print(exper.number)
breakpoint = ptfa().create_breakpoint(sample, number=4)
percn_row = breakpoint[0]
percn_col = breakpoint[1]
exper = mulbi(ret_matrix, sample)
exper.fit(9, percn_row=percn_row, percn_col=percn_col)
exper.summary()
test_multiperiod_bivariate()
class Persistence()
def _init_(self, sample):
This function makes initialization.
input :
sample (DataFrame): Data for analysis. The structure of the sample:
The first column : sample indicator
The second column : timestamp
The higher order columns: the variables.
def _shift(self, series, lag):
This private function shift the time series with lags.
input :
series (Series): The series need to be shifted with lags.
lag (int): The lag order.
def fit(self, lags):
This function calculate the persistence with lags.
input :
lags (list): the lags that need to be analyzed.
def summary(self, periodic=False, export=False):
This function prints the result summary and exports table. The Fisher coefficient and the Spearman coefficient are both calculated.
input :
periodic (boolean): whether prints periodic result. The DEFAULT setting is False.
export (boolean): whether export the summary table. The DEFAULT setting is False.
output :
df (DataFrame): If export is True, then output the summary table.
Example
import numpy as np
import pandas as pd
from portfolio_analysis import Persistence as pste
# generate time
year = np.ones((3000,1), dtype=int)*2020
id = np.linspace(1, 3000, 3000, dtype=int)
for i in range(19):
year = np.append(year, (2019-i)*np.ones((3000,1), dtype=int))
id = np.append(id, np.linspace(1, 3000, 3000, dtype=int))
# generate character
character_1 = np.random.normal(0, 1, 20*3000)
character_2 = np.random.normal(0, 1, 20*3000)
# generate future return
ret=character_1*-0.5 + character_2*0.5 + np.random.normal(0,1,20*3000)
# create sample containing future return, character, time
sample = np.array([id, year, ret, character_1, character_2]).T
sample = pd.DataFrame(sample, columns=['id', 'year', 'ret', 'character_1', 'character_2'])
exper = pste(sample)
exper.fit(lags=[1, 2, 3])
exper.summary(periodic=True)
exper.summary()
=======================================================================================================================
+--------+----------+------------+-----------+----------+------------+-----------+----------+------------+-----------+
| Time | id_lag_1 | year_lag_1 | ret_lag_1 | id_lag_2 | year_lag_2 | ret_lag_2 | id_lag_3 | year_lag_3 | ret_lag_3 |
+--------+----------+------------+-----------+----------+------------+-----------+----------+------------+-----------+
| 2001.0 | -0.01191 | -0.00334 | 0.02361 | -0.01781 | 0.00886 | -0.02894 | -0.00263 | -0.0131 | -0.00058 |
| 2002.0 | -0.01199 | -0.0176 | -0.03603 | 0.00258 | -0.01285 | -0.00237 | -0.0294 | 0.00956 | -0.00281 |
| 2003.0 | -0.01074 | -0.03747 | 0.00879 | 0.00161 | 0.00559 | -0.009 | 0.00415 | 0.00091 | -0.01175 |
| 2004.0 | 0.01954 | -0.01125 | -0.00944 | 0.00546 | 0.00239 | -0.02387 | -0.00457 | -0.00225 | -0.00341 |
| 2005.0 | -0.00924 | -0.01317 | 0.01217 | -0.01098 | -0.02188 | 0.01794 | -0.00123 | 0.0042 | 0.02049 |
| 2006.0 | -0.00811 | 0.02284 | -0.00611 | 0.00417 | 0.01633 | -0.00517 | -0.00661 | -0.01671 | 0.0038 |
| 2007.0 | -0.02182 | 0.00383 | 0.03477 | -0.01294 | -0.01041 | -0.01589 | -0.02979 | 0.00703 | -0.00808 |
| 2008.0 | -0.01375 | -0.0061 | -0.00717 | 0.0116 | -0.00816 | -0.02017 | 0.01595 | -0.01796 | 0.01091 |
| 2009.0 | 0.0303 | 0.01339 | -0.05158 | 0.0105 | 0.00794 | 0.01445 | -0.02718 | -0.03998 | 0.00076 |
| 2010.0 | -0.00215 | -0.0053 | -0.03419 | -0.00931 | 0.0032 | -0.01369 | -0.01174 | 0.00524 | -0.00814 |
| 2011.0 | 0.03012 | 0.03217 | 0.0206 | 0.00162 | -0.00661 | -0.0418 | -0.01987 | 0.00034 | -0.01522 |
| 2012.0 | 0.00614 | 0.02679 | -0.00315 | -0.01214 | -0.0222 | -0.01302 | -0.02656 | 0.01336 | 0.00475 |
| 2013.0 | 0.01331 | 0.01011 | -0.02019 | 0.01789 | 0.02888 | 0.01926 | -0.01949 | 0.01759 | -0.0042 |
| 2014.0 | -0.02874 | -0.00777 | -0.00271 | 0.00561 | 0.01307 | 0.02344 | -0.01049 | -0.00115 | -0.00471 |
| 2015.0 | -0.01492 | 0.00798 | -0.00376 | 0.00942 | -0.00938 | -0.01007 | 0.00626 | 0.00371 | -0.00552 |
| 2016.0 | 0.00516 | 0.00175 | 0.01016 | 0.02137 | -0.02389 | 0.00064 | 0.00778 | -0.01682 | 0.00409 |
| 2017.0 | 0.00593 | -0.01336 | -0.00072 | -0.01063 | 0.00522 | 0.01871 | -0.00298 | -0.01108 | -0.04003 |
| 2018.0 | 0.02177 | -0.00555 | -0.0257 | -0.0033 | -0.01959 | -0.00221 | nan | nan | nan |
| 2019.0 | -0.01153 | -0.01477 | -0.0089 | nan | nan | nan | nan | nan | nan |
| 2020.0 | nan | nan | nan | nan | nan | nan | nan | nan | nan |
+--------+----------+------------+-----------+----------+------------+-----------+----------+------------+-----------+
+----------+----------+------------+-----------+----------+------------+-----------+----------+------------+-----------+
| Variable | id_lag_1 | year_lag_1 | ret_lag_1 | id_lag_2 | year_lag_2 | ret_lag_2 | id_lag_3 | year_lag_3 | ret_lag_3 |
+----------+----------+------------+-----------+----------+------------+-----------+----------+------------+-----------+
| Average | -0.00066 | -0.00089 | -0.00524 | 0.00082 | -0.00242 | -0.0051 | -0.00932 | -0.00336 | -0.00351 |
+----------+----------+------------+-----------+----------+------------+-----------+----------+------------+-----------+
class Tangency_porfolio():
This class is to calculate the tangency portfolio given the asset and the risk-free rate.
def _init_(self, rf, mu, cov_mat):
input :
rf (float): risk-free rate
mu (array/Series): stock rate of return
cov_mat (matrix): covariance matrix of stock rate of return
def _portfolio_weight(self):
output :
weight (array): weight of assets in tangency portfolio
def _sharpe_ratio(self):
output:
sr (float): the sharpe ratio of the tangency portoflio
def fit(self):
this function fits the function _portfolio_weight and _sharpe_ratio
def print(self):
print the result
Example
def test_tangency_portfolio():
'''
This function is for testing rangency_portfolio
'''
import numpy as np
from portfolio_analysis import Tangency_portfolio as tanport
# construct the sample data 1
mu = np.array([0.0427, 0.0015, 0.0285])
cov_mat = np.mat([[0.01, 0.0018, 0.0011], [0.0018, 0.0109, 0.0026], [0.0011, 0.0026, 0.0199]])
rf = 0.005
# calculate the weight and the sharpe ratio
portfolio = tanport(rf, mu, cov_mat)
print(portfolio._portfolio_weight())
print(portfolio.fit())
portfolio.print()
# construct the sample data 2
mu = np.array([0.0427, 0.0015, 0.0285, 0.0028])
cov_mat = np.mat([[0.01, 0.0018, 0.0011, 0], [0.0018, 0.0109, 0.0026, 0], [0.0011, 0.0026, 0.0199, 0], [0, 0, 0, 0.1]])
rf = 0.005
# calculate the weight and the sharpe ratio
portfolio = tanport(rf, mu, cov_mat)
print(portfolio._portfolio_weight())
print(portfolio.fit())
portfolio.print()
test_tangency_portfolio()
================================================================================================================================
[[ 1.02682298]
[-0.32625112]
[ 0.29942815]]
(matrix([[ 1.02682298],
[-0.32625112],
[ 0.29942815]]), 0.4202276695645767)
+--------+---------+----------+---------+
| Weight | asset1 | asset2 | asset3 |
+--------+---------+----------+---------+
| | 1.02682 | -0.32625 | 0.29943 |
+--------+---------+----------+---------+
[[ 1.03285649]
[-0.32816815]
[ 0.30118756]
[-0.00587591]]
(matrix([[ 1.03285649],
[-0.32816815],
[ 0.30118756],
[-0.00587591]]), 0.42028525345017165)
+--------+---------+----------+---------+----------+
| Weight | asset1 | asset2 | asset3 | asset4 |
+--------+---------+----------+---------+----------+
| | 1.03286 | -0.32817 | 0.30119 | -0.00588 |
+--------+---------+----------+---------+----------+
class Spanning_test():
This module is designed for spanning test. Three asymptotic estimates and one small sample estimates are contained. The construction is based on
R. Kan, G. Zhou, Test of Mean-Variance Spanning, Annals of Economics and Finance, 2012, 13-1, 145-193.
def _init_(self, Rn, Rk):
input :
Rn (ndarray/Series/DataFrame) : The assets to be tested.
Rk (ndarray/Series/DataFrame) : The fundamental assets.
def _cov(self):
This function calculates the covariance.
def _regress(self):
This function regresses Rn on Rk and return the eigen value and U statistics for building estimates of hypothesis tests.
output :
eigen1 (float) : the eigen value #1
eigen2 (float) : the eigen value #2
U (float) : the U statistics
def _build_statistics(self):
This function build three asymptotic estimates and one small sample estimate. The asymptotic estimates include likelihood ratio (LR), Wald test (W), Lagrange multiplier test (LM). The one small sample estimate is F-test corresponding to likelihood ratio. The asymptotic estimates satisfy the chi-square distribution with freedom 2N, where N is the number of test assets. The small sample estimate satisfies the F-distribution with coefficient, 2N, 2(T-K-N) for N>1, and 2, (T-K-1) for N=1.
output :
perc (array) : the quantiles of chi-square distribution at 90%, 95%, 99%.
perc_F (array) : the quantiles of F distribution at 90%, 95%, 99%.
[LR, chi_LR] (float) : The LR estimate and p-value of test.
[W, chi_W] (float) : The Wald estimate and p-value of test.
[LM, chi_LM] (float) : The LM estimate and p-value of test.
[LR_F, f_LR] (float) : The F estimate and p-value of test.
def fit(self):
This function fits the model
output :
perc (array) : the quantiles of chi-square distribution at 90%, 95%, 99%.
perc_F (array) : the quantiles of F distribution at 90%, 95%, 99%.
[LR, chi_LR] (float) : The LR estimate and p-value of test.
[W, chi_W] (float) : The Wald estimate and p-value of test.
[LM, chi_LM] (float) : The LM estimate and p-value of test.
[LR_F, f_LR] (float) : The F estimate and p-value of test.
def summary(self):
This function print the result.
Example
# %% test Spanning test
def test_spanning_test():
'''
This function is for testing spanning test
'''
import numpy as np
from portfolio_analysis import Spanning_test as span
factor1 = np.random.normal(loc=0.1, scale=1.0, size=(240, 1))
factor2 = np.random.normal(loc=0.2, scale=2.0, size=(240, 1))
factor3 = np.random.normal(loc=0.5, scale=4.5, size=(240, 1))
factor4 = 0.1 * factor1 + 0.5 * factor2 + 0.4 * factor3
factor5 = -0.2 * factor1 - 0.1 * factor2 + 1.3 * factor3
factor6 = 1.0 * factor1 - 0.5 * factor2 + 0.5 * factor3
factor7 = 0.2 * factor1 + 0.1 * factor2 + 0.7 * factor3
factor8 = -0.1 * factor1 -0.1 * factor2 + 1.2 * factor3
factor9 = -0.3 * factor1 - 0.2 * factor2 + 1.5 * factor3
factor10 = 0.9 * factor1 - 0.5 * factor2 + 0.6 * factor3
factor11 = 0.2 * factor1 - 0.1 * factor2 + 0.9 * factor3
factornew1 = np.random.normal(loc=0.3, scale=2.0, size=(240, 1))
factork = np.block([factor1, factor2, factor3, factor4, factor5, factor6, factor7, factor8, factor9])
factorn = np.block([factor10, factor11])
model1 = span(factorn, factork)
model1._regress()
model1._build_statistics()
model1.fit()
model1.summary()
model2 = span(factornew1, factork)
model2._regress()
model2._build_statistics()
model2.fit()
model2.summary()
test_spanning_test()
================================================================================================================================
+--------+----------+---------+----------+---------+-----------+----------+------------+----------+-----------+----------+------------+-----+---+---+
| asset | alpha | p-value | delta | F-test | p-value-F | LR | p-value-LR | W | p-value-W | LM | p-value-LM | T | N | K |
+--------+----------+---------+----------+---------+-----------+----------+------------+----------+-----------+----------+------------+-----+---+---+
| asset0 | -0.00000 | 0.13810 | -0.00000 | 3.10291 | 0.01543 | 12.83472 | 0.01211 | 13.14587 | 0.01058 | 12.53381 | 0.01379 | 240 | 2 | 9 |
| asset1 | -0.00000 | 0.97109 | -0.00000 | 3.10291 | 0.01543 | 12.83472 | 0.01211 | 13.14587 | 0.01058 | 12.53381 | 0.01379 | 240 | 2 | 9 |
+--------+----------+---------+----------+---------+-----------+----------+------------+----------+-----------+----------+------------+-----+---+---+
+--------+---------+---------+---------+----------+-----------+----------+------------+----------+-----------+----------+------------+-----+---+---+
| asset | alpha | p-value | delta | F-test | p-value-F | LR | p-value-LR | W | p-value-W | LM | p-value-LM | T | N | K |
+--------+---------+---------+---------+----------+-----------+----------+------------+----------+-----------+----------+------------+-----+---+---+
| asset0 | 0.47970 | 0.00029 | 1.04366 | 10.56632 | 0.00004 | 21.09647 | 0.00003 | 22.05146 | 0.00002 | 20.19584 | 0.00004 | 240 | 1 | 9 |
+--------+---------+---------+---------+----------+-----------+----------+------------+----------+-----------+----------+------------+-----+---+---+
fama_macbeth
This module is designed for Fama_Macbeth regression(1976).
Fama-Macbeth Regression follows two steps:
- Specify the model and take cross-sectional regression.
- Take the time-series average of regression coefficient
For more details, please read Empirical Asset Pricing: The Cross Section of Stock Returns. Bali, Engle, Murray, 2016.
class Fama_macbeth_regress():
Package Needed: numpy, statsmodels, scipy, prettytable.
def _init_(self, sample):
input :
sample (ndarray/DataFrame): data for analysis. The structure of the sample :
The first column is dependent variable/ test portfolio return.
The second to the last-1 columns are independent variable/ factor loadings.
The last column is the time label.
def divide_by_time(self, sample):
This function group the sample by time.
input :
sample (ndarray/DataFrame): The data for analysis in the _init_ function.
output :
groups_by_time (list): The sample grouped by time.
def cross_sectional_regress(self, add_constant=True, normalization=True, **kwargs):
This function conducts the first step of Fama-Macebth Regression Fama-Macbeth, that taking the cross-sectional regression for each period.
input :
add_constant (boolean): whether add intercept when take the cross-sectional regression.
normalization (boolean): Whether conduct normalization.
output :
parameters (ndarray): The regression coefficient/factor risk premium, whose rows are the group coefficient and columns are regression variable.
tvalue (ndarray): t value for the coefficient.
rsquare (list): The r-square.
adjrsq (list): The adjust r-square.
n (list): The sample quantity in each group.
def time_series_average(self, **kwargs):
This function conducts the second step of Fama-Macbeth regression, take the time series average of cross section regression.
def fit(self, **kwargs):
This function fits the model by running the time_series_average function.
Example
import numpy as np
from fama_macbeth import Fama_macbeth_regress
# construct sample
year=np.ones((3000,1),dtype=int)*2020
for i in range(19):
year=np.append(year,(2019-i)*np.ones((3000,1),dtype=int))
character=np.random.normal(0,1,(2,20*3000))
# print('Character:',character)
ret=np.array([-0.5,-1]).dot(character)+np.random.normal(0,1,20*3000)
sample=np.array([ret,character[0],character[1],year]).T
# print('Sample:',sample)
# print(sample.shape)
model = Fama_macbeth_regress(sample)
result = model.fit(add_constant=False)
print(result)
=========================================================================
para_average: [-0.501 -1.003]
tvalue: [-111.857 -202.247]
R: 0.5579113793318332
ADJ_R: 0.5576164569698131
sample number N: 3000.0
def summary_by_time(self):
This function summarize the cross-section regression result at each time.
Package needed: prettytable.
Example
# continue the previous code
model.summary_by_time()
==========================================================================
+--------+-----------------+----------+--------------+---------------+
| Year | Param | R Square | Adj R Square | Sample Number |
+--------+-----------------+----------+--------------+---------------+
| 2001.0 | [-0.499 -0.990] | 0.53 | 0.53 | 3000 |
| 2002.0 | [-0.524 -0.987] | 0.56 | 0.56 | 3000 |
| 2003.0 | [-0.544 -1.015] | 0.58 | 0.58 | 3000 |
| 2004.0 | [-0.474 -0.948] | 0.53 | 0.53 | 3000 |
| 2005.0 | [-0.502 -1.007] | 0.57 | 0.57 | 3000 |
| 2006.0 | [-0.497 -0.981] | 0.55 | 0.55 | 3000 |
| 2007.0 | [-0.526 -1.020] | 0.57 | 0.57 | 3000 |
| 2008.0 | [-0.476 -1.024] | 0.56 | 0.56 | 3000 |
| 2009.0 | [-0.533 -1.011] | 0.57 | 0.57 | 3000 |
| 2010.0 | [-0.493 -1.029] | 0.57 | 0.57 | 3000 |
| 2011.0 | [-0.504 -0.975] | 0.55 | 0.55 | 3000 |
| 2012.0 | [-0.508 -1.002] | 0.56 | 0.56 | 3000 |
| 2013.0 | [-0.474 -1.015] | 0.56 | 0.56 | 3000 |
| 2014.0 | [-0.503 -0.998] | 0.55 | 0.55 | 3000 |
| 2015.0 | [-0.485 -1.034] | 0.55 | 0.55 | 3000 |
| 2016.0 | [-0.514 -1.005] | 0.57 | 0.57 | 3000 |
| 2017.0 | [-0.498 -1.016] | 0.58 | 0.58 | 3000 |
| 2018.0 | [-0.475 -0.994] | 0.55 | 0.55 | 3000 |
| 2019.0 | [-0.487 -0.974] | 0.54 | 0.54 | 3000 |
| 2020.0 | [-0.511 -1.031] | 0.56 | 0.56 | 3000 |
+--------+-----------------+----------+--------------+---------------+
def summary(self, charactername=None):
This function summarize the final result.
input :
charactername : The factors' name in the cross-section regression model.
Example
# continue the previous code
model.summary()
================================================================================
+-----------------+---------------------+-----------+---------------+-----------+
| Param | Param Tvalue | Average R | Average adj R | Average n |
+-----------------+---------------------+-----------+---------------+-----------+
| [-0.501 -1.003] | [-111.857 -202.247] | 0.558 | 0.558 | 3000.0 |
+-----------------+---------------------+-----------+---------------+-----------+
def plot(self, figsize=(14, 7), together=False, window=None, select=None, **kwargs):
This function plots the regression slopes of the FM regression.
input :
figsize (tuple) : Figsize.
together (boolean) : Whether print the slope in one figure.
window (int) : The window of moving average slopes.
select (list) : Only print the selected slopes.
Example
from fama_macbeth import Fama_macbeth_regress as fmr
model = fmr(test_data_1)
model.fit()
model.plot(together=True, window=10)
class Factor_mimicking_portfolio
This module is designed for generating factor mimicking portfolio following the Fama-French (1993) conventions, and then calculating factor risk premium.
Fama-French (1993) conventions.
| Size\Factor | Low(<=30%) | Medium(30%< & <=70%) | High(>70%) |
|---|---|---|---|
| Small(<=50%) | S/L | S/M | S/H |
| Big(>50%) | B/L | B/M | B/H |
-
Group stocks by two dimensions. One dimension is size, divided by 50% small stocks and 50% big stocks. The other is the factor, divided by 30% tail factor stocks, 30%~70% factor stocks, and 70%~100% factor stocks.
-
Calculate market value weighted portfolio return and factor risk premium.
$$ SMB=1/3(S/L+S/M+S/H)-1/3(B/L+B/M+B/H) $$
$$ Factor=1/2(S/H+B/H)-1/2(S/L+B/L) $$
-
In Fama-French (1993), the factor is book-to-market ratio, and other literatures follow the same way to construct factor mimicking portfolio. The return of each portfolio is represented by the market value weighted portfolio return.
def _init_(self, sample, perc_row=[0, 50, 100], perc_col=[0, 30, 70, 100], percn_row=None, percn_col=None, weight=True):
This function initializes the object.
input :
sample (ndarray/DataFrame): data for analysis. The structure of the sample :
The first column is dependent variable/ test portfolio return.
The second is the first factor.
The third is the second factor.
The fourth is the timestamp.
The fifth is the weight.
perc_row (list/array): The percentile points that divide stocks by the first factor. The Default percentile is [0, 50, 100].
perc_col (list/array): The percentile points that divide stocks by the second factor. The Default percentile is [0, 30, 70, 100].
percn_row (list/array): The percentile that divide stocks by the first factor.
percn_col (list/array): The percentile that divide stocks by the second factor.
weight (array/Series): Whether the portfolio return calculated by weight. The Default is True.
def portfolio_return_time(self):
This function is to construct portfolio and calculate the average return and difference matrix.
output :
diff (ndarray): The differenced portfolio return matrix.
Example
'''
TEST Factor_mimicking_portfolio
construct sample:
1. 20 Periods
2. 3000 Observations for each Period
3. Character negative with return following the return=character*-0.5+sigma where sigma~N(0,1)
'''
import numpy as np
from fama_macbeth import Factor_mimicking_portfolio
# construct sample
year=np.ones((3000,1),dtype=int)*2020
for i in range(19):
year=np.append(year,(2019-i)*np.ones((3000,1),dtype=int))
character=np.random.normal(0, 1, (2, 20*3000))
weight = np.random.uniform(0, 1, (1, 20*3000))
# print('Character:',character)
ret=np.array([-0.5,-1]).dot(character)+np.random.normal(0,1,20*3000)
sample=np.array([ret, character[0], character[1], year, weight[0]]).T
# print('Sample:',sample)
# print(sample.shape)
model = Factor_mimicking_portfolio(sample)
portfolio_return_time = model.portfolio_return_time()
print('portfolio_return_time:', portfolio_return_time)
print('portfolio_return_time:', np.shape(portfolio_return_time))
========================================================================
portfolio_return_time:
[[[ 1.6302854 1.5920872 1.54199455 1.47560967 1.60182404
1.48860463 1.70067317 1.57084898 1.52938766 1.54919833
1.58910675 1.44369383 1.6489323 1.57230951 1.64104889
1.52816059 1.53197648 1.44067358 1.55358692 1.60347805]
[ 0.27087317 0.37938255 0.46473997 0.43118946 0.36934624
0.3215685 0.51716485 0.3740702 0.38663032 0.44333387
0.38917603 0.31347239 0.30760233 0.41415477 0.45250083
0.4439825 0.35821053 0.40601508 0.40495275 0.46236114]
[-0.77286286 -0.67348462 -0.79216628 -0.76712914 -0.73108828
-0.74141791 -0.85011447 -0.65743291 -0.57583562 -0.80490414
-0.64311824 -0.79901273 -0.81325556 -0.84443278 -0.80362147
-0.75246184 -0.61693674 -0.69909426 -0.68554981 -0.6564971 ]
[-2.40314826 -2.26557182 -2.33416083 -2.24273881 -2.33291232
-2.23002254 -2.55078764 -2.22828188 -2.10522328 -2.35410248
-2.23222499 -2.24270656 -2.46218786 -2.41674229 -2.44467035
-2.28062243 -2.14891322 -2.13976784 -2.23913673 -2.25997515]]
[[ 0.73368397 0.87086931 0.69626265 0.83424514 0.75825827
0.65550255 0.79076344 0.77316807 0.82031302 0.83320932
0.76971902 0.81248391 0.74568233 0.7749383 0.69168886
0.7511554 0.70757116 0.75320784 0.78223447 0.73699303]
[-0.55494493 -0.4097451 -0.42006211 -0.36317491 -0.47791724
-0.40042274 -0.36004971 -0.39127871 -0.4712118 -0.33368187
-0.48957933 -0.41103346 -0.46612991 -0.39504384 -0.34021312
-0.41049521 -0.33209925 -0.39212119 -0.42890556 -0.40389983]
[-1.63941363 -1.52575966 -1.55711119 -1.45657452 -1.53325438
-1.5163362 -1.4984305 -1.50929504 -1.52485715 -1.60331314
-1.56591033 -1.60738805 -1.77875307 -1.4963315 -1.65246163
-1.55526031 -1.40809313 -1.49853102 -1.56149388 -1.48409324]
[-2.3730976 -2.39662897 -2.25337384 -2.29081966 -2.29151265
-2.17183875 -2.28919394 -2.28246311 -2.34517017 -2.43652246
-2.33562934 -2.41987196 -2.5244354 -2.27126981 -2.34415049
-2.30641572 -2.11566429 -2.25173887 -2.34372835 -2.22108628]]
[[-0.89660143 -0.72121789 -0.8457319 -0.64136454 -0.84356577
-0.83310208 -0.90990973 -0.79768091 -0.70907464 -0.71598901
-0.81938773 -0.63120993 -0.90324997 -0.7973712 -0.94936003
-0.77700518 -0.82440531 -0.68746574 -0.77135245 -0.86648502]
[-0.82581811 -0.78912765 -0.88480208 -0.79436437 -0.84726347
-0.72199124 -0.87721456 -0.7653489 -0.85784212 -0.77701574
-0.87875536 -0.72450585 -0.77373224 -0.80919861 -0.79271394
-0.85447771 -0.69030979 -0.79813627 -0.83385831 -0.86626098]
[-0.86655077 -0.85227505 -0.76494491 -0.68944538 -0.8021661
-0.77491829 -0.64831603 -0.85186213 -0.94902153 -0.798409
-0.92279209 -0.80837532 -0.96549751 -0.65189873 -0.84884016
-0.80279847 -0.79115639 -0.79943676 -0.87594408 -0.82759615]
[ 0.03005066 -0.13105715 0.08078699 -0.04808085 0.04139968
0.05818379 0.26159369 -0.05418122 -0.23994689 -0.08241999
-0.10340436 -0.17716539 -0.06224754 0.14547248 0.10051987
-0.02579329 0.03324893 -0.11197102 -0.10459162 0.03888887]]]
portfolio_return_time:
(3, 4, 20)
def portfolio_return(self):
This function is to construct factor risk premium.
output :
return_row : The first factor risk premium. The Default is size factor.
return_col : The second factor risk premium.
def portfolio_return_horizon(self, period, log):
This function is to construct horizon pricing factor. For details, read Horizon Pricing, JFQA, 2016, 51(6): 1769-1793.
input :
period (int): The lagged period for constructing factor risk premium return.
log(boolean): whether use log return.
output :
return_row_multi : The first factor risk premium. The DEFAULT is size factor.
return_col_multi : The second factor premium.
Example
# Continue the previous code
portfolio_return = model.portfolio_return()
print('portfolio_return_row: \n', portfolio_return[0])
print('portfolio_return_row:', np.shape(portfolio_return[0]))
print('portfolio_return_col: \n', portfolio_return[1])
print('portfolio_return_col:', np.shape(portfolio_return[1]))
==============================================================
portfolio_return_row:
1970-01-01 00:00:00.000002001 -0.639730
1970-01-01 00:00:00.000002002 -0.623419
1970-01-01 00:00:00.000002003 -0.603673
1970-01-01 00:00:00.000002004 -0.543314
1970-01-01 00:00:00.000002005 -0.612899
1970-01-01 00:00:00.000002006 -0.567957
1970-01-01 00:00:00.000002007 -0.543462
1970-01-01 00:00:00.000002008 -0.617268
1970-01-01 00:00:00.000002009 -0.688971
1970-01-01 00:00:00.000002010 -0.593458
1970-01-01 00:00:00.000002011 -0.681085
1970-01-01 00:00:00.000002012 -0.585314
1970-01-01 00:00:00.000002013 -0.676182
1970-01-01 00:00:00.000002014 -0.528249
1970-01-01 00:00:00.000002015 -0.622599
1970-01-01 00:00:00.000002016 -0.615019
1970-01-01 00:00:00.000002017 -0.568156
1970-01-01 00:00:00.000002018 -0.599252
1970-01-01 00:00:00.000002019 -0.646437
1970-01-01 00:00:00.000002020 -0.630363
dtype: float64
portfolio_return_row: (20,)
portfolio_return_col:
1970-01-01 00:00:00.000002001 -1.582065
1970-01-01 00:00:00.000002002 -1.597753
1970-01-01 00:00:00.000002003 -1.502249
1970-01-01 00:00:00.000002004 -1.527213
1970-01-01 00:00:00.000002005 -1.527675
1970-01-01 00:00:00.000002006 -1.447892
1970-01-01 00:00:00.000002007 -1.526129
1970-01-01 00:00:00.000002008 -1.521642
1970-01-01 00:00:00.000002009 -1.563447
1970-01-01 00:00:00.000002010 -1.624348
1970-01-01 00:00:00.000002011 -1.557086
1970-01-01 00:00:00.000002012 -1.613248
1970-01-01 00:00:00.000002013 -1.682957
1970-01-01 00:00:00.000002014 -1.514180
1970-01-01 00:00:00.000002015 -1.562767
1970-01-01 00:00:00.000002016 -1.537610
1970-01-01 00:00:00.000002017 -1.410443
1970-01-01 00:00:00.000002018 -1.501159
1970-01-01 00:00:00.000002019 -1.562486
1970-01-01 00:00:00.000002020 -1.480724
dtype: float64
portfolio_return_col: (20,)
time_series_regress
class TS_regress()
This class is designed for time series regression,
$$ r_{i,t} = \beta_if_t + \epsilon_{i,t} $$
to obtain the beta for each asset.
def _init_(self, list_y, factor):
This function initializes the object.
input :
list_y (list/DataFrame): The return matrix with i rows and t columns.
factor (ndarray or DataFrame): The factor risk premium return series.
def ts_regress(self, newey_west=True):
This function is for conducting the time series regression.
input :
newey_west (boolean)： conduct the newey_west adjustment or not.
output :
self.alpha (list): The regression alpha.
self.e_mat (ndarray): The error matrix.
Example
from statsmodels.base.model import Model
from statsmodels.tools.tools import add_constant
from EAP.time_series_regress import TS_regress
X = np.random.normal(loc=0.0, scale=1.0, size=(2000,10))
y_list = []
for i in range(10) :
b = np.random.uniform(low=0.1, high=1.1, size=(10,1))
e = np.random.normal(loc=0.0, scale=1.0, size=(2000,1))
y = X.dot(b) + e
y_list.append(y)
re = TS_regress(y_list, X)
def fit(self, **kwargs):
This function runs the function, ts_regress.
Example
# continue the previous code
re.fit()
def summary(self):
This function summarize the result, including the GRS test.
Example
# continue the previous code
re.summary()
=============================================================================
----------------------------------- GRS Test --------------------------------
GRS Statistics:
[[0.67160203]]
GRS p_value:
[[0.75175471]]
------------------------------------------------------------------------------
def grs(self):
This function conducts the GRS test.
output :
grs_stats (list): The GRS statistics.
p_value (list): The p_value.
Example
# continue the previous code
print(re.grs())
==============================================
(array([[0.67160203]]), array([[0.75175471]]))
cross_section_regress
class CS_regress()
def _init_(self, y_list, factor):
This function initializes the class.
input :
y_list (list/DataFrame): The assets return series list.
factor (ndarray/DataFrame): The factor risk premium series.
def ts_regress(self):
This function conducts the time series regression.
output :
beta(ndarray[N, c]) : The betas for each asset.
err_mat (ndarray): The error matrix.
def ave(self):
This function conducts the average operation on the assets returns series list.
output :
np.mean(self.y_list, axis=1) : The average of the assets returns series list.
def cs_regress(self, beta, err_mat, constant=True, gls=True, **kwargs):
This function takes the cross-sectional regression.
input :
beta (ndarray): The betas from the output of the function ts_regress().
err_mat (ndarray) : The error matrix from the output of the function ts_regress().
constant (boolean): add constant or not. The default is add constant.
gls (boolean): GLS regression or OLS regression. The default is GLS regression.
output :
params (array): The params of the cross regression model.
resid (array): The residue of the cross regression model.
Example
from statsmodels.regression.linear_model import GLS
from EAP.cross_section_regress import CS_regress
import numpy as np
X = np.random.normal(loc=0, scale=0.1, size=(2000,3))
y_list = []
for i in range(100) :
b = np.random.uniform(low=-1, high=1, size=(3,1))
e = np.random.normal(loc=0.0, scale=0.5, size=(2000,1))
alpha = np.random.normal(loc=0.0, scale=0.5)
y = X.dot(b) + e
y_list.append(y)
print(np.mean(X, axis= 0)) # average return of the factor risk premium
========================================================================
[-0.00496423 0.00146649 -0.0004722 ]
def cov_mat(self, beta, err_mat, shanken=True, constant=True, gls=True, **kwargs):
This function calculates the covariance matrix of the cross regression model.
input :
beta (ndarray): The betas from the output of the function ts_regress().
err_mat (ndarray): The error matrix from the output of the function ts_regress().
shanken (boolean): Take the shanken adjustment or not. The default is True.
constant (boolean): add constant or not.
gls (boolean): GLS regression or OLS regression. The default is GLS regression.
output :
param_cov_mat (ndarray): The covariance matrix of the parameters.
resid_cov_mat (ndarray): The covariance matrix of the residue.
def t_test(self, param_cov_mat, params):
This function takes t-test for parameters.
input :
param_cov_mat (ndarray): The covariance matrix of the parameters from the function cov_mat.
params (ndarray): The parameters from the function cs_regress.
output :
t_value (ndarray): The t-value for statistical inference.
p_value (ndarray): The p-value for statistical inference.
def union_test(self, resid_cov_mat, resid):
This function takes union test for parameters.
input :
resid_cov_mat (ndarray): The covariance matrix of the residue.
resid (ndarray): The residue from the function cs_regress.
output :
chi_square (list): The chi-square statistics.
p_value (list): The p-value corresponding to the chi-square.
def fit(self, **kwargs):
This function runs the cross-sectional regression and takes the statistical inference.
def summary(self):
This function print the summary.
Example
# continue the previous code
print("\n---------------------GLS: Constant=True shanken=True------------------------\n")
re = CS_regress(y_list, X)
re.fit()
re.summary()
print("\n------------------------------------------------------------------------\n")
print("\n---------------------GLS: Constant=False shanken=True------------------------\n")
re = CS_regress(y_list, X)
re.fit(constant=False)
re.summary()
print("\n------------------------------------------------------------------------\n")
print("\n---------------------GLS: Constant=True shanken=False------------------------\n")
re = CS_regress(y_list, X)
re.fit(shanken=False)
re.summary()
print("\n------------------------------------------------------------------------\n")
print("\n---------------------GLS: Constant=False shanken=False------------------------\n")
re = CS_regress(y_list, X)
re.fit(constant=False, shanken=False)
re.summary()
print("\n------------------------------------------------------------------------\n")
print("\n---------------------OLS: Constant=True shanken=True------------------------\n")
re = CS_regress(y_list, X)
re.fit(gls=False)
re.summary()
print("\n------------------------------------------------------------------------\n")
print("\n---------------------OLS: Constant=False shanken=True------------------------\n")
re = CS_regress(y_list, X)
re.fit(constant=False, gls=False)
re.summary()
print("\n------------------------------------------------------------------------\n")
print("\n---------------------OLS: Constant=True shanken=False------------------------\n")
re = CS_regress(y_list, X)
re.fit(shanken=False, gls=False)
re.summary()
print("\n------------------------------------------------------------------------\n")
print("\n---------------------OLS: Constant=False shanken=False------------------------\n")
re = CS_regress(y_list, X)
re.fit(constant=False, shanken=False, gls=False)
re.summary()
print("\n------------------------------------------------------------------------\n")
================================================================================================================================
---------------------GLS: Constant=True shanken=True------------------------
-------------------------- Risk Premium ------------------------------
+-----------------------+---------------+--------------+
| params | t_value | p_value |
+-----------------------+---------------+--------------+
| -0.004239493082637248 | [-1.49931456] | [0.13394995] |
| 0.0018754489425203834 | [0.64798047] | [0.517072] |
| -0.002623980021497935 | [-0.92194337] | [0.35666937] |
+-----------------------+---------------+--------------+
----------------------------------------------------------------------
----------------------------- Alpha test -----------------------------
+-----------------+----------------+
| chi-square | p_value |
+-----------------+----------------+
| [[89.27084753]] | [[0.69922497]] |
+-----------------+----------------+
----------------------------------------------------------------------
------------------------------------------------------------------------
---------------------GLS: Constant=False shanken=True------------------------
-------------------------- Risk Premium ------------------------------
+------------------------+---------------+--------------+
| params | t_value | p_value |
+------------------------+---------------+--------------+
| -0.0044337140100835495 | [-1.56801135] | [0.11703675] |
| 0.0014489988306153607 | [0.50064261] | [0.61667778] |
| -0.0025199902303684996 | [-0.8854116] | [0.37604117] |
+------------------------+---------------+--------------+
----------------------------------------------------------------------
----------------------------- Alpha test -----------------------------
+------------------+----------------+
| chi-square | p_value |
+------------------+----------------+
| [[123.73200185]] | [[0.03486519]] |
+------------------+----------------+
----------------------------------------------------------------------
------------------------------------------------------------------------
---------------------GLS: Constant=True shanken=False------------------------
-------------------------- Risk Premium ------------------------------
+-----------------------+---------------+--------------+
| params | t_value | p_value |
+-----------------------+---------------+--------------+
| -0.004239493082637248 | [-1.50013478] | [0.13373741] |
| 0.0018754489425203834 | [0.64838824] | [0.51680835] |
| -0.002623980021497935 | [-0.92243422] | [0.35641345] |
+-----------------------+---------------+--------------+
----------------------------------------------------------------------
----------------------------- Alpha test -----------------------------
+-----------------+---------+
| chi-square | p_value |
+-----------------+---------+
| [[32.53458229]] | [[1.]] |
+-----------------+---------+
----------------------------------------------------------------------
------------------------------------------------------------------------
---------------------GLS: Constant=False shanken=False------------------------
-------------------------- Risk Premium ------------------------------
+------------------------+---------------+--------------+
| params | t_value | p_value |
+------------------------+---------------+--------------+
| -0.0044337140100835495 | [-1.56885941] | [0.11683897] |
| 0.0014489988306153607 | [0.50095408] | [0.6164586] |
| -0.0025199902303684996 | [-0.88587763] | [0.37579002] |
+------------------------+---------------+--------------+
----------------------------------------------------------------------
----------------------------- Alpha test -----------------------------
+------------------+---------+
| chi-square | p_value |
+------------------+---------+
| [[-49.33885529]] | [[1.]] |
+------------------+---------+
----------------------------------------------------------------------
------------------------------------------------------------------------
---------------------OLS: Constant=True shanken=True------------------------
-------------------------- Risk Premium ------------------------------
+------------------------+---------------+--------------+
| params | t_value | p_value |
+------------------------+---------------+--------------+
| -0.004191679829911098 | [-1.46410802] | [0.14332167] |
| 0.0026957168215120215 | [0.91917806] | [0.35811334] |
| -0.0028054613152236852 | [-0.9776489] | [0.3283663] |
+------------------------+---------------+--------------+
----------------------------------------------------------------------
----------------------------- Alpha test -----------------------------
+------------------+----------------+
| chi-square | p_value |
+------------------+----------------+
| [[105.04417306]] | [[0.27097431]] |
+------------------+----------------+
----------------------------------------------------------------------
------------------------------------------------------------------------
---------------------OLS: Constant=False shanken=True------------------------
-------------------------- Risk Premium ------------------------------
+-----------------------+---------------+--------------+
| params | t_value | p_value |
+-----------------------+---------------+--------------+
| -0.004314458572417905 | [-1.50700942] | [0.13196625] |
| 0.002435573118655651 | [0.83048514] | [0.40636372] |
| -0.002772551881136359 | [-0.96619054] | [0.33406572] |
+-----------------------+---------------+--------------+
----------------------------------------------------------------------
----------------------------- Alpha test -----------------------------
+------------------+----------------+
| chi-square | p_value |
+------------------+----------------+
| [[117.95438501]] | [[0.07282442]] |
+------------------+----------------+
----------------------------------------------------------------------
------------------------------------------------------------------------
---------------------OLS: Constant=True shanken=False------------------------
-------------------------- Risk Premium ------------------------------
+------------------------+---------------+--------------+
| params | t_value | p_value |
+------------------------+---------------+--------------+
| -0.004191679829911098 | [-1.46507223] | [0.14305847] |
| 0.0026957168215120215 | [0.91987006] | [0.35775165] |
| -0.0028054613152236852 | [-0.9782681] | [0.32806011] |
+------------------------+---------------+--------------+
----------------------------------------------------------------------
----------------------------- Alpha test -----------------------------
+------------------+---------------+
| chi-square | p_value |
+------------------+---------------+
| [[144.80511192]] | [[0.0011985]] |
+------------------+---------------+
----------------------------------------------------------------------
------------------------------------------------------------------------
---------------------OLS: Constant=False shanken=False------------------------
-------------------------- Risk Premium ------------------------------
+-----------------------+---------------+--------------+
| params | t_value | p_value |
+-----------------------+---------------+--------------+
| -0.004314458572417905 | [-1.50798575] | [0.13171619] |
| 0.002435573118655651 | [0.8311002] | [0.40601628] |
| -0.002772551881136359 | [-0.96679254] | [0.3337647] |
+-----------------------+---------------+--------------+
----------------------------------------------------------------------
----------------------------- Alpha test -----------------------------
+------------------+----------------+
| chi-square | p_value |
+------------------+----------------+
| [[100.02211446]] | [[0.39645777]] |
+------------------+----------------+
----------------------------------------------------------------------
------------------------------------------------------------------------
adjust
This module consists of several common adjustment method in factor analysis.
def ols(y, x, constant=True):
The function is for OLS regression, which is equal to the OLS module in package statsmodels.
input :
y (ndarray): The dependent variable.
x (ndarray): The explanatory variable.
constant (boolean): add constant or not in OLS model. The default is True.
output :
result (OLSRegressResult): The result of the regression.
import numpy as np
from statsmodels.base.model import Model
from statsmodels.tools.tools import add_constant
from EAP.adjust import newey_west, newey_west_t, ols, white_t
from EAP.adjust import white
X = np.random.normal(loc=0.0, scale=1.0, size=(2000,10))
b = np.random.uniform(low=0.1, high=1.1, size=(10,1))
e = np.random.normal(loc=0.0, scale=1.0, size=(2000,1))
y = X.dot(b) + e + 1.0
re = ols(y, X, constant=True)
print('\nTrue b : ', b)
print('\nEstimated b : ', re.params)
print('\nresidue : ', re.resid.shape)
====================================================
True b : [[0.59169091]
[0.91342353]
[0.19599503]
[0.9112773 ]
[0.70647024]
[0.41873624]
[0.64871071]
[0.20685505]
[0.13172035]
[0.82358063]]
Estimated b : [1.00206596 0.57602159 0.91832825 0.2104454 0.935377 0.71526534
0.39181771 0.65432445 0.22666925 0.13173488 0.83208811]
residue : (2000,)
def white(y, X, **kwargs):
This function is for the White test. White estimate of variance:
X(r,c): r is sample number, c is variable number, S0 is covariance matrix of residue.
The variance estimate is
$$
V_{ols}=T(X^X)^{-1}S_0(X^X)^{-1}.
$$
The white estimation of S0 is
$$
S_0=\frac 1T X^`(XR).
$$
input :
y (ndarray): The dependent variable.
X (ndarray): The explanatory variable.
output :
V_ols (ndarray): The white variance estimate
Example
# continue the previous code
import numpy as np
from statsmodels.api import add_constant
X = np.random.normal(loc=0.0, scale=1.0, size=(2000,10))
b = np.random.uniform(low=0.1, high=1.1, size=(10,1))
e = np.random.normal(loc=0.0, scale=1.0, size=(2000,1))
y = X.dot(b) + e + 1.0
re = white(y, X, constant=True)
np.set_printoptions(formatter={'float':'{:0.3f}'.format})
print(re*100)
X = add_constant(X)
r, c = np.shape(X)
print('\n', 1/r*X.T.dot(X).dot(re).dot(X.T.dot(X)))
============================================================================
[[0.052 0.004 0.002 0.002 0.000 -0.002 0.002 -0.004 -0.001 0.000 0.003]
[0.004 0.056 0.002 -0.002 -0.003 -0.004 -0.001 -0.001 -0.003 0.004 0.001]
[0.002 0.002 0.049 -0.003 -0.003 0.003 0.000 -0.002 -0.002 -0.003 0.002]
[0.002 -0.002 -0.003 0.051 -0.002 -0.002 0.004 -0.000 -0.000 -0.001 0.002]
[0.000 -0.003 -0.003 -0.002 0.054 0.004 0.000 -0.001 0.000 -0.001 0.003]
[-0.002 -0.004 0.003 -0.002 0.004 0.055 -0.001 0.000 0.000 -0.002 0.001]
[0.002 -0.001 0.000 0.004 0.000 -0.001 0.053 -0.003 -0.005 -0.002 0.004]
[-0.004 -0.001 -0.002 -0.000 -0.001 0.000 -0.003 0.057 -0.001 -0.001 -0.002]
[-0.001 -0.003 -0.002 -0.000 0.000 0.000 -0.005 -0.001 0.051 0.003 0.000]
[0.000 0.004 -0.003 -0.001 -0.001 -0.002 -0.002 -0.001 0.003 0.049 0.002]
[0.003 0.001 0.002 0.002 0.003 0.001 0.004 -0.002 0.000 0.002 0.052]]
[[1.036 0.029 -0.028 0.031 0.007 -0.067 -0.004 0.003 0.029 -0.022 -0.041]
[0.029 1.001 0.020 -0.056 -0.066 -0.023 0.000 -0.010 -0.070 0.069 0.023]
[-0.028 0.020 0.972 -0.057 -0.019 0.058 -0.048 -0.002 0.084 -0.005 0.045]
[0.031 -0.056 -0.057 1.004 -0.004 0.017 0.017 -0.072 -0.008 -0.042 0.041]
[0.007 -0.066 -0.019 -0.004 1.024 0.045 -0.035 0.017 0.003 0.006 0.029]
[-0.067 -0.023 0.058 0.017 0.045 1.125 0.010 -0.014 0.037 0.053 -0.017]
[-0.004 0.000 -0.048 0.017 -0.035 0.010 1.053 -0.022 -0.047 0.047 0.035]
[0.003 -0.010 -0.002 -0.072 0.017 -0.014 -0.022 0.955 -0.007 -0.002 -0.019]
[0.029 -0.070 0.084 -0.008 0.003 0.037 -0.047 -0.007 1.008 -0.025 0.025]
[-0.022 0.069 -0.005 -0.042 0.006 0.053 0.047 -0.002 -0.025 1.010 0.026]
[-0.041 0.023 0.045 0.041 0.029 -0.017 0.035 -0.019 0.025 0.026 1.058]]
def newey_west(y, X, J=None):
This function is for Newey-West adjustment. Newey-West estimate of variance:
X(r,c): r is sample number, c is variable number, and S0 is covariance matrix of residue.
The estimate variance is
$$
V_{ols}=T(X^X)^{-1}S_0(X^X)^{-1}.
$$
The Newey-West estimate variance of S0 is
$$
S_0= \frac1T X^(XR)+\frac1T \sum_j\sum_tw_je_te_{t-j}(X_tX^{t-j}+X{t-j}X^`_t).
$$
input :
y (ndarray): The dependent variable.
X (ndarray): The explanatory variable.
J (int): The lag.
output :
V_ols (ndarray): The Newey-West variance estimate.
Example
# continue the previous code
import numpy as np
from statsmodels.stats.sandwich_covariance import cov_hac
X = np.random.normal(loc=0.0, scale=1.0, size=(10000,10))
b = np.random.uniform(low=0.1, high=1.1, size=(10,1))
e = np.random.normal(loc=0.0, scale=1.0, size=(10000,1))
y = X.dot(b) + e + 1.0
re = newey_west(y, X, constant=False)
np.set_printoptions(formatter={'float':'{:0.2f}'.format})
print(re)
# X = add_constant(X)
r, c = np.shape(X)
print('\n', 1/r*X.T.dot(X).dot(re).dot(X.T.dot(X)))
result = ols(y, X, constant=False)
print('\n', cov_hac(result))
print('\n', 1/r*X.T.dot(X).dot(cov_hac(result)).dot(X.T.dot(X)))
========================================================================
[[0.00 -0.00 -0.00 0.00 0.00 0.00 -0.00 0.00 -0.00 -0.00]
[-0.00 0.00 -0.00 -0.00 -0.00 0.00 -0.00 -0.00 0.00 -0.00]
[-0.00 -0.00 0.00 -0.00 -0.00 -0.00 -0.00 -0.00 -0.00 0.00]
[0.00 -0.00 -0.00 0.00 -0.00 -0.00 -0.00 0.00 -0.00 -0.00]
[0.00 -0.00 -0.00 -0.00 0.00 0.00 -0.00 -0.00 0.00 0.00]
[0.00 0.00 -0.00 -0.00 0.00 0.00 -0.00 -0.00 -0.00 0.00]
[-0.00 -0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 0.00]
[0.00 -0.00 -0.00 0.00 -0.00 -0.00 0.00 0.00 -0.00 -0.00]
[-0.00 0.00 -0.00 -0.00 0.00 -0.00 0.00 -0.00 0.00 0.00]
[-0.00 -0.00 0.00 -0.00 0.00 0.00 0.00 -0.00 0.00 0.00]]
[[2.08 0.00 -0.09 -0.01 -0.03 -0.05 -0.02 0.00 -0.02 0.01]
[0.00 2.01 0.04 -0.00 0.00 -0.03 -0.00 -0.01 -0.00 0.02]
[-0.09 0.04 1.99 -0.02 0.01 0.00 -0.01 -0.08 0.03 0.02]
[-0.01 -0.00 -0.02 1.96 -0.00 -0.05 -0.01 -0.04 -0.01 -0.02]
[-0.03 0.00 0.01 -0.00 1.98 0.06 0.00 0.04 -0.01 -0.05]
[-0.05 -0.03 0.00 -0.05 0.06 1.94 -0.01 -0.00 -0.01 -0.02]
[-0.02 -0.00 -0.01 -0.01 0.00 -0.01 2.04 -0.00 0.01 -0.07]
[0.00 -0.01 -0.08 -0.04 0.04 -0.00 -0.00 1.89 -0.05 -0.02]
[-0.02 -0.00 0.03 -0.01 -0.01 -0.01 0.01 -0.05 1.97 -0.01]
[0.01 0.02 0.02 -0.02 -0.05 -0.02 -0.07 -0.02 -0.01 1.93]]
[[0.00 -0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 -0.00]
[-0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 0.00 -0.00 -0.00]
[0.00 0.00 0.00 -0.00 -0.00 0.00 -0.00 -0.00 -0.00 0.00]
[0.00 -0.00 -0.00 0.00 0.00 -0.00 -0.00 -0.00 -0.00 -0.00]
[0.00 0.00 -0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00]
[0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 -0.00 -0.00 -0.00]
[-0.00 -0.00 -0.00 -0.00 0.00 -0.00 0.00 0.00 -0.00 0.00]
[0.00 0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 -0.00 0.00]
[0.00 -0.00 -0.00 -0.00 0.00 -0.00 -0.00 -0.00 0.00 0.00]
[-0.00 -0.00 0.00 -0.00 0.00 -0.00 0.00 0.00 0.00 0.00]]
[[2.07 -0.05 -0.04 0.02 0.06 -0.11 -0.08 0.03 0.05 0.02]
[-0.05 1.91 0.10 0.01 0.07 0.00 0.01 0.02 -0.09 0.03]
[-0.04 0.10 2.05 -0.06 0.01 0.07 -0.06 -0.11 -0.15 0.04]
[0.02 0.01 -0.06 1.87 0.04 -0.05 -0.02 -0.10 -0.01 -0.06]
[0.06 0.07 0.01 0.04 2.00 0.11 0.05 0.03 -0.00 -0.04]
[-0.11 0.00 0.07 -0.05 0.11 1.91 0.00 -0.05 -0.05 -0.05]
[-0.08 0.01 -0.06 -0.02 0.05 0.00 1.99 0.03 -0.02 -0.10]
[0.03 0.02 -0.11 -0.10 0.03 -0.05 0.03 2.01 -0.10 0.06]
[0.05 -0.09 -0.15 -0.01 -0.00 -0.05 -0.02 -0.10 2.16 0.01]
[0.02 0.03 0.04 -0.06 -0.04 -0.05 -0.10 0.06 0.01 1.97]]
def white_t(y, X, params=None, side='Two', **kwargs):
This function constructs t-test based on White variance estimate.
input :
y (ndarray): The dependent variable.
X (ndarray): The explanatory variable.
params (ndarray): Already have parameters or not. The default is None.
side ()
output :
t_value (ndarray): The t-value of parameters.
p_value (ndarray): The p-value of parameters.
Example
import numpy as np
X = np.random.normal(loc=0.0, scale=1.0, size=(10000,10))
b = np.random.uniform(low=-0.5, high=0.5, size=(10,1))
e = np.random.normal(loc=0.0, scale=1.0, size=(10000,1))
y = X.dot(b) + e + 1.0
re = white_t(y, X, constant=False)
np.set_printoptions(formatter={'float':'{:0.2f}'.format})
print('t_value : ', re[0], '\np_value : ', re[1])
print('b :', b.T)
=========================================================================
t_value : [2.50 34.58 13.23 6.56 -17.64 -34.69 -16.40 13.84 28.90 30.64]
p_value : [0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00]
b : [[0.02 0.49 0.18 0.09 -0.25 -0.49 -0.22 0.19 0.44 0.43]]
def newey_west_t(y, X, params=None):
This function constructs t-test based on Newey-West variance estimate.
input :
y (ndarray): The dependent variable.
X (ndarray): The explanatory variable.
params (ndarray): Already have parameters or not. The default is None.
output :
t_value (ndarray): The t-value of parameters.
p_value (ndarray): The p-value of parameters.
Example
import numpy as np
X = np.random.normal(loc=0.0, scale=1.0, size=(10000,10))
b = np.random.uniform(low=-0.5, high=0.5, size=(10,1))
e = np.random.normal(loc=0.0, scale=1.0, size=(10000,1))
y = X.dot(b) + e + 1.0
re = newey_west_t(y, X, constant=True)
np.set_printoptions(formatter={'float':'{:0.2f}'.format})
print('t_value : ', re[0], '\np_value : ', re[1])
print('b :', b.T)
=================================================================================
t_value : [135.08 -17.19 13.80 34.95 14.61 21.31 48.56 -44.62 2.75 -28.71 51.63]
p_value : [0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00]
b : [[-0.14 0.10 0.25 0.11 0.16 0.40 -0.36 0.03 -0.21 0.40]]
util
def plot(portfolio, pattern='scatter', alpha=False, percentage=True, figsize=(14, 7), pos=0.0, **kwargs):
input :
portfolio (ptf_analysis): The fitted portfolio.
pattern (str): The plot patterns, including 'scatter', 'line', and 'bar' for univariate analysis, and including '3d' and 'scatter' for bivariate analysis.
alpha (boolean): Whether plot the factor adjusted alpha. The DEFAULT is False.
percentage (boolean): Whether plot the return and alpha in percentage. The DEFAULT is True.
figsize (tuple): Set the figure size. The DEFAULT is (14, 7).
pos (str): Adjust the position of the axes in 3d figure of bivariate analysis.
kwargs: The keywords of plot in seaborn and matplotlib.
Example
from EAP.util import plot
from EAP.portfolio_analysis import univariate, bivariate
uni = univariate(sample).fit()
plot(uni)
bi = bivariate(sample).fit()
plot(bi)
Univariate
Bivariate: 3d
time_frequency
This module is designed for time frequency asset pricing model, including Fourier Transform based method and Wavelet based method.
class Wavelet():
This class is designed for decomposing the series using wavelet method, basing on the package pywt.
def _init_(self, series):
input:
series (array) : the series to be decomposed.
def _decompose(self, wave, mode, level=None):
This function is designed for decomposing the series using given wavelet family, mode and level.
input :
wave (str) : The chosen wavelet family, which is the same in pywt.
mode (str) : choose multiscale or single scale. 'multi' denotes multiscale. 'single' denotes single scale.
level (int) : the level of multiscale. If 'multi' is chosen, it must be set.
output :
wave_dec (list): The decomposed details including (CA, CN, CN-1,..., C1).
def _pick_details(self):
This function is designed for picking the details of decomposed series at different level.
output:
pick_series (list): pick the detail series at each level. Each elements in list only contains the details at that level.
def _rebuild(self, mode='constant'):
This function is designed for rebuilding the detail series from the picked series at each level.
input:
mode (str): The recomposed method.
output:
wave_rec (list): The recomposed series from the details at each level.
def fit(self, wave, mode, level, output=False):
This function is designed for fitting the model.
input :
wave (str) : The chosen wavelet family, which is the same in pywt.
mode (str) : choose multiscale or single scale. 'multi' denotes multiscale. 'single' denotes single scale.
level (int) : the level of multiscale. If 'multi' is chosen, it must be set.
output (boolean): whether output the result. The DEFAULT is False.
output :
wave_rec (list): The recomposed series from the details at each level, if output is True.
class wavelet_pricing():
This module is designed for wavelet pricing model.
def _init_(self, rets, factors):
input :
rets (ndarray/Series/DataFrame): the dependent variables of the return.
factors (ndarray/Series/DataFrame): the independent variables of factors.
def wavelet_dec_rec(self, **kwargs):
This function is designed for wavelet decomposing and recomposing.
input :
kwargs : the kwargs include wave family, mode, and level of wavelet.
output :
rets_dec_s (list): The recomposed detail series of returns (rets).
factors_dec_s (list): The recomposed detail series of factors (factors).
def wavelet_regression(self, **kwargs):
This function is designed for OLS regression of detail series between return and factors at each level.
input :
**kwargs : the kwargs include 'constant': whether the regression includes the constant.
output :
regress (list): the regression results of OLS in package statsmodels.
def fit(self, wave, mode, level, win=None, robust=False, constant=True):
This function is designed for fitting the model.
input :
wave (str) : The chosen wavelet family, which is the same in pywt.
mode (str) : choose multiscale or single scale. 'multi' denotes multiscale. 'single' denotes single scale.
level (int) : the level of multiscale. If 'multi' is chosen, it must be set.
win (int): The rolling window if rolling regression is used.
robust (boolean): whether use the robust covariance matrix.
constant (boolean): whether includes the constant in regression. The DEFAULT is True.
def summary(self, export=False):
This function is designed for printing the summary.
input :
export (boolean): whether export the summary table. The DEFAULT is False.
output :
df (DataFrame): if export is True, then return the summary table.
Demo
portfolio_analysis
Market System Risk (Beta)
Market system risk origins from CAPM (Sharpe, 1965), whose form can be
$$ E(R_i)=R_f+\beta_i[E(R_M)-R_f]. $$
If market is in equilibrium, then the only factor that would drive asset excess return is market system risk premium. Once asset take more market system risk premium, more excess return should be paid. Thus, according to the theory, excess return has positive correlation with betas, which measures quantity of market system risk taken by asset.
In empirical study, stocks are sorted by rolling beta (window=12 months) in ascending order and hereafter grouped into 5 or 10 groups. The average return of stocks between the head group and the tail group testing significantly and the corresponding ascending order of group return suggest the positive correlation of excess return and beta. The univariate and bivariate portfolio analysis are both conducted.
# %% import package
import pandas as pd
import sys, os
sys.path.append(os.path.abspath(".."))
# %% import data
# Monthly return of stocks in China security market
month_return = pd.read_hdf('.\\data\\month_return.h5', key='month_return')
beta = pd.read_hdf('.\\data\\beta.hdf5', key='data')
The dataset contains monthly China A share stock between 2000-01-01 to 2021-12-31 from the CSMAR dataset. WARNING: Do Not use dataset in this demo for any commercial purpose. Since the data are loaded, some preprocessing procedures should be conducted.
# %% data preprocessing
# select the A share stock
month_return = month_return[month_return['Markettype'].isin([1, 4, 16])]
# forward the monthly return for each stock
# emrwd is the return including dividend
month_return['emrwd'] = month_return.groupby(['Stkcd'])['Mretwd'].shift(-1)
# emrnd is the return including no dividend
month_return['emrnd'] = month_return.groupby(['Stkcd'])['Mretnd'].shift(-1)
# % distinguish the stocks whose size is among the up 30% stocks in each month
def percentile(stocks) :
return stocks >= stocks.quantile(q=.3)
month_return['cap'] = month_return.groupby(['Trdmnt'])['Msmvttl'].apply(percentile)
Construct market portfolio return.
# %% construct market portfolio return
import numpy as np
market_portfolio_return = month_return['Mretwd'].groupby(month_return['Trdmnt']).apply(np.mean)
market_portfolio_return.name = 'market_portfolio_return'
month_return = pd.merge(month_return, market_portfolio_return, on=['Trdmnt'])
month_return = month_return.sort_values(['Stkcd', 'Trdmnt'])
Calculate beta.
# %% calculate beta
import statsmodels.api as sm
import numpy as np
reg = month_return.set_index(['Stkcd', 'Trdmnt'])[['Mretwd', 'market_portfolio_return']].dropna()
beta = pd.Series(index=reg.index, dtype=float, name='beta')
for i in reg.groupby('Stkcd'):
row, col = np.shape(i[1])
for j in range(row-12):
model = sm.OLS(i[1].iloc[j:j+12, 0], sm.add_constant(i[1].iloc[j:j+12, 1])).fit()
beta.loc[i[1].index[j+11]] = model.params[1]
reg = pd.merge(reg, beta, left_index=True, right_index=True)
Data need further preprocessing.
# %% Data preprocessing: merge data
month_return['Date_merge'] = pd.to_datetime(month_return['Trdmnt'])
month_return = month_return.set_index(['Stkcd', 'Trdmnt'])
month_return = pd.merge(month_return, beta, left_index=True, right_index=True)
# construct label
# data starts from 2000-01
return_company = month_return[month_return['Date_merge']>='2000-01']
Due to specific requirement of the IPO, some dominant company would purchase a small listed company and join the A share market. Thus, in the research by Liu et al. (2016), the stocks whose size is below the 30% are abandoned.
# %% construct test_data for bivariate analysis
# dataset 1
from portfolio_analysis import Bivariate, Univariate
import numpy as np
# select stocks whose size is among the up 30% stocks in each month and whose trading
# days are more than or equal to 10 days
test_data_1 = return_company[(return_company['cap']==True) & (return_company['Ndaytrd']>=10)]
test_data_1 = test_data_1[['emrwd', 'Msmvttl', 'beta', 'Date_merge']].dropna()
test_data_1 = test_data_1[(test_data_1['Date_merge'] >= '2000-01-01') & (test_data_1['Date_merge'] <= '2019-12-01')]
# Univariate analysis
uni_1 = Univariate(np.array(test_data_1[['emrwd', 'beta', 'Date_merge']]), number=9)
uni_1.summary_and_test()
uni_1.print_summary_by_time()
uni_1.print_summary()
===================================================================================================
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+
| Group | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Diff |
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+
| Average | 0.006 | 0.01 | 0.011 | 0.012 | 0.013 | 0.011 | 0.012 | 0.011 | 0.012 | 0.007 | 0.001 |
| T-Test | 1.213 | 1.937 | 1.996 | 2.017 | 2.155 | 1.752 | 1.905 | 1.74 | 1.745 | 1.02 | 0.294 |
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+
===================================================================================================
# Independent-sort Bivariate Analysis
bi_1 = Bivariate(np.array(test_data_1), number=4)
bi_1.average_by_time()
bi_1.summary_and_test()
bi_1.print_summary_by_time()
bi_1.print_summary()
===============================================================
+-------+-------+--------+--------+--------+--------+--------+
| Group | 1 | 2 | 3 | 4 | 5 | Diff |
+-------+-------+--------+--------+--------+--------+--------+
| 1 | 0.009 | 0.014 | 0.014 | 0.015 | 0.014 | 0.005 |
| | 1.436 | 2.308 | 2.093 | 2.179 | 1.888 | 1.85 |
| 2 | 0.006 | 0.013 | 0.013 | 0.013 | 0.011 | 0.005 |
| | 0.996 | 2.115 | 2.008 | 1.931 | 1.633 | 2.147 |
| 3 | 0.008 | 0.01 | 0.01 | 0.01 | 0.008 | 0.001 |
| | 1.333 | 1.779 | 1.669 | 1.603 | 1.174 | 0.24 |
| 4 | 0.008 | 0.009 | 0.01 | 0.011 | 0.008 | 0.0 |
| | 1.496 | 1.66 | 1.622 | 1.687 | 1.173 | 0.065 |
| 5 | 0.009 | 0.01 | 0.013 | 0.01 | 0.006 | -0.003 |
| | 1.928 | 1.882 | 2.103 | 1.533 | 0.86 | -0.914 |
| Diff | 0.0 | -0.004 | -0.001 | -0.005 | -0.008 | -0.008 |
| | 0.106 | -1.31 | -0.301 | -1.425 | -2.13 | -2.738 |
+-------+-------+--------+--------+--------+--------+--------+
===============================================================
# Dependent-sort Bivariate analysis
bi_1_de = Bivariate(test_data_1, number=4)
bi_1_de.fit(conditional=True)
bi_1_de.print_summary_by_time()
bi_1_de.print_summary()
==================================================================
+----------+--------+--------+--------+--------+--------+--------+
| Group | beta1 | beta2 | beta3 | beta4 | beta5 | Diff |
+----------+--------+--------+--------+--------+--------+--------+
| Msmvttl1 | 0.011 | 0.015 | 0.013 | 0.016 | 0.013 | 0.002 |
| | 1.818 | 2.347 | 1.945 | 2.329 | 1.81 | 0.911 |
| Msmvttl2 | 0.007 | 0.013 | 0.014 | 0.012 | 0.012 | 0.005 |
| | 1.219 | 2.15 | 2.099 | 1.764 | 1.689 | 1.875 |
| Msmvttl3 | 0.009 | 0.01 | 0.01 | 0.01 | 0.008 | -0.001 |
| | 1.547 | 1.736 | 1.613 | 1.58 | 1.169 | -0.169 |
| Msmvttl4 | 0.008 | 0.01 | 0.009 | 0.01 | 0.008 | -0.0 |
| | 1.552 | 1.71 | 1.45 | 1.639 | 1.167 | -0.065 |
| Msmvttl5 | 0.008 | 0.01 | 0.01 | 0.01 | 0.006 | -0.001 |
| | 1.662 | 2.052 | 1.895 | 1.661 | 0.983 | -0.357 |
| Diff | -0.003 | -0.005 | -0.003 | -0.006 | -0.007 | -0.004 |
| | -0.858 | -1.316 | -0.757 | -1.652 | -1.855 | -1.152 |
+----------+--------+--------+--------+--------+--------+--------+
==================================================================
The result from dataset #1 is consistent with literatures that in univariate analysis the differenced return is not significant since the t-value is below 2.3, and in bivariate analysis the differenced return in most part is insignificant since the t-value is less than 2.3, suggesting that market system risk factor provides no excess return. The way of sorting plays no transitional role on the result.
# %% construct test_data for bivariate analysis
# dataset 2
from portfolio_analysis import Bivariate, Univariate
import numpy as np
# select stocks whose size is among the up 30% stocks in each month and whose trading
# days are more than or equal to 10 days
test_data_2 = return_company[(return_company['Ndaytrd']>=10)]
test_data_2 = test_data_2[['emrwd', 'Msmvttl', 'beta', 'Date_merge']].dropna()
test_data_2 = test_data_2[(test_data_2['Date_merge'] >= '2000-01-01') & (test_data_2['Date_merge'] <= '2019-12-01')]
# Univariate analysis
uni_2 = Univariate(np.array(test_data_2[['emrwd', 'beta', 'Date_merge']]), number=9)
uni_2.summary_and_test()
uni_2.print_summary_by_time()
uni_2.print_summary()
====================================================================================================
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+
| Group | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Diff |
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+
| Average | 0.008 | 0.012 | 0.013 | 0.016 | 0.016 | 0.015 | 0.017 | 0.015 | 0.014 | 0.012 | 0.004 |
| T-Test | 1.608 | 2.214 | 2.281 | 2.492 | 2.451 | 2.388 | 2.537 | 2.296 | 2.104 | 1.637 | 1.043 |
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+
====================================================================================================
# Independent-sort Bivariate Analysis
bi_2 = Bivariate(np.array(test_data_2), number=4)
bi_2.average_by_time()
bi_2.summary_and_test()
bi_2.print_summary_by_time()
bi_2.print_summary()
===============================================================
+-------+--------+--------+--------+--------+--------+--------+
| Group | 1 | 2 | 3 | 4 | 5 | Diff |
+-------+--------+--------+--------+--------+--------+--------+
| 1 | 0.019 | 0.023 | 0.026 | 0.027 | 0.027 | 0.008 |
| | 2.657 | 3.184 | 3.538 | 3.44 | 3.017 | 2.203 |
| 2 | 0.011 | 0.014 | 0.015 | 0.017 | 0.016 | 0.004 |
| | 1.782 | 2.22 | 2.235 | 2.502 | 2.152 | 1.785 |
| 3 | 0.007 | 0.013 | 0.014 | 0.013 | 0.01 | 0.003 |
| | 1.236 | 2.23 | 2.122 | 1.89 | 1.505 | 1.379 |
| 4 | 0.008 | 0.01 | 0.009 | 0.011 | 0.009 | 0.001 |
| | 1.493 | 1.775 | 1.52 | 1.718 | 1.291 | 0.31 |
| 5 | 0.009 | 0.011 | 0.012 | 0.01 | 0.006 | -0.004 |
| | 1.916 | 1.919 | 1.887 | 1.556 | 0.846 | -1.035 |
| Diff | -0.01 | -0.012 | -0.014 | -0.017 | -0.021 | -0.011 |
| | -2.132 | -2.866 | -3.566 | -3.669 | -3.58 | -2.665 |
+-------+--------+--------+--------+--------+--------+--------+
===============================================================
# Dependent-sort Biviraite Analysis
bi_2_de = Bivariate(test_data_2, number=4)
bi_2_de.fit(conditional=True)
bi_2_de.print_summary_by_time()
bi_2_de.print_summary()
==================================================================
+----------+--------+--------+--------+--------+--------+--------+
| Group | beta1 | beta2 | beta3 | beta4 | beta5 | Diff |
+----------+--------+--------+--------+--------+--------+--------+
| Msmvttl1 | 0.02 | 0.027 | 0.024 | 0.028 | 0.026 | 0.006 |
| | 2.947 | 3.413 | 3.471 | 3.469 | 3.052 | 1.81 |
| Msmvttl2 | 0.012 | 0.013 | 0.017 | 0.018 | 0.015 | 0.002 |
| | 1.982 | 2.069 | 2.484 | 2.554 | 2.054 | 1.127 |
| Msmvttl3 | 0.008 | 0.014 | 0.013 | 0.012 | 0.011 | 0.003 |
| | 1.391 | 2.3 | 2.052 | 1.841 | 1.545 | 1.154 |
| Msmvttl4 | 0.007 | 0.01 | 0.01 | 0.01 | 0.009 | 0.001 |
| | 1.353 | 1.778 | 1.657 | 1.577 | 1.235 | 0.41 |
| Msmvttl5 | 0.008 | 0.01 | 0.011 | 0.009 | 0.006 | -0.001 |
| | 1.679 | 1.898 | 1.938 | 1.484 | 0.982 | -0.391 |
| Diff | -0.012 | -0.017 | -0.014 | -0.018 | -0.019 | -0.007 |
| | -2.766 | -3.373 | -3.389 | -3.916 | -3.651 | -1.77 |
+----------+--------+--------+--------+--------+--------+--------+
The result from dataset #2 is consistent with literatures that in univariate analysis the differenced return is not significant since the t-value is below 2.3, and in bivariate analysis the differenced return in most part is insignificant since the t-value is less than 2.3, suggesting that market system risk factor provides no excess return. The dependent-sort would weaken the significance of portfolio return.
Size Effect
Size effect, discovered by Fama and French(1993), is probably the most famous and common phenomenon in the main capital markets. Size, as a characteristic of company, is able to predict the future stock return that the bigger company tend to have low return in the future. Fama and French take the effect as a proxy for some background risk factor, probably default risk and bankruptcy risk. Like the US stock market, China A share market exists such effect as well (Liu et al., 2016), which would be constructed and tested as follows.
Stocks are sorted by firm size in ascending order and hereafter grouped into 5 or 10 groups. The average return of stocks between the head group and the tail group testing significantly and the corresponding descending order of group return suggest the existence of size effect.
# %% import package
import pandas as pd
import sys, os
sys.path.append(os.path.abspath(".."))
# %% import data
# Monthly return of Stocks in China Security Market
month_return = pd.read_hdf('.\data\month_return.h5', key='month_return')
The dataset contains monthly China A share stock between 2000-01-01 to 2021-12-31 from the CSMAR dataset. WARNING: Do Not use dataset in this demo for any commercial purpose. Since the data are loaded, some preprocessing procedures should be conducted.
import datetime as dt
# TimeStamp the tradetime
month_return['Time'] = pd.to_datetime(month_return['Trdmnt'])
# convert the time string to the timestamp
month_return['numberTime'] = month_return['Time'].apply(dt.datetime.timestamp)
# forward the monthly return for each stock
month_return['emrwd'] = month_return.groupby(['Stkcd'])['Mretwd'].shift(-1) # emrwd is the return including dividend
month_return['emrnd'] = month_return.groupby(['Stkcd'])['Mretnd'].shift(-1) # emrnd is the return including no dividend
# select the A share stock
month_return = month_return[month_return['Markettype'].isin([1, 4, 16])]
There are several characteristics in A share market, which therefore should be analyzed respectively.
The first specification is the shell effect. Due to specific requirement of the IPO, some dominant company would purchase a small listed company and join the A share market. Thus, in the research by Liu et al. (2016), the stocks whose size is below the 30% are abandoned.
# %% distinguish the stocks whose size is among the up 30% stocks in each month
def percentile(stocks) :
return stocks >= stocks.quantile(q=.3)
month_return['cap'] = month_return.groupby(['Trdmnt'])['Msmvttl'].apply(percentile)
The second specification is the time interval. Before 2017, the size effect is relatively more significant, while since 2017, especially between 2017 and 2019, big companies perform better, and therefore the size effect are neutralized. According to these two specifications, four datasets are formed.
# %% construct test_data for univariate analysis
# dataset 1
from portfolio_analysis import Univariate
import numpy as np
# select stocks whose size is among the up 30% stocks in each month and whose trading
# days are more than or equal to 10 days
test_data_1 = month_return[(month_return['cap']==True) & (month_return['Ndaytrd']>=10)]
# construct data for univariate analysis
test_data_1 = test_data_1[['emrwd', 'Msmvttl', 'Time']].dropna()
test_data_1 = test_data_1[(test_data_1['Time'] >= '2000-01-01') & (test_data_1['Time'] <= '2019-12-01')]
# analysis
uni_1 = Univariate(np.array(test_data_1), number=9)
uni_1.average_by_time()
uni_1.summary_and_test()
uni_1.print_summary_by_time()
uni_1.print_summary()
==========================================================================================================================
+---------------------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+
| Time | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | diff |
+---------------------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+
| 2000-01-01 00:00:00 | 0.124 | 0.144 | 0.126 | 0.129 | 0.1 | 0.129 | 0.095 | 0.103 | 0.114 | 0.135 | 0.011 |
| 2000-02-01 00:00:00 | 0.155 | 0.122 | 0.075 | 0.12 | 0.053 | 0.064 | 0.054 | 0.04 | 0.022 | 0.009 | -0.146 |
| 2000-03-01 00:00:00 | 0.007 | 0.022 | 0.012 | 0.01 | 0.004 | 0.002 | 0.016 | 0.015 | 0.017 | 0.033 | 0.026 |
| 2000-04-01 00:00:00 | 0.034 | 0.042 | 0.042 | 0.043 | 0.03 | 0.024 | 0.049 | 0.022 | 0.021 | 0.021 | -0.013 |
| 2000-05-01 00:00:00 | 0.008 | 0.041 | 0.046 | 0.015 | 0.029 | 0.022 | 0.007 | 0.03 | 0.044 | 0.021 | 0.013 |
| 2000-06-01 00:00:00 | 0.06 | 0.067 | 0.045 | 0.038 | 0.051 | 0.042 | 0.029 | 0.036 | 0.032 | 0.045 | -0.016 |
| 2000-07-01 00:00:00 | 0.017 | -0.003 | 0.003 | 0.001 | -0.013 | -0.008 | -0.014 | -0.003 | -0.012 | -0.028 | -0.045 |
| 2000-08-01 00:00:00 | -0.027 | -0.025 | -0.032 | -0.056 | -0.061 | -0.055 | -0.04 | -0.065 | -0.054 | -0.056 | -0.029 |
| 2000-09-01 00:00:00 | 0.038 | 0.049 | 0.034 | 0.034 | 0.038 | 0.022 | 0.031 | 0.015 | 0.013 | 0.002 | -0.036 |
| 2000-10-01 00:00:00 | 0.056 | 0.069 | 0.063 | 0.063 | 0.063 | 0.069 | 0.042 | 0.046 | 0.053 | 0.059 | 0.004 |
| 2000-11-01 00:00:00 | 0.009 | 0.013 | 0.011 | 0.008 | -0.002 | 0.014 | 0.01 | 0.0 | -0.012 | -0.024 | -0.033 |
| 2000-12-01 00:00:00 | 0.0 | -0.008 | -0.018 | -0.007 | -0.01 | -0.014 | 0.001 | -0.007 | -0.008 | -0.019 | -0.019 |
| 2001-01-01 00:00:00 | -0.077 | -0.058 | -0.067 | -0.064 | -0.053 | -0.055 | -0.063 | -0.055 | -0.048 | -0.05 | 0.027 |
| 2001-02-01 00:00:00 | 0.096 | 0.072 | 0.085 | 0.074 | 0.088 | 0.079 | 0.075 | 0.061 | 0.065 | 0.056 | -0.04 |
| 2001-03-01 00:00:00 | 0.015 | 0.009 | -0.01 | -0.001 | -0.007 | -0.011 | 0.001 | -0.012 | -0.009 | -0.017 | -0.032 |
| 2001-04-01 00:00:00 | 0.073 | 0.045 | 0.051 | 0.049 | 0.038 | 0.03 | 0.039 | 0.029 | 0.016 | 0.01 | -0.063 |
| 2001-05-01 00:00:00 | 0.018 | 0.01 | 0.012 | 0.012 | 0.019 | 0.002 | -0.005 | 0.015 | -0.01 | -0.002 | -0.02 |
| 2001-06-01 00:00:00 | -0.138 | -0.138 | -0.129 | -0.134 | -0.141 | -0.149 | -0.123 | -0.131 | -0.13 | -0.13 | 0.009 |
| 2001-07-01 00:00:00 | -0.031 | -0.035 | -0.034 | -0.039 | -0.038 | -0.041 | -0.04 | -0.03 | -0.034 | -0.049 | -0.018 |
| 2001-08-01 00:00:00 | -0.055 | -0.067 | -0.048 | -0.067 | -0.048 | -0.047 | -0.046 | -0.047 | -0.05 | -0.022 | 0.033 |
| 2001-09-01 00:00:00 | -0.062 | -0.054 | -0.052 | -0.057 | -0.056 | -0.066 | -0.053 | -0.046 | -0.053 | -0.028 | 0.034 |
| 2001-10-01 00:00:00 | 0.057 | 0.057 | 0.042 | 0.054 | 0.046 | 0.039 | 0.041 | 0.034 | 0.039 | 0.021 | -0.035 |
| 2001-11-01 00:00:00 | -0.067 | -0.082 | -0.069 | -0.078 | -0.067 | -0.063 | -0.067 | -0.058 | -0.05 | -0.047 | 0.021 |
| 2001-12-01 00:00:00 | -0.141 | -0.14 | -0.119 | -0.121 | -0.117 | -0.116 | -0.108 | -0.1 | -0.087 | -0.062 | 0.079 |
| 2002-01-01 00:00:00 | 0.035 | 0.044 | 0.043 | 0.036 | 0.03 | 0.032 | 0.028 | 0.025 | 0.016 | 0.011 | -0.024 |
| 2002-02-01 00:00:00 | 0.097 | 0.08 | 0.076 | 0.078 | 0.069 | 0.076 | 0.076 | 0.056 | 0.061 | 0.032 | -0.065 |
| 2002-03-01 00:00:00 | 0.057 | 0.059 | 0.048 | 0.037 | 0.053 | 0.042 | 0.028 | 0.037 | 0.031 | 0.033 | -0.025 |
| 2002-04-01 00:00:00 | -0.095 | -0.089 | -0.095 | -0.093 | -0.092 | -0.095 | -0.09 | -0.089 | -0.092 | -0.075 | 0.02 |
| 2002-05-01 00:00:00 | 0.116 | 0.115 | 0.11 | 0.113 | 0.122 | 0.114 | 0.142 | 0.123 | 0.152 | 0.158 | 0.042 |
| 2002-06-01 00:00:00 | -0.036 | -0.034 | -0.03 | -0.034 | -0.041 | -0.04 | -0.04 | -0.049 | -0.041 | -0.045 | -0.009 |
| 2002-07-01 00:00:00 | 0.011 | 0.004 | 0.005 | -0.0 | 0.009 | 0.008 | 0.007 | 0.011 | -0.003 | 0.005 | -0.006 |
| 2002-08-01 00:00:00 | -0.058 | -0.056 | -0.065 | -0.059 | -0.057 | -0.059 | -0.054 | -0.046 | -0.05 | -0.047 | 0.011 |
| 2002-09-01 00:00:00 | -0.073 | -0.06 | -0.059 | -0.053 | -0.049 | -0.057 | -0.045 | -0.045 | -0.049 | -0.044 | 0.028 |
| 2002-10-01 00:00:00 | -0.084 | -0.093 | -0.087 | -0.079 | -0.071 | -0.076 | -0.077 | -0.053 | -0.046 | -0.033 | 0.052 |
| 2002-11-01 00:00:00 | -0.059 | -0.055 | -0.056 | -0.058 | -0.051 | -0.062 | -0.05 | -0.05 | -0.05 | -0.045 | 0.013 |
| 2002-12-01 00:00:00 | 0.115 | 0.111 | 0.09 | 0.103 | 0.099 | 0.085 | 0.076 | 0.078 | 0.078 | 0.095 | -0.02 |
| 2003-01-01 00:00:00 | 0.015 | 0.012 | 0.019 | 0.01 | 0.01 | 0.012 | 0.014 | 0.012 | 0.004 | 0.006 | -0.009 |
| 2003-02-01 00:00:00 | -0.03 | -0.037 | -0.032 | -0.031 | -0.023 | -0.026 | -0.022 | -0.009 | -0.0 | 0.013 | 0.043 |
| 2003-03-01 00:00:00 | -0.07 | -0.041 | -0.05 | -0.048 | -0.037 | -0.02 | -0.023 | 0.002 | 0.002 | 0.033 | 0.104 |
| 2003-04-01 00:00:00 | 0.028 | 0.041 | 0.027 | 0.038 | 0.042 | 0.034 | 0.057 | 0.047 | 0.054 | 0.058 | 0.03 |
| 2003-05-01 00:00:00 | -0.067 | -0.063 | -0.074 | -0.07 | -0.079 | -0.072 | -0.082 | -0.056 | -0.06 | -0.065 | 0.002 |
| 2003-06-01 00:00:00 | -0.036 | -0.044 | -0.037 | -0.031 | -0.043 | -0.023 | -0.022 | -0.015 | 0.006 | 0.016 | 0.052 |
| 2003-07-01 00:00:00 | -0.02 | -0.016 | -0.027 | -0.041 | -0.029 | -0.037 | -0.032 | -0.025 | -0.029 | -0.043 | -0.022 |
| 2003-08-01 00:00:00 | -0.044 | -0.043 | -0.056 | -0.035 | -0.034 | -0.037 | -0.045 | -0.049 | -0.041 | -0.039 | 0.006 |
| 2003-09-01 00:00:00 | -0.081 | -0.077 | -0.073 | -0.066 | -0.062 | -0.064 | -0.042 | -0.032 | -0.023 | 0.011 | 0.092 |
| 2003-10-01 00:00:00 | 0.008 | 0.022 | 0.026 | 0.035 | 0.033 | 0.015 | 0.026 | 0.018 | 0.014 | 0.03 | 0.022 |
| 2003-11-01 00:00:00 | -0.019 | -0.021 | -0.028 | -0.016 | 0.01 | 0.013 | 0.022 | 0.022 | 0.035 | 0.088 | 0.106 |
| 2003-12-01 00:00:00 | 0.091 | 0.103 | 0.097 | 0.099 | 0.084 | 0.081 | 0.067 | 0.067 | 0.075 | 0.047 | -0.044 |
| 2004-01-01 00:00:00 | 0.122 | 0.097 | 0.083 | 0.093 | 0.11 | 0.081 | 0.077 | 0.074 | 0.071 | 0.051 | -0.072 |
| 2004-02-01 00:00:00 | 0.042 | 0.046 | 0.035 | 0.052 | 0.052 | 0.029 | 0.036 | 0.033 | 0.028 | 0.028 | -0.014 |
| 2004-03-01 00:00:00 | -0.103 | -0.086 | -0.1 | -0.1 | -0.091 | -0.093 | -0.083 | -0.101 | -0.086 | -0.116 | -0.013 |
| 2004-04-01 00:00:00 | -0.029 | -0.017 | -0.009 | -0.025 | -0.014 | -0.03 | -0.019 | -0.026 | -0.035 | -0.024 | 0.005 |
| 2004-05-01 00:00:00 | -0.128 | -0.131 | -0.135 | -0.134 | -0.132 | -0.126 | -0.114 | -0.124 | -0.111 | -0.085 | 0.043 |
| 2004-06-01 00:00:00 | -0.026 | -0.034 | -0.022 | -0.022 | 0.004 | 0.007 | 0.01 | 0.005 | 0.021 | 0.003 | 0.028 |
| 2004-07-01 00:00:00 | -0.049 | -0.046 | -0.052 | -0.057 | -0.058 | -0.059 | -0.062 | -0.066 | -0.042 | -0.036 | 0.013 |
| 2004-08-01 00:00:00 | 0.061 | 0.043 | 0.053 | 0.045 | 0.053 | 0.064 | 0.057 | 0.062 | 0.056 | 0.062 | 0.001 |
| 2004-09-01 00:00:00 | -0.075 | -0.053 | -0.076 | -0.048 | -0.057 | -0.066 | -0.061 | -0.03 | -0.018 | -0.053 | 0.022 |
| 2004-10-01 00:00:00 | 0.059 | 0.05 | 0.04 | 0.041 | 0.049 | 0.046 | 0.032 | 0.025 | 0.002 | -0.005 | -0.064 |
| 2004-11-01 00:00:00 | -0.078 | -0.08 | -0.086 | -0.079 | -0.09 | -0.093 | -0.077 | -0.066 | -0.076 | -0.048 | 0.03 |
| 2004-12-01 00:00:00 | -0.076 | -0.073 | -0.084 | -0.079 | -0.079 | -0.08 | -0.078 | -0.078 | -0.069 | -0.047 | 0.029 |
| 2005-01-01 00:00:00 | 0.112 | 0.11 | 0.107 | 0.102 | 0.116 | 0.115 | 0.117 | 0.095 | 0.093 | 0.093 | -0.019 |
| 2005-02-01 00:00:00 | -0.147 | -0.137 | -0.138 | -0.133 | -0.117 | -0.121 | -0.112 | -0.121 | -0.088 | -0.086 | 0.06 |
| 2005-03-01 00:00:00 | -0.107 | -0.076 | -0.084 | -0.049 | -0.067 | -0.05 | -0.041 | -0.037 | -0.008 | 0.012 | 0.119 |
| 2005-04-01 00:00:00 | -0.015 | -0.024 | -0.026 | -0.033 | -0.04 | -0.054 | -0.059 | -0.079 | -0.077 | -0.1 | -0.085 |
| 2005-05-01 00:00:00 | -0.001 | 0.001 | -0.001 | -0.003 | 0.003 | -0.011 | -0.004 | 0.011 | -0.005 | 0.037 | 0.038 |
| 2005-06-01 00:00:00 | -0.083 | -0.07 | -0.079 | -0.07 | -0.058 | -0.063 | -0.053 | -0.036 | -0.012 | 0.015 | 0.097 |
| 2005-07-01 00:00:00 | 0.169 | 0.184 | 0.163 | 0.159 | 0.131 | 0.132 | 0.127 | 0.139 | 0.073 | 0.048 | -0.121 |
| 2005-08-01 00:00:00 | 0.02 | 0.008 | 0.007 | 0.025 | 0.028 | 0.024 | 0.035 | 0.036 | 0.016 | -0.013 | -0.034 |
| 2005-09-01 00:00:00 | -0.071 | -0.05 | -0.067 | -0.043 | -0.062 | -0.055 | -0.056 | -0.042 | -0.057 | -0.053 | 0.019 |
| 2005-10-01 00:00:00 | 0.018 | 0.01 | 0.019 | 0.005 | 0.016 | 0.016 | -0.014 | -0.014 | -0.019 | -0.004 | -0.022 |
| 2005-11-01 00:00:00 | 0.016 | 0.01 | 0.018 | 0.022 | 0.033 | 0.043 | 0.047 | 0.067 | 0.062 | 0.079 | 0.063 |
| 2005-12-01 00:00:00 | 0.098 | 0.067 | 0.09 | 0.088 | 0.094 | 0.119 | 0.141 | 0.12 | 0.13 | 0.088 | -0.01 |
| 2006-01-01 00:00:00 | 0.034 | 0.026 | 0.023 | 0.019 | 0.021 | 0.017 | 0.017 | -0.007 | 0.022 | 0.046 | 0.012 |
| 2006-02-01 00:00:00 | -0.002 | 0.001 | 0.006 | 0.008 | 0.022 | 0.025 | 0.042 | 0.048 | 0.048 | 0.025 | 0.027 |
| 2006-03-01 00:00:00 | 0.093 | 0.106 | 0.101 | 0.089 | 0.122 | 0.118 | 0.133 | 0.145 | 0.16 | 0.127 | 0.034 |
| 2006-04-01 00:00:00 | 0.297 | 0.251 | 0.284 | 0.265 | 0.261 | 0.222 | 0.266 | 0.201 | 0.208 | 0.156 | -0.141 |
| 2006-05-01 00:00:00 | 0.065 | 0.091 | 0.067 | 0.052 | 0.058 | 0.04 | 0.048 | 0.045 | 0.013 | 0.02 | -0.045 |
| 2006-06-01 00:00:00 | -0.002 | -0.038 | -0.039 | -0.022 | -0.043 | -0.043 | -0.051 | -0.059 | -0.056 | -0.088 | -0.086 |
| 2006-07-01 00:00:00 | 0.029 | 0.016 | 0.042 | 0.028 | 0.042 | 0.029 | 0.057 | 0.031 | 0.04 | 0.024 | -0.005 |
| 2006-08-01 00:00:00 | 0.049 | 0.056 | 0.049 | 0.039 | 0.038 | 0.052 | 0.026 | 0.042 | 0.041 | 0.044 | -0.005 |
| 2006-09-01 00:00:00 | -0.011 | 0.01 | 0.016 | -0.013 | -0.029 | 0.004 | -0.01 | 0.029 | 0.014 | 0.034 | 0.045 |
| 2006-10-01 00:00:00 | 0.014 | 0.024 | 0.034 | 0.038 | 0.058 | 0.055 | 0.063 | 0.079 | 0.139 | 0.183 | 0.169 |
| 2006-11-01 00:00:00 | 0.055 | 0.032 | 0.036 | 0.043 | 0.072 | 0.061 | 0.088 | 0.097 | 0.099 | 0.17 | 0.115 |
| 2006-12-01 00:00:00 | 0.296 | 0.254 | 0.262 | 0.251 | 0.233 | 0.239 | 0.232 | 0.209 | 0.254 | 0.173 | -0.122 |
| 2007-01-01 00:00:00 | 0.254 | 0.179 | 0.218 | 0.187 | 0.26 | 0.177 | 0.139 | 0.162 | 0.128 | 0.066 | -0.188 |
| 2007-02-01 00:00:00 | 0.196 | 0.203 | 0.179 | 0.163 | 0.171 | 0.175 | 0.142 | 0.103 | 0.072 | 0.09 | -0.107 |
| 2007-03-01 00:00:00 | 0.389 | 0.32 | 0.358 | 0.298 | 0.342 | 0.341 | 0.329 | 0.362 | 0.337 | 0.262 | -0.127 |
| 2007-04-01 00:00:00 | 0.067 | 0.093 | 0.064 | 0.065 | 0.178 | 0.113 | 0.081 | 0.092 | 0.143 | 0.118 | 0.051 |
| 2007-05-01 00:00:00 | -0.205 | -0.205 | -0.177 | -0.162 | -0.144 | -0.171 | -0.121 | -0.109 | -0.064 | -0.028 | 0.176 |
| 2007-06-01 00:00:00 | 0.235 | 0.26 | 0.231 | 0.228 | 0.216 | 0.2 | 0.192 | 0.196 | 0.182 | 0.186 | -0.049 |
| 2007-07-01 00:00:00 | 0.093 | 0.095 | 0.108 | 0.086 | 0.133 | 0.093 | 0.108 | 0.131 | 0.161 | 0.183 | 0.09 |
| 2007-08-01 00:00:00 | 0.025 | 0.015 | 0.043 | 0.059 | 0.03 | 0.046 | 0.018 | 0.038 | 0.082 | 0.073 | 0.048 |
| 2007-09-01 00:00:00 | -0.113 | -0.135 | -0.115 | -0.099 | -0.099 | -0.115 | -0.093 | -0.091 | -0.072 | 0.016 | 0.129 |
| 2007-10-01 00:00:00 | -0.038 | -0.058 | -0.05 | -0.084 | -0.048 | -0.112 | -0.091 | -0.13 | -0.163 | -0.184 | -0.147 |
| 2007-11-01 00:00:00 | 0.207 | 0.201 | 0.219 | 0.213 | 0.218 | 0.209 | 0.23 | 0.192 | 0.192 | 0.135 | -0.073 |
| 2007-12-01 00:00:00 | -0.061 | -0.058 | -0.075 | -0.052 | -0.058 | -0.06 | -0.065 | -0.078 | -0.079 | -0.141 | -0.081 |
| 2008-01-01 00:00:00 | 0.11 | 0.096 | 0.1 | 0.089 | 0.083 | 0.068 | 0.063 | 0.05 | 0.03 | 0.012 | -0.097 |
| 2008-02-01 00:00:00 | -0.188 | -0.189 | -0.196 | -0.202 | -0.204 | -0.199 | -0.214 | -0.211 | -0.233 | -0.212 | -0.023 |
| 2008-03-01 00:00:00 | -0.061 | -0.091 | -0.055 | -0.055 | -0.048 | -0.038 | -0.013 | 0.003 | 0.03 | 0.057 | 0.118 |
| 2008-04-01 00:00:00 | 0.002 | -0.017 | -0.03 | -0.039 | -0.035 | -0.039 | -0.053 | -0.045 | -0.054 | -0.089 | -0.091 |
| 2008-05-01 00:00:00 | -0.275 | -0.261 | -0.249 | -0.262 | -0.252 | -0.239 | -0.247 | -0.242 | -0.227 | -0.215 | 0.06 |
| 2008-06-01 00:00:00 | 0.114 | 0.102 | 0.107 | 0.105 | 0.081 | 0.074 | 0.08 | 0.05 | 0.044 | -0.005 | -0.119 |
| 2008-07-01 00:00:00 | -0.244 | -0.214 | -0.223 | -0.248 | -0.229 | -0.235 | -0.253 | -0.226 | -0.239 | -0.169 | 0.075 |
| 2008-08-01 00:00:00 | -0.101 | -0.085 | -0.112 | -0.075 | -0.082 | -0.084 | -0.064 | -0.046 | -0.041 | -0.016 | 0.085 |
| 2008-09-01 00:00:00 | -0.261 | -0.263 | -0.251 | -0.261 | -0.271 | -0.265 | -0.26 | -0.273 | -0.261 | -0.257 | 0.003 |
| 2008-10-01 00:00:00 | 0.233 | 0.211 | 0.233 | 0.211 | 0.202 | 0.175 | 0.162 | 0.166 | 0.15 | 0.12 | -0.112 |
| 2008-11-01 00:00:00 | 0.116 | 0.053 | 0.073 | 0.073 | 0.043 | 0.054 | 0.064 | 0.052 | 0.041 | -0.002 | -0.118 |
| 2008-12-01 00:00:00 | 0.157 | 0.155 | 0.167 | 0.186 | 0.17 | 0.175 | 0.167 | 0.161 | 0.147 | 0.104 | -0.053 |
| 2009-01-01 00:00:00 | 0.091 | 0.081 | 0.091 | 0.093 | 0.073 | 0.084 | 0.077 | 0.064 | 0.06 | 0.06 | -0.031 |
| 2009-02-01 00:00:00 | 0.244 | 0.249 | 0.213 | 0.229 | 0.205 | 0.217 | 0.209 | 0.187 | 0.213 | 0.178 | -0.066 |
| 2009-03-01 00:00:00 | 0.07 | 0.076 | 0.085 | 0.074 | 0.049 | 0.039 | 0.078 | 0.025 | 0.065 | 0.046 | -0.025 |
| 2009-04-01 00:00:00 | 0.078 | 0.071 | 0.085 | 0.075 | 0.045 | 0.054 | 0.051 | 0.038 | 0.062 | 0.046 | -0.031 |
| 2009-05-01 00:00:00 | 0.038 | 0.035 | 0.049 | 0.052 | 0.037 | 0.052 | 0.049 | 0.081 | 0.072 | 0.145 | 0.107 |
| 2009-06-01 00:00:00 | 0.138 | 0.163 | 0.12 | 0.155 | 0.136 | 0.13 | 0.166 | 0.167 | 0.179 | 0.195 | 0.057 |
| 2009-07-01 00:00:00 | -0.155 | -0.136 | -0.135 | -0.147 | -0.146 | -0.168 | -0.171 | -0.177 | -0.194 | -0.245 | -0.09 |
| 2009-08-01 00:00:00 | 0.022 | 0.022 | 0.049 | 0.02 | 0.032 | 0.035 | 0.036 | 0.046 | 0.045 | 0.049 | 0.028 |
| 2009-09-01 00:00:00 | 0.125 | 0.117 | 0.133 | 0.126 | 0.133 | 0.115 | 0.108 | 0.11 | 0.107 | 0.085 | -0.039 |
| 2009-10-01 00:00:00 | 0.16 | 0.155 | 0.174 | 0.175 | 0.151 | 0.147 | 0.142 | 0.112 | 0.103 | 0.078 | -0.082 |
| 2009-11-01 00:00:00 | 0.038 | 0.027 | 0.03 | 0.029 | 0.024 | 0.001 | 0.005 | -0.001 | -0.006 | 0.008 | -0.03 |
| 2009-12-01 00:00:00 | -0.02 | -0.026 | -0.024 | -0.042 | -0.012 | -0.019 | -0.038 | -0.04 | -0.075 | -0.103 | -0.084 |
| 2010-01-01 00:00:00 | 0.068 | 0.062 | 0.059 | 0.073 | 0.055 | 0.057 | 0.058 | 0.047 | 0.039 | 0.021 | -0.048 |
| 2010-02-01 00:00:00 | 0.055 | 0.037 | 0.043 | 0.043 | 0.053 | 0.043 | 0.009 | 0.01 | 0.016 | 0.015 | -0.04 |
| 2010-03-01 00:00:00 | -0.085 | -0.067 | -0.082 | -0.071 | -0.059 | -0.083 | -0.078 | -0.053 | -0.067 | -0.081 | 0.004 |
| 2010-04-01 00:00:00 | -0.088 | -0.092 | -0.095 | -0.075 | -0.067 | -0.079 | -0.072 | -0.071 | -0.081 | -0.094 | -0.006 |
| 2010-05-01 00:00:00 | -0.081 | -0.097 | -0.083 | -0.099 | -0.092 | -0.103 | -0.099 | -0.098 | -0.097 | -0.077 | 0.005 |
| 2010-06-01 00:00:00 | 0.147 | 0.149 | 0.151 | 0.17 | 0.148 | 0.142 | 0.132 | 0.133 | 0.135 | 0.131 | -0.016 |
| 2010-07-01 00:00:00 | 0.108 | 0.112 | 0.098 | 0.094 | 0.081 | 0.085 | 0.122 | 0.079 | 0.059 | 0.019 | -0.089 |
| 2010-08-01 00:00:00 | -0.004 | 0.009 | 0.012 | -0.004 | -0.016 | 0.008 | 0.013 | 0.015 | 0.019 | 0.017 | 0.021 |
| 2010-09-01 00:00:00 | 0.108 | 0.074 | 0.085 | 0.097 | 0.08 | 0.103 | 0.105 | 0.092 | 0.148 | 0.155 | 0.047 |
| 2010-10-01 00:00:00 | 0.036 | 0.021 | 0.002 | 0.015 | 0.01 | 0.019 | 0.02 | -0.001 | -0.035 | -0.066 | -0.102 |
| 2010-11-01 00:00:00 | -0.024 | -0.025 | -0.031 | -0.036 | -0.026 | -0.035 | -0.034 | -0.02 | -0.006 | 0.006 | 0.03 |
| 2010-12-01 00:00:00 | -0.058 | -0.061 | -0.059 | -0.05 | -0.074 | -0.064 | -0.068 | -0.067 | -0.051 | -0.018 | 0.04 |
| 2011-01-01 00:00:00 | 0.098 | 0.093 | 0.11 | 0.096 | 0.105 | 0.103 | 0.101 | 0.097 | 0.069 | 0.052 | -0.046 |
| 2011-02-01 00:00:00 | 0.004 | -0.018 | -0.023 | -0.017 | -0.026 | -0.038 | -0.023 | -0.027 | -0.033 | -0.02 | -0.024 |
| 2011-03-01 00:00:00 | -0.054 | -0.036 | -0.052 | -0.05 | -0.027 | -0.035 | -0.039 | -0.039 | -0.02 | -0.022 | 0.032 |
| 2011-04-01 00:00:00 | -0.081 | -0.067 | -0.055 | -0.083 | -0.082 | -0.076 | -0.084 | -0.085 | -0.077 | -0.066 | 0.016 |
| 2011-05-01 00:00:00 | 0.034 | 0.031 | 0.042 | 0.023 | 0.041 | 0.032 | 0.031 | 0.036 | 0.03 | 0.03 | -0.004 |
| 2011-06-01 00:00:00 | 0.033 | 0.026 | 0.038 | 0.021 | 0.017 | 0.022 | 0.024 | 0.016 | -0.0 | -0.017 | -0.05 |
| 2011-07-01 00:00:00 | -0.017 | -0.032 | -0.026 | -0.032 | -0.036 | -0.034 | -0.034 | -0.047 | -0.041 | -0.054 | -0.036 |
| 2011-08-01 00:00:00 | -0.123 | -0.115 | -0.124 | -0.131 | -0.136 | -0.128 | -0.141 | -0.125 | -0.111 | -0.093 | 0.029 |
| 2011-09-01 00:00:00 | 0.041 | 0.045 | 0.046 | 0.041 | 0.047 | 0.026 | 0.052 | 0.045 | 0.036 | 0.034 | -0.006 |
| 2011-10-01 00:00:00 | -0.045 | -0.038 | -0.029 | -0.04 | -0.041 | -0.042 | -0.045 | -0.049 | -0.056 | -0.069 | -0.024 |
| 2011-11-01 00:00:00 | -0.17 | -0.17 | -0.174 | -0.151 | -0.164 | -0.159 | -0.137 | -0.13 | -0.102 | -0.082 | 0.087 |
| 2011-12-01 00:00:00 | -0.016 | -0.018 | -0.006 | -0.018 | -0.018 | 0.003 | -0.013 | -0.0 | -0.002 | 0.045 | 0.062 |
| 2012-01-01 00:00:00 | 0.143 | 0.138 | 0.135 | 0.136 | 0.129 | 0.128 | 0.131 | 0.119 | 0.109 | 0.072 | -0.071 |
| 2012-02-01 00:00:00 | -0.081 | -0.061 | -0.075 | -0.08 | -0.077 | -0.078 | -0.073 | -0.079 | -0.071 | -0.074 | 0.007 |
| 2012-03-01 00:00:00 | 0.088 | 0.069 | 0.064 | 0.073 | 0.07 | 0.064 | 0.063 | 0.053 | 0.063 | 0.072 | -0.016 |
| 2012-04-01 00:00:00 | 0.022 | 0.024 | 0.025 | 0.017 | 0.017 | 0.033 | 0.024 | 0.028 | 0.038 | 0.008 | -0.014 |
| 2012-05-01 00:00:00 | -0.06 | -0.06 | -0.061 | -0.073 | -0.067 | -0.066 | -0.071 | -0.071 | -0.058 | -0.057 | 0.003 |
| 2012-06-01 00:00:00 | -0.11 | -0.094 | -0.092 | -0.103 | -0.099 | -0.089 | -0.087 | -0.082 | -0.075 | -0.054 | 0.057 |
| 2012-07-01 00:00:00 | 0.042 | 0.045 | 0.033 | 0.026 | 0.033 | 0.0 | 0.01 | -0.022 | -0.034 | -0.056 | -0.098 |
| 2012-08-01 00:00:00 | 0.003 | 0.004 | 0.002 | -0.005 | 0.004 | 0.002 | 0.022 | 0.007 | 0.029 | 0.044 | 0.04 |
| 2012-09-01 00:00:00 | -0.004 | 0.002 | 0.008 | -0.0 | -0.015 | 0.0 | -0.012 | -0.02 | -0.017 | -0.016 | -0.012 |
| 2012-10-01 00:00:00 | -0.119 | -0.121 | -0.125 | -0.113 | -0.124 | -0.113 | -0.123 | -0.103 | -0.097 | -0.059 | 0.06 |
| 2012-11-01 00:00:00 | 0.164 | 0.178 | 0.184 | 0.163 | 0.163 | 0.182 | 0.181 | 0.166 | 0.171 | 0.172 | 0.008 |
| 2012-12-01 00:00:00 | 0.07 | 0.072 | 0.066 | 0.069 | 0.065 | 0.054 | 0.065 | 0.061 | 0.049 | 0.057 | -0.013 |
| 2013-01-01 00:00:00 | 0.044 | 0.033 | 0.036 | 0.037 | 0.038 | 0.043 | 0.042 | 0.039 | 0.024 | -0.004 | -0.047 |
| 2013-02-01 00:00:00 | -0.032 | -0.024 | -0.031 | -0.027 | -0.047 | -0.041 | -0.047 | -0.057 | -0.04 | -0.05 | -0.018 |
| 2013-03-01 00:00:00 | -0.032 | -0.032 | -0.025 | -0.026 | -0.031 | -0.027 | -0.019 | -0.017 | -0.026 | -0.021 | 0.011 |
| 2013-04-01 00:00:00 | 0.158 | 0.154 | 0.147 | 0.142 | 0.152 | 0.156 | 0.15 | 0.125 | 0.125 | 0.067 | -0.091 |
| 2013-05-01 00:00:00 | -0.16 | -0.157 | -0.157 | -0.157 | -0.154 | -0.154 | -0.164 | -0.151 | -0.154 | -0.136 | 0.024 |
| 2013-06-01 00:00:00 | 0.073 | 0.084 | 0.079 | 0.069 | 0.054 | 0.07 | 0.073 | 0.045 | 0.062 | 0.014 | -0.058 |
| 2013-07-01 00:00:00 | 0.102 | 0.093 | 0.076 | 0.064 | 0.102 | 0.072 | 0.082 | 0.063 | 0.069 | 0.058 | -0.045 |
| 2013-08-01 00:00:00 | 0.053 | 0.064 | 0.046 | 0.045 | 0.048 | 0.061 | 0.043 | 0.051 | 0.07 | 0.047 | -0.006 |
| 2013-09-01 00:00:00 | -0.025 | -0.023 | -0.016 | -0.035 | -0.039 | -0.033 | -0.034 | -0.029 | -0.034 | -0.04 | -0.014 |
| 2013-10-01 00:00:00 | 0.092 | 0.095 | 0.083 | 0.083 | 0.084 | 0.083 | 0.055 | 0.063 | 0.052 | 0.039 | -0.054 |
| 2013-11-01 00:00:00 | -0.034 | -0.029 | -0.038 | -0.032 | -0.045 | -0.027 | -0.028 | -0.047 | -0.033 | -0.046 | -0.012 |
| 2013-12-01 00:00:00 | 0.001 | 0.017 | 0.038 | 0.057 | 0.027 | 0.002 | 0.036 | 0.002 | 0.012 | -0.052 | -0.053 |
| 2014-01-01 00:00:00 | 0.047 | 0.042 | 0.044 | 0.044 | 0.045 | 0.015 | 0.023 | 0.016 | -0.003 | -0.021 | -0.068 |
| 2014-02-01 00:00:00 | -0.023 | -0.02 | -0.04 | -0.038 | -0.039 | -0.039 | -0.043 | -0.051 | -0.041 | -0.028 | -0.005 |
| 2014-03-01 00:00:00 | -0.009 | -0.027 | -0.031 | -0.028 | -0.026 | -0.012 | -0.018 | -0.026 | -0.009 | -0.005 | 0.005 |
| 2014-04-01 00:00:00 | 0.027 | 0.035 | 0.034 | 0.028 | 0.05 | 0.025 | 0.02 | 0.022 | 0.018 | 0.002 | -0.024 |
| 2014-05-01 00:00:00 | 0.064 | 0.059 | 0.046 | 0.054 | 0.055 | 0.031 | 0.037 | 0.038 | 0.026 | 0.019 | -0.045 |
| 2014-06-01 00:00:00 | 0.09 | 0.076 | 0.076 | 0.068 | 0.06 | 0.082 | 0.075 | 0.067 | 0.065 | 0.079 | -0.012 |
| 2014-07-01 00:00:00 | 0.065 | 0.06 | 0.06 | 0.054 | 0.044 | 0.057 | 0.038 | 0.053 | 0.041 | 0.004 | -0.061 |
| 2014-08-01 00:00:00 | 0.152 | 0.141 | 0.143 | 0.124 | 0.119 | 0.114 | 0.127 | 0.101 | 0.09 | 0.064 | -0.089 |
| 2014-09-01 00:00:00 | 0.044 | 0.018 | 0.014 | 0.017 | 0.014 | 0.013 | 0.014 | 0.004 | 0.015 | 0.029 | -0.015 |
| 2014-10-01 00:00:00 | 0.067 | 0.049 | 0.062 | 0.07 | 0.045 | 0.04 | 0.048 | 0.055 | 0.076 | 0.123 | 0.056 |
| 2014-11-01 00:00:00 | -0.08 | -0.069 | -0.055 | -0.049 | -0.046 | -0.022 | 0.002 | -0.004 | 0.074 | 0.246 | 0.327 |
| 2014-12-01 00:00:00 | 0.108 | 0.105 | 0.094 | 0.097 | 0.087 | 0.068 | 0.077 | 0.082 | 0.062 | -0.026 | -0.135 |
| 2015-01-01 00:00:00 | 0.078 | 0.077 | 0.09 | 0.087 | 0.094 | 0.099 | 0.088 | 0.104 | 0.073 | 0.052 | -0.026 |
| 2015-02-01 00:00:00 | 0.259 | 0.235 | 0.248 | 0.252 | 0.229 | 0.214 | 0.228 | 0.209 | 0.184 | 0.142 | -0.116 |
| 2015-03-01 00:00:00 | 0.213 | 0.168 | 0.14 | 0.166 | 0.162 | 0.168 | 0.155 | 0.153 | 0.154 | 0.203 | -0.01 |
| 2015-04-01 00:00:00 | 0.302 | 0.264 | 0.261 | 0.253 | 0.252 | 0.252 | 0.204 | 0.182 | 0.119 | 0.036 | -0.266 |
| 2015-05-01 00:00:00 | -0.114 | -0.147 | -0.155 | -0.158 | -0.149 | -0.145 | -0.119 | -0.144 | -0.133 | -0.079 | 0.035 |
| 2015-06-01 00:00:00 | -0.212 | -0.204 | -0.201 | -0.192 | -0.177 | -0.176 | -0.15 | -0.17 | -0.154 | -0.159 | 0.052 |
| 2015-07-01 00:00:00 | -0.151 | -0.156 | -0.145 | -0.149 | -0.161 | -0.136 | -0.177 | -0.177 | -0.15 | -0.133 | 0.018 |
| 2015-08-01 00:00:00 | 0.012 | 0.0 | -0.017 | -0.004 | -0.016 | -0.022 | -0.028 | -0.045 | -0.062 | -0.053 | -0.065 |
| 2015-09-01 00:00:00 | 0.257 | 0.252 | 0.26 | 0.243 | 0.206 | 0.236 | 0.222 | 0.21 | 0.186 | 0.123 | -0.134 |
| 2015-10-01 00:00:00 | 0.152 | 0.146 | 0.116 | 0.116 | 0.096 | 0.063 | 0.069 | 0.049 | 0.024 | 0.009 | -0.143 |
| 2015-11-01 00:00:00 | 0.07 | 0.065 | 0.038 | 0.03 | 0.049 | 0.026 | 0.034 | 0.018 | 0.024 | 0.032 | -0.038 |
| 2015-12-01 00:00:00 | -0.309 | -0.309 | -0.31 | -0.31 | -0.311 | -0.295 | -0.301 | -0.308 | -0.278 | -0.243 | 0.066 |
| 2016-01-01 00:00:00 | -0.012 | -0.031 | -0.023 | -0.032 | -0.028 | -0.021 | -0.021 | -0.025 | -0.013 | -0.025 | -0.013 |
| 2016-02-01 00:00:00 | 0.204 | 0.21 | 0.204 | 0.209 | 0.196 | 0.19 | 0.172 | 0.171 | 0.162 | 0.132 | -0.072 |
| 2016-03-01 00:00:00 | 0.002 | -0.007 | -0.012 | -0.034 | -0.013 | -0.019 | -0.035 | -0.032 | -0.032 | -0.036 | -0.038 |
| 2016-04-01 00:00:00 | -0.017 | -0.009 | -0.006 | -0.012 | 0.0 | 0.007 | 0.002 | -0.01 | -0.005 | 0.001 | 0.018 |
| 2016-05-01 00:00:00 | 0.077 | 0.092 | 0.074 | 0.082 | 0.051 | 0.058 | 0.051 | 0.033 | 0.02 | 0.01 | -0.067 |
| 2016-06-01 00:00:00 | -0.012 | -0.011 | -0.029 | -0.014 | -0.022 | -0.033 | -0.007 | -0.017 | 0.031 | 0.028 | 0.041 |
| 2016-07-01 00:00:00 | 0.064 | 0.052 | 0.043 | 0.035 | 0.034 | 0.045 | 0.037 | 0.035 | 0.033 | 0.031 | -0.033 |
| 2016-08-01 00:00:00 | -0.025 | -0.015 | -0.015 | -0.021 | -0.028 | -0.028 | -0.026 | -0.029 | -0.03 | -0.034 | -0.009 |
| 2016-09-01 00:00:00 | 0.04 | 0.038 | 0.05 | 0.046 | 0.037 | 0.023 | 0.026 | 0.026 | 0.018 | 0.024 | -0.016 |
| 2016-10-01 00:00:00 | 0.03 | 0.016 | 0.029 | 0.025 | 0.014 | 0.015 | 0.016 | 0.014 | 0.036 | 0.045 | 0.015 |
| 2016-11-01 00:00:00 | -0.057 | -0.059 | -0.065 | -0.076 | -0.059 | -0.07 | -0.067 | -0.061 | -0.062 | -0.063 | -0.006 |
| 2016-12-01 00:00:00 | -0.037 | -0.036 | -0.041 | -0.035 | -0.032 | -0.03 | -0.03 | -0.018 | -0.008 | 0.012 | 0.049 |
| 2017-01-01 00:00:00 | 0.045 | 0.048 | 0.045 | 0.041 | 0.039 | 0.04 | 0.038 | 0.051 | 0.036 | 0.036 | -0.009 |
| 2017-02-01 00:00:00 | -0.017 | -0.025 | -0.022 | -0.015 | -0.017 | -0.022 | -0.01 | -0.016 | 0.002 | 0.002 | 0.02 |
| 2017-03-01 00:00:00 | -0.076 | -0.085 | -0.058 | -0.069 | -0.068 | -0.062 | -0.033 | -0.025 | -0.029 | -0.005 | 0.071 |
| 2017-04-01 00:00:00 | -0.085 | -0.089 | -0.084 | -0.075 | -0.083 | -0.069 | -0.073 | -0.061 | -0.059 | -0.009 | 0.075 |
| 2017-05-01 00:00:00 | 0.029 | 0.026 | 0.032 | 0.043 | 0.035 | 0.04 | 0.042 | 0.051 | 0.062 | 0.05 | 0.02 |
| 2017-06-01 00:00:00 | -0.013 | -0.014 | 0.005 | -0.008 | -0.004 | 0.016 | 0.004 | 0.023 | 0.019 | 0.021 | 0.034 |
| 2017-07-01 00:00:00 | 0.047 | 0.033 | 0.041 | 0.037 | 0.026 | 0.032 | 0.036 | 0.017 | 0.039 | 0.022 | -0.025 |
| 2017-08-01 00:00:00 | 0.008 | 0.021 | 0.007 | 0.016 | 0.017 | 0.017 | 0.012 | 0.017 | 0.002 | 0.005 | -0.003 |
| 2017-09-01 00:00:00 | -0.031 | -0.029 | -0.02 | -0.021 | -0.032 | -0.03 | -0.021 | -0.011 | -0.002 | 0.029 | 0.06 |
| 2017-10-01 00:00:00 | -0.087 | -0.079 | -0.085 | -0.068 | -0.066 | -0.057 | -0.053 | -0.044 | -0.047 | -0.022 | 0.065 |
| 2017-11-01 00:00:00 | -0.026 | -0.027 | -0.028 | -0.023 | -0.014 | -0.018 | -0.01 | -0.01 | -0.007 | 0.003 | 0.029 |
| 2017-12-01 00:00:00 | -0.05 | -0.041 | -0.039 | -0.039 | -0.031 | -0.022 | -0.021 | -0.023 | 0.009 | 0.036 | 0.086 |
| 2018-01-01 00:00:00 | -0.07 | -0.052 | -0.055 | -0.052 | -0.037 | -0.036 | -0.031 | -0.034 | -0.03 | -0.048 | 0.022 |
| 2018-02-01 00:00:00 | 0.068 | 0.056 | 0.056 | 0.054 | 0.038 | 0.032 | 0.035 | 0.017 | 0.005 | -0.022 | -0.09 |
| 2018-03-01 00:00:00 | -0.033 | -0.054 | -0.045 | -0.039 | -0.042 | -0.042 | -0.034 | -0.043 | -0.036 | -0.034 | -0.001 |
| 2018-04-01 00:00:00 | -0.019 | -0.026 | -0.024 | -0.006 | -0.013 | -0.018 | -0.016 | -0.01 | 0.003 | 0.014 | 0.032 |
| 2018-05-01 00:00:00 | -0.12 | -0.12 | -0.112 | -0.116 | -0.109 | -0.119 | -0.097 | -0.104 | -0.09 | -0.08 | 0.04 |
| 2018-06-01 00:00:00 | -0.004 | -0.012 | -0.017 | 0.002 | -0.007 | -0.022 | -0.001 | -0.003 | -0.003 | -0.002 | 0.001 |
| 2018-07-01 00:00:00 | -0.087 | -0.081 | -0.077 | -0.084 | -0.086 | -0.086 | -0.08 | -0.083 | -0.079 | -0.059 | 0.028 |
| 2018-08-01 00:00:00 | -0.01 | -0.011 | -0.017 | -0.014 | -0.008 | 0.0 | -0.02 | -0.005 | 0.003 | 0.019 | 0.029 |
| 2018-09-01 00:00:00 | -0.089 | -0.099 | -0.098 | -0.115 | -0.114 | -0.112 | -0.111 | -0.093 | -0.092 | -0.095 | -0.006 |
| 2018-10-01 00:00:00 | 0.062 | 0.065 | 0.073 | 0.062 | 0.043 | 0.066 | 0.038 | 0.035 | 0.025 | 0.008 | -0.054 |
| 2018-11-01 00:00:00 | -0.042 | -0.045 | -0.052 | -0.055 | -0.046 | -0.05 | -0.045 | -0.041 | -0.041 | -0.042 | -0.001 |
| 2018-12-01 00:00:00 | -0.038 | -0.032 | -0.03 | -0.017 | -0.024 | -0.013 | -0.023 | 0.003 | 0.015 | 0.029 | 0.068 |
| 2019-01-01 00:00:00 | 0.245 | 0.234 | 0.228 | 0.224 | 0.232 | 0.227 | 0.2 | 0.212 | 0.214 | 0.171 | -0.074 |
| 2019-02-01 00:00:00 | 0.111 | 0.097 | 0.114 | 0.102 | 0.115 | 0.099 | 0.106 | 0.102 | 0.096 | 0.063 | -0.048 |
| 2019-03-01 00:00:00 | -0.053 | -0.043 | -0.046 | -0.035 | -0.038 | -0.036 | -0.055 | -0.042 | -0.048 | -0.014 | 0.039 |
| 2019-04-01 00:00:00 | -0.051 | -0.052 | -0.052 | -0.047 | -0.053 | -0.064 | -0.065 | -0.07 | -0.07 | -0.065 | -0.015 |
| 2019-05-01 00:00:00 | -0.001 | -0.016 | 0.004 | -0.004 | -0.02 | -0.001 | -0.001 | 0.011 | 0.021 | 0.041 | 0.042 |
| 2019-06-01 00:00:00 | -0.026 | -0.029 | -0.021 | -0.03 | -0.028 | -0.015 | -0.018 | -0.013 | -0.0 | 0.009 | 0.035 |
| 2019-07-01 00:00:00 | -0.01 | -0.01 | -0.008 | -0.004 | -0.012 | -0.01 | -0.0 | -0.008 | -0.001 | -0.004 | 0.005 |
| 2019-08-01 00:00:00 | 0.022 | 0.013 | 0.012 | 0.009 | 0.007 | 0.014 | 0.018 | 0.003 | 0.02 | 0.004 | -0.018 |
| 2019-09-01 00:00:00 | -0.008 | -0.01 | -0.013 | -0.0 | -0.015 | -0.001 | -0.008 | -0.006 | 0.001 | 0.011 | 0.019 |
| 2019-10-01 00:00:00 | -0.019 | -0.033 | -0.032 | -0.023 | -0.032 | -0.024 | -0.024 | -0.011 | -0.004 | -0.009 | 0.01 |
| 2019-11-01 00:00:00 | 0.082 | 0.081 | 0.073 | 0.091 | 0.078 | 0.078 | 0.084 | 0.077 | 0.084 | 0.079 | -0.003 |
| 2019-12-01 00:00:00 | 0.009 | -0.011 | 0.007 | 0.019 | 0.005 | 0.029 | 0.015 | 0.022 | 0.002 | 0.002 | -0.007 |
+---------------------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+
+---------+-------+-------+-------+-------+------+-------+-------+-------+-------+-------+--------+
| Group | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Diff |
+---------+-------+-------+-------+-------+------+-------+-------+-------+-------+-------+--------+
| Average | 0.014 | 0.012 | 0.011 | 0.01 | 0.01 | 0.008 | 0.009 | 0.008 | 0.009 | 0.008 | -0.006 |
| T-Test | 2.105 | 1.805 | 1.77 | 1.668 | 1.63 | 1.39 | 1.587 | 1.316 | 1.682 | 1.512 | -1.48 |
+---------+-------+-------+-------+-------+------+-------+-------+-------+-------+-------+--------+
The first dataset contains no below 30% stocks from 2000-01-01 to 2019-12-01. The size effect is insignificant since the t-test statistics is -1.48 whose absolute value is no more than 2 corresponding to the significance level at 0.05.
# %% dataset 2
# select stocks whose trading days are more than or equal to 10 days
test_data_2 = month_return[month_return['Ndaytrd']>=10]
# construct data for univariate analysis
test_data_2 = test_data_2[['emrwd', 'Msmvttl', 'Time']].dropna()
# time interval between 2000-01-01 to 2019-12-01
test_data_2 = test_data_2[(test_data_2['Time'] >= '2000-01-01') & (test_data_2['Time'] <= '2019-12-01')]
# using Univariate class to conduct analysis
uni_2 = Univariate(np.array(test_data_2), number=9)
uni_2.average_by_time()
uni_2.summary_and_test()
uni_2.print_summary_by_time()
uni_2.print_summary()
==========================================================================================================================
+---------------------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+
| Time | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | diff |
+---------------------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+
| 2000-01-01 00:00:00 | 0.164 | 0.167 | 0.126 | 0.139 | 0.131 | 0.12 | 0.118 | 0.094 | 0.113 | 0.125 | -0.039 |
| 2000-02-01 00:00:00 | 0.208 | 0.203 | 0.128 | 0.151 | 0.085 | 0.113 | 0.052 | 0.053 | 0.044 | 0.002 | -0.206 |
| 2000-03-01 00:00:00 | 0.001 | 0.035 | 0.019 | 0.006 | 0.024 | 0.012 | -0.008 | 0.017 | 0.014 | 0.032 | 0.032 |
| 2000-04-01 00:00:00 | 0.056 | 0.06 | 0.052 | 0.038 | 0.047 | 0.034 | 0.028 | 0.039 | 0.025 | 0.021 | -0.035 |
| 2000-05-01 00:00:00 | 0.019 | 0.021 | 0.032 | 0.02 | 0.044 | 0.019 | 0.024 | 0.014 | 0.031 | 0.034 | 0.015 |
| 2000-06-01 00:00:00 | 0.108 | 0.057 | 0.056 | 0.062 | 0.047 | 0.047 | 0.05 | 0.029 | 0.035 | 0.041 | -0.067 |
| 2000-07-01 00:00:00 | 0.053 | 0.039 | 0.023 | 0.009 | -0.001 | -0.002 | -0.006 | -0.015 | -0.007 | -0.021 | -0.074 |
| 2000-08-01 00:00:00 | 0.016 | -0.027 | -0.033 | -0.022 | -0.038 | -0.053 | -0.059 | -0.045 | -0.059 | -0.056 | -0.072 |
| 2000-09-01 00:00:00 | 0.065 | 0.058 | 0.049 | 0.048 | 0.034 | 0.035 | 0.026 | 0.029 | 0.014 | 0.007 | -0.057 |
| 2000-10-01 00:00:00 | 0.073 | 0.063 | 0.064 | 0.059 | 0.066 | 0.064 | 0.062 | 0.053 | 0.051 | 0.054 | -0.019 |
| 2000-11-01 00:00:00 | -0.002 | 0.028 | 0.025 | 0.008 | 0.014 | 0.005 | 0.006 | 0.011 | -0.003 | -0.024 | -0.023 |
| 2000-12-01 00:00:00 | -0.024 | -0.019 | -0.012 | -0.006 | -0.012 | -0.006 | -0.014 | -0.003 | -0.003 | -0.02 | 0.003 |
| 2001-01-01 00:00:00 | -0.098 | -0.062 | -0.067 | -0.072 | -0.062 | -0.062 | -0.052 | -0.064 | -0.051 | -0.049 | 0.05 |
| 2001-02-01 00:00:00 | 0.114 | 0.103 | 0.088 | 0.088 | 0.079 | 0.084 | 0.079 | 0.076 | 0.062 | 0.058 | -0.056 |
| 2001-03-01 00:00:00 | 0.04 | 0.019 | 0.001 | 0.012 | -0.005 | -0.003 | -0.009 | 0.002 | -0.014 | -0.015 | -0.055 |
| 2001-04-01 00:00:00 | 0.096 | 0.087 | 0.084 | 0.066 | 0.047 | 0.048 | 0.031 | 0.036 | 0.025 | 0.012 | -0.084 |
| 2001-05-01 00:00:00 | 0.016 | 0.007 | 0.017 | 0.016 | 0.01 | 0.013 | 0.011 | -0.001 | 0.005 | -0.006 | -0.022 |
| 2001-06-01 00:00:00 | -0.133 | -0.143 | -0.135 | -0.135 | -0.133 | -0.138 | -0.143 | -0.129 | -0.127 | -0.134 | -0.002 |
| 2001-07-01 00:00:00 | -0.001 | -0.013 | -0.021 | -0.03 | -0.037 | -0.037 | -0.041 | -0.04 | -0.032 | -0.043 | -0.042 |
| 2001-08-01 00:00:00 | -0.087 | -0.059 | -0.069 | -0.065 | -0.053 | -0.062 | -0.048 | -0.043 | -0.047 | -0.032 | 0.055 |
| 2001-09-01 00:00:00 | -0.057 | -0.064 | -0.059 | -0.058 | -0.056 | -0.057 | -0.065 | -0.046 | -0.056 | -0.033 | 0.024 |
| 2001-10-01 00:00:00 | 0.079 | 0.066 | 0.064 | 0.057 | 0.048 | 0.051 | 0.039 | 0.042 | 0.035 | 0.027 | -0.052 |
| 2001-11-01 00:00:00 | -0.09 | -0.083 | -0.077 | -0.073 | -0.072 | -0.075 | -0.064 | -0.067 | -0.054 | -0.047 | 0.044 |
| 2001-12-01 00:00:00 | -0.166 | -0.135 | -0.149 | -0.142 | -0.126 | -0.123 | -0.115 | -0.109 | -0.095 | -0.067 | 0.099 |
| 2002-01-01 00:00:00 | 0.095 | 0.052 | 0.041 | 0.038 | 0.044 | 0.036 | 0.029 | 0.03 | 0.018 | 0.014 | -0.081 |
| 2002-02-01 00:00:00 | 0.102 | 0.099 | 0.09 | 0.089 | 0.081 | 0.075 | 0.072 | 0.073 | 0.062 | 0.037 | -0.065 |
| 2002-03-01 00:00:00 | 0.081 | 0.067 | 0.054 | 0.057 | 0.055 | 0.041 | 0.045 | 0.032 | 0.037 | 0.031 | -0.049 |
| 2002-04-01 00:00:00 | -0.077 | -0.083 | -0.082 | -0.092 | -0.094 | -0.092 | -0.092 | -0.089 | -0.091 | -0.081 | -0.004 |
| 2002-05-01 00:00:00 | 0.091 | 0.091 | 0.106 | 0.113 | 0.114 | 0.116 | 0.118 | 0.136 | 0.133 | 0.156 | 0.065 |
| 2002-06-01 00:00:00 | -0.026 | -0.032 | -0.034 | -0.033 | -0.034 | -0.036 | -0.043 | -0.04 | -0.047 | -0.042 | -0.016 |
| 2002-07-01 00:00:00 | 0.023 | 0.014 | 0.011 | 0.01 | 0.001 | 0.003 | 0.008 | 0.009 | 0.003 | 0.004 | -0.019 |
| 2002-08-01 00:00:00 | -0.063 | -0.06 | -0.055 | -0.059 | -0.06 | -0.062 | -0.057 | -0.053 | -0.047 | -0.049 | 0.014 |
| 2002-09-01 00:00:00 | -0.051 | -0.071 | -0.06 | -0.074 | -0.057 | -0.047 | -0.054 | -0.05 | -0.044 | -0.048 | 0.004 |
| 2002-10-01 00:00:00 | -0.097 | -0.091 | -0.09 | -0.089 | -0.085 | -0.08 | -0.073 | -0.076 | -0.05 | -0.038 | 0.059 |
| 2002-11-01 00:00:00 | -0.029 | -0.053 | -0.052 | -0.056 | -0.056 | -0.054 | -0.057 | -0.054 | -0.05 | -0.047 | -0.018 |
| 2002-12-01 00:00:00 | 0.134 | 0.123 | 0.113 | 0.114 | 0.098 | 0.101 | 0.092 | 0.08 | 0.075 | 0.09 | -0.044 |
| 2003-01-01 00:00:00 | 0.018 | 0.022 | 0.023 | 0.015 | 0.016 | 0.01 | 0.013 | 0.013 | 0.009 | 0.005 | -0.013 |
| 2003-02-01 00:00:00 | -0.042 | -0.031 | -0.042 | -0.034 | -0.033 | -0.033 | -0.021 | -0.022 | -0.007 | 0.01 | 0.052 |
| 2003-03-01 00:00:00 | -0.094 | -0.067 | -0.081 | -0.067 | -0.038 | -0.051 | -0.035 | -0.011 | 0.005 | 0.021 | 0.115 |
| 2003-04-01 00:00:00 | 0.037 | 0.039 | 0.028 | 0.032 | 0.034 | 0.037 | 0.038 | 0.049 | 0.054 | 0.055 | 0.018 |
| 2003-05-01 00:00:00 | -0.055 | -0.061 | -0.068 | -0.066 | -0.07 | -0.072 | -0.075 | -0.079 | -0.057 | -0.065 | -0.01 |
| 2003-06-01 00:00:00 | -0.05 | -0.049 | -0.041 | -0.039 | -0.037 | -0.036 | -0.03 | -0.023 | -0.007 | 0.013 | 0.063 |
| 2003-07-01 00:00:00 | -0.001 | -0.014 | -0.016 | -0.017 | -0.023 | -0.037 | -0.034 | -0.033 | -0.021 | -0.043 | -0.042 |
| 2003-08-01 00:00:00 | -0.054 | -0.056 | -0.053 | -0.043 | -0.051 | -0.037 | -0.035 | -0.046 | -0.047 | -0.037 | 0.017 |
| 2003-09-01 00:00:00 | -0.114 | -0.096 | -0.086 | -0.08 | -0.075 | -0.065 | -0.066 | -0.044 | -0.028 | 0.003 | 0.117 |
| 2003-10-01 00:00:00 | 0.002 | 0.003 | 0.009 | 0.012 | 0.024 | 0.029 | 0.028 | 0.026 | 0.014 | 0.024 | 0.022 |
| 2003-11-01 00:00:00 | -0.069 | -0.038 | -0.033 | -0.016 | -0.034 | -0.006 | 0.004 | 0.025 | 0.032 | 0.07 | 0.138 |
| 2003-12-01 00:00:00 | 0.111 | 0.105 | 0.102 | 0.096 | 0.099 | 0.097 | 0.084 | 0.068 | 0.073 | 0.052 | -0.058 |
| 2004-01-01 00:00:00 | 0.145 | 0.125 | 0.102 | 0.12 | 0.08 | 0.104 | 0.091 | 0.076 | 0.074 | 0.056 | -0.089 |
| 2004-02-01 00:00:00 | 0.048 | 0.055 | 0.054 | 0.044 | 0.035 | 0.055 | 0.038 | 0.033 | 0.034 | 0.026 | -0.022 |
| 2004-03-01 00:00:00 | -0.115 | -0.124 | -0.105 | -0.098 | -0.093 | -0.098 | -0.095 | -0.084 | -0.096 | -0.107 | 0.008 |
| 2004-04-01 00:00:00 | 0.017 | -0.013 | -0.009 | -0.03 | -0.003 | -0.025 | -0.021 | -0.025 | -0.023 | -0.033 | -0.049 |
| 2004-05-01 00:00:00 | -0.139 | -0.132 | -0.13 | -0.128 | -0.134 | -0.132 | -0.13 | -0.116 | -0.122 | -0.091 | 0.048 |
| 2004-06-01 00:00:00 | -0.072 | -0.059 | -0.054 | -0.025 | -0.027 | -0.023 | 0.01 | 0.005 | 0.014 | 0.008 | 0.08 |
| 2004-07-01 00:00:00 | -0.066 | -0.061 | -0.053 | -0.05 | -0.047 | -0.055 | -0.061 | -0.064 | -0.061 | -0.032 | 0.034 |
| 2004-08-01 00:00:00 | 0.031 | 0.051 | 0.053 | 0.056 | 0.048 | 0.051 | 0.056 | 0.057 | 0.06 | 0.059 | 0.028 |
| 2004-09-01 00:00:00 | -0.129 | -0.091 | -0.081 | -0.067 | -0.066 | -0.053 | -0.064 | -0.058 | -0.028 | -0.04 | 0.089 |
| 2004-10-01 00:00:00 | 0.109 | 0.063 | 0.06 | 0.056 | 0.047 | 0.048 | 0.037 | 0.041 | 0.01 | -0.001 | -0.11 |
| 2004-11-01 00:00:00 | -0.089 | -0.092 | -0.093 | -0.077 | -0.086 | -0.08 | -0.091 | -0.08 | -0.07 | -0.056 | 0.033 |
| 2004-12-01 00:00:00 | -0.045 | -0.062 | -0.084 | -0.077 | -0.081 | -0.075 | -0.084 | -0.076 | -0.078 | -0.052 | -0.006 |
| 2005-01-01 00:00:00 | 0.114 | 0.105 | 0.112 | 0.113 | 0.109 | 0.102 | 0.118 | 0.115 | 0.094 | 0.092 | -0.022 |
| 2005-02-01 00:00:00 | -0.137 | -0.14 | -0.132 | -0.142 | -0.136 | -0.136 | -0.12 | -0.113 | -0.108 | -0.086 | 0.05 |
| 2005-03-01 00:00:00 | -0.14 | -0.125 | -0.092 | -0.096 | -0.081 | -0.053 | -0.065 | -0.037 | -0.026 | 0.004 | 0.144 |
| 2005-04-01 00:00:00 | 0.019 | -0.013 | -0.023 | -0.02 | -0.023 | -0.032 | -0.052 | -0.055 | -0.081 | -0.094 | -0.112 |
| 2005-05-01 00:00:00 | 0.001 | 0.0 | -0.001 | 0.004 | -0.003 | -0.001 | -0.006 | -0.001 | -0.002 | 0.029 | 0.028 |
| 2005-06-01 00:00:00 | -0.1 | -0.1 | -0.083 | -0.08 | -0.073 | -0.068 | -0.064 | -0.054 | -0.028 | 0.011 | 0.111 |
| 2005-07-01 00:00:00 | 0.258 | 0.196 | 0.192 | 0.174 | 0.173 | 0.152 | 0.136 | 0.124 | 0.119 | 0.05 | -0.208 |
| 2005-08-01 00:00:00 | 0.081 | 0.027 | 0.031 | 0.025 | -0.002 | 0.027 | 0.029 | 0.029 | 0.027 | -0.004 | -0.085 |
| 2005-09-01 00:00:00 | -0.083 | -0.056 | -0.06 | -0.067 | -0.058 | -0.052 | -0.056 | -0.056 | -0.048 | -0.052 | 0.031 |
| 2005-10-01 00:00:00 | 0.032 | 0.028 | 0.037 | 0.017 | 0.015 | 0.01 | 0.013 | -0.003 | -0.014 | -0.012 | -0.044 |
| 2005-11-01 00:00:00 | -0.011 | -0.005 | 0.001 | 0.017 | 0.012 | 0.023 | 0.032 | 0.053 | 0.067 | 0.073 | 0.085 |
| 2005-12-01 00:00:00 | -0.008 | 0.056 | 0.076 | 0.09 | 0.078 | 0.091 | 0.11 | 0.13 | 0.127 | 0.096 | 0.104 |
| 2006-01-01 00:00:00 | 0.094 | 0.047 | 0.026 | 0.032 | 0.021 | 0.022 | 0.017 | 0.019 | -0.001 | 0.043 | -0.051 |
| 2006-02-01 00:00:00 | -0.037 | -0.008 | -0.004 | -0.002 | 0.004 | 0.006 | 0.031 | 0.028 | 0.057 | 0.027 | 0.064 |
| 2006-03-01 00:00:00 | 0.139 | 0.007 | 0.082 | 0.08 | 0.099 | 0.113 | 0.105 | 0.133 | 0.139 | 0.151 | 0.011 |
| 2006-04-01 00:00:00 | 1.07 | 0.313 | 0.307 | 0.308 | 0.274 | 0.269 | 0.258 | 0.237 | 0.213 | 0.164 | -0.906 |
| 2006-05-01 00:00:00 | 0.07 | 0.079 | 0.066 | 0.083 | 0.065 | 0.071 | 0.039 | 0.053 | 0.024 | 0.021 | -0.049 |
| 2006-06-01 00:00:00 | 0.001 | 0.005 | -0.014 | -0.012 | -0.037 | -0.028 | -0.041 | -0.059 | -0.047 | -0.084 | -0.085 |
| 2006-07-01 00:00:00 | 0.022 | 0.03 | 0.025 | 0.023 | 0.032 | 0.033 | 0.035 | 0.045 | 0.04 | 0.027 | 0.005 |
| 2006-08-01 00:00:00 | 0.113 | 0.065 | 0.062 | 0.049 | 0.052 | 0.041 | 0.046 | 0.036 | 0.037 | 0.043 | -0.07 |
| 2006-09-01 00:00:00 | -0.01 | -0.013 | -0.018 | -0.002 | 0.016 | -0.017 | -0.011 | -0.0 | 0.019 | 0.029 | 0.039 |
| 2006-10-01 00:00:00 | -0.011 | -0.007 | -0.003 | 0.022 | 0.025 | 0.035 | 0.063 | 0.059 | 0.105 | 0.171 | 0.182 |
| 2006-11-01 00:00:00 | 0.011 | 0.036 | 0.035 | 0.05 | 0.035 | 0.042 | 0.069 | 0.085 | 0.095 | 0.153 | 0.141 |
| 2006-12-01 00:00:00 | 0.305 | 0.269 | 0.26 | 0.286 | 0.257 | 0.25 | 0.224 | 0.234 | 0.241 | 0.19 | -0.115 |
| 2007-01-01 00:00:00 | 0.257 | 0.244 | 0.241 | 0.223 | 0.217 | 0.186 | 0.245 | 0.136 | 0.15 | 0.083 | -0.175 |
| 2007-02-01 00:00:00 | 0.272 | 0.261 | 0.216 | 0.204 | 0.191 | 0.164 | 0.175 | 0.143 | 0.085 | 0.087 | -0.185 |
| 2007-03-01 00:00:00 | 0.332 | 0.329 | 0.343 | 0.363 | 0.339 | 0.322 | 0.336 | 0.348 | 0.347 | 0.283 | -0.049 |
| 2007-04-01 00:00:00 | 0.199 | 0.088 | 0.089 | 0.081 | 0.071 | 0.131 | 0.111 | 0.079 | 0.106 | 0.135 | -0.064 |
| 2007-05-01 00:00:00 | -0.22 | -0.23 | -0.216 | -0.211 | -0.189 | -0.155 | -0.159 | -0.13 | -0.092 | -0.04 | 0.181 |
| 2007-06-01 00:00:00 | 0.296 | 0.287 | 0.278 | 0.244 | 0.236 | 0.236 | 0.212 | 0.186 | 0.189 | 0.185 | -0.111 |
| 2007-07-01 00:00:00 | 0.198 | 0.127 | 0.104 | 0.099 | 0.094 | 0.096 | 0.115 | 0.108 | 0.143 | 0.18 | -0.018 |
| 2007-08-01 00:00:00 | 0.046 | 0.016 | 0.018 | 0.025 | 0.035 | 0.042 | 0.029 | 0.04 | 0.054 | 0.075 | 0.029 |
| 2007-09-01 00:00:00 | -0.124 | -0.139 | -0.115 | -0.117 | -0.121 | -0.099 | -0.117 | -0.097 | -0.084 | -0.007 | 0.117 |
| 2007-10-01 00:00:00 | 0.009 | -0.013 | -0.019 | -0.052 | -0.049 | -0.075 | -0.08 | -0.1 | -0.134 | -0.187 | -0.196 |
| 2007-11-01 00:00:00 | 0.184 | 0.205 | 0.204 | 0.208 | 0.21 | 0.21 | 0.22 | 0.216 | 0.2 | 0.148 | -0.036 |
| 2007-12-01 00:00:00 | -0.054 | -0.06 | -0.063 | -0.051 | -0.077 | -0.047 | -0.059 | -0.069 | -0.084 | -0.12 | -0.067 |
| 2008-01-01 00:00:00 | 0.116 | 0.109 | 0.117 | 0.107 | 0.101 | 0.083 | 0.076 | 0.065 | 0.043 | 0.017 | -0.099 |
| 2008-02-01 00:00:00 | -0.174 | -0.171 | -0.181 | -0.182 | -0.199 | -0.201 | -0.199 | -0.217 | -0.224 | -0.212 | -0.039 |
| 2008-03-01 00:00:00 | -0.087 | -0.091 | -0.077 | -0.075 | -0.069 | -0.051 | -0.049 | -0.006 | 0.017 | 0.043 | 0.13 |
| 2008-04-01 00:00:00 | 0.006 | -0.007 | -0.008 | -0.003 | -0.026 | -0.039 | -0.027 | -0.059 | -0.048 | -0.078 | -0.084 |
| 2008-05-01 00:00:00 | -0.239 | -0.234 | -0.266 | -0.275 | -0.249 | -0.26 | -0.239 | -0.25 | -0.234 | -0.221 | 0.018 |
| 2008-06-01 00:00:00 | 0.137 | 0.118 | 0.116 | 0.111 | 0.108 | 0.103 | 0.072 | 0.076 | 0.052 | 0.005 | -0.132 |
| 2008-07-01 00:00:00 | -0.207 | -0.224 | -0.227 | -0.233 | -0.223 | -0.238 | -0.241 | -0.238 | -0.229 | -0.194 | 0.013 |
| 2008-08-01 00:00:00 | -0.117 | -0.104 | -0.09 | -0.098 | -0.101 | -0.08 | -0.085 | -0.061 | -0.044 | -0.026 | 0.09 |
| 2008-09-01 00:00:00 | -0.225 | -0.232 | -0.249 | -0.265 | -0.247 | -0.266 | -0.272 | -0.262 | -0.275 | -0.248 | -0.023 |
| 2008-10-01 00:00:00 | 0.231 | 0.215 | 0.219 | 0.221 | 0.225 | 0.223 | 0.185 | 0.161 | 0.157 | 0.131 | -0.101 |
| 2008-11-01 00:00:00 | 0.155 | 0.13 | 0.094 | 0.097 | 0.061 | 0.068 | 0.053 | 0.065 | 0.041 | 0.013 | -0.142 |
| 2008-12-01 00:00:00 | 0.149 | 0.161 | 0.163 | 0.159 | 0.162 | 0.187 | 0.162 | 0.169 | 0.158 | 0.119 | -0.03 |
| 2009-01-01 00:00:00 | 0.124 | 0.116 | 0.094 | 0.084 | 0.092 | 0.09 | 0.073 | 0.081 | 0.057 | 0.063 | -0.061 |
| 2009-02-01 00:00:00 | 0.255 | 0.254 | 0.235 | 0.246 | 0.226 | 0.224 | 0.21 | 0.209 | 0.198 | 0.186 | -0.069 |
| 2009-03-01 00:00:00 | 0.102 | 0.11 | 0.078 | 0.074 | 0.081 | 0.073 | 0.038 | 0.066 | 0.041 | 0.05 | -0.052 |
| 2009-04-01 00:00:00 | 0.096 | 0.092 | 0.106 | 0.07 | 0.085 | 0.062 | 0.057 | 0.047 | 0.045 | 0.056 | -0.041 |
| 2009-05-01 00:00:00 | 0.112 | 0.081 | 0.061 | 0.039 | 0.04 | 0.055 | 0.039 | 0.053 | 0.078 | 0.124 | 0.012 |
| 2009-06-01 00:00:00 | 0.134 | 0.125 | 0.133 | 0.136 | 0.143 | 0.155 | 0.129 | 0.153 | 0.182 | 0.183 | 0.05 |
| 2009-07-01 00:00:00 | -0.124 | -0.141 | -0.151 | -0.144 | -0.147 | -0.139 | -0.155 | -0.171 | -0.18 | -0.236 | -0.112 |
| 2009-08-01 00:00:00 | 0.055 | 0.041 | 0.044 | 0.024 | 0.03 | 0.037 | 0.032 | 0.035 | 0.04 | 0.052 | -0.003 |
| 2009-09-01 00:00:00 | 0.124 | 0.133 | 0.129 | 0.128 | 0.12 | 0.132 | 0.12 | 0.112 | 0.108 | 0.092 | -0.032 |
| 2009-10-01 00:00:00 | 0.167 | 0.173 | 0.153 | 0.158 | 0.163 | 0.178 | 0.144 | 0.142 | 0.109 | 0.084 | -0.083 |
| 2009-11-01 00:00:00 | 0.052 | 0.039 | 0.035 | 0.029 | 0.035 | 0.032 | 0.006 | 0.005 | -0.005 | 0.004 | -0.048 |
| 2009-12-01 00:00:00 | -0.016 | -0.011 | -0.033 | -0.026 | -0.018 | -0.031 | -0.019 | -0.035 | -0.049 | -0.1 | -0.084 |
| 2010-01-01 00:00:00 | 0.09 | 0.082 | 0.078 | 0.064 | 0.061 | 0.068 | 0.059 | 0.057 | 0.043 | 0.025 | -0.065 |
| 2010-02-01 00:00:00 | 0.086 | 0.067 | 0.064 | 0.053 | 0.039 | 0.042 | 0.046 | 0.017 | 0.017 | 0.011 | -0.075 |
| 2010-03-01 00:00:00 | -0.056 | -0.063 | -0.082 | -0.084 | -0.072 | -0.068 | -0.07 | -0.078 | -0.063 | -0.073 | -0.017 |
| 2010-04-01 00:00:00 | -0.088 | -0.08 | -0.073 | -0.088 | -0.094 | -0.077 | -0.08 | -0.065 | -0.078 | -0.089 | -0.0 |
| 2010-05-01 00:00:00 | -0.082 | -0.083 | -0.087 | -0.083 | -0.091 | -0.094 | -0.099 | -0.101 | -0.098 | -0.081 | 0.001 |
| 2010-06-01 00:00:00 | 0.168 | 0.164 | 0.153 | 0.149 | 0.149 | 0.164 | 0.143 | 0.138 | 0.133 | 0.13 | -0.038 |
| 2010-07-01 00:00:00 | 0.107 | 0.106 | 0.09 | 0.113 | 0.097 | 0.096 | 0.084 | 0.109 | 0.075 | 0.027 | -0.08 |
| 2010-08-01 00:00:00 | 0.025 | -0.012 | -0.007 | 0.002 | 0.007 | -0.004 | -0.008 | 0.016 | 0.02 | 0.016 | -0.009 |
| 2010-09-01 00:00:00 | 0.062 | 0.078 | 0.074 | 0.098 | 0.082 | 0.091 | 0.093 | 0.098 | 0.114 | 0.156 | 0.094 |
| 2010-10-01 00:00:00 | 0.039 | 0.036 | 0.04 | 0.028 | 0.014 | 0.012 | 0.016 | 0.018 | -0.015 | -0.06 | -0.099 |
| 2010-11-01 00:00:00 | -0.007 | -0.023 | -0.015 | -0.024 | -0.029 | -0.035 | -0.027 | -0.034 | -0.018 | 0.007 | 0.014 |
| 2010-12-01 00:00:00 | -0.031 | -0.055 | -0.053 | -0.059 | -0.06 | -0.058 | -0.067 | -0.065 | -0.065 | -0.025 | 0.006 |
| 2011-01-01 00:00:00 | 0.099 | 0.104 | 0.101 | 0.093 | 0.106 | 0.096 | 0.105 | 0.102 | 0.085 | 0.059 | -0.04 |
| 2011-02-01 00:00:00 | 0.034 | 0.004 | -0.008 | -0.001 | -0.019 | -0.024 | -0.036 | -0.022 | -0.027 | -0.027 | -0.06 |
| 2011-03-01 00:00:00 | -0.029 | -0.04 | -0.039 | -0.051 | -0.046 | -0.046 | -0.029 | -0.037 | -0.034 | -0.019 | 0.01 |
| 2011-04-01 00:00:00 | -0.062 | -0.074 | -0.068 | -0.075 | -0.06 | -0.081 | -0.081 | -0.081 | -0.083 | -0.067 | -0.005 |
| 2011-05-01 00:00:00 | 0.044 | 0.045 | 0.035 | 0.03 | 0.046 | 0.025 | 0.034 | 0.032 | 0.036 | 0.029 | -0.015 |
| 2011-06-01 00:00:00 | 0.04 | 0.029 | 0.03 | 0.033 | 0.033 | 0.021 | 0.016 | 0.024 | 0.011 | -0.012 | -0.052 |
| 2011-07-01 00:00:00 | 0.008 | -0.009 | -0.014 | -0.019 | -0.031 | -0.031 | -0.035 | -0.033 | -0.047 | -0.052 | -0.06 |
| 2011-08-01 00:00:00 | -0.109 | -0.117 | -0.122 | -0.119 | -0.121 | -0.133 | -0.13 | -0.137 | -0.122 | -0.096 | 0.013 |
| 2011-09-01 00:00:00 | 0.054 | 0.044 | 0.046 | 0.04 | 0.046 | 0.044 | 0.039 | 0.046 | 0.039 | 0.035 | -0.019 |
| 2011-10-01 00:00:00 | -0.03 | -0.022 | -0.042 | -0.048 | -0.027 | -0.038 | -0.045 | -0.04 | -0.055 | -0.065 | -0.035 |
| 2011-11-01 00:00:00 | -0.177 | -0.178 | -0.169 | -0.171 | -0.172 | -0.152 | -0.164 | -0.142 | -0.12 | -0.085 | 0.092 |
| 2011-12-01 00:00:00 | 0.01 | -0.007 | -0.021 | -0.023 | -0.007 | -0.014 | -0.009 | -0.007 | -0.004 | 0.035 | 0.025 |
| 2012-01-01 00:00:00 | 0.16 | 0.155 | 0.149 | 0.142 | 0.137 | 0.136 | 0.127 | 0.127 | 0.117 | 0.082 | -0.078 |
| 2012-02-01 00:00:00 | -0.079 | -0.081 | -0.073 | -0.07 | -0.076 | -0.077 | -0.076 | -0.078 | -0.073 | -0.074 | 0.004 |
| 2012-03-01 00:00:00 | 0.061 | 0.064 | 0.069 | 0.084 | 0.065 | 0.068 | 0.072 | 0.06 | 0.057 | 0.069 | 0.008 |
| 2012-04-01 00:00:00 | 0.04 | 0.029 | 0.012 | 0.023 | 0.023 | 0.02 | 0.023 | 0.031 | 0.032 | 0.013 | -0.028 |
| 2012-05-01 00:00:00 | -0.018 | -0.035 | -0.055 | -0.058 | -0.061 | -0.07 | -0.068 | -0.071 | -0.062 | -0.061 | -0.043 |
| 2012-06-01 00:00:00 | -0.125 | -0.108 | -0.095 | -0.101 | -0.097 | -0.102 | -0.093 | -0.087 | -0.081 | -0.057 | 0.068 |
| 2012-07-01 00:00:00 | 0.068 | 0.064 | 0.055 | 0.047 | 0.032 | 0.033 | 0.013 | 0.005 | -0.023 | -0.053 | -0.121 |
| 2012-08-01 00:00:00 | 0.014 | 0.016 | -0.007 | 0.004 | 0.004 | -0.001 | -0.001 | 0.018 | 0.017 | 0.039 | 0.026 |
| 2012-09-01 00:00:00 | 0.012 | 0.01 | 0.004 | -0.001 | 0.003 | -0.0 | -0.01 | -0.008 | -0.018 | -0.016 | -0.028 |
| 2012-10-01 00:00:00 | -0.095 | -0.12 | -0.115 | -0.12 | -0.122 | -0.116 | -0.124 | -0.116 | -0.105 | -0.066 | 0.029 |
| 2012-11-01 00:00:00 | 0.167 | 0.175 | 0.165 | 0.169 | 0.181 | 0.164 | 0.174 | 0.179 | 0.166 | 0.175 | 0.008 |
| 2012-12-01 00:00:00 | 0.062 | 0.057 | 0.073 | 0.071 | 0.071 | 0.064 | 0.059 | 0.065 | 0.056 | 0.054 | -0.008 |
| 2013-01-01 00:00:00 | 0.06 | 0.041 | 0.041 | 0.041 | 0.037 | 0.034 | 0.039 | 0.041 | 0.036 | 0.005 | -0.055 |
| 2013-02-01 00:00:00 | -0.025 | -0.026 | -0.017 | -0.03 | -0.03 | -0.025 | -0.048 | -0.045 | -0.047 | -0.053 | -0.028 |
| 2013-03-01 00:00:00 | -0.023 | -0.048 | -0.04 | -0.031 | -0.032 | -0.027 | -0.027 | -0.019 | -0.021 | -0.022 | 0.002 |
| 2013-04-01 00:00:00 | 0.177 | 0.155 | 0.157 | 0.153 | 0.153 | 0.146 | 0.151 | 0.152 | 0.132 | 0.076 | -0.102 |
| 2013-05-01 00:00:00 | -0.139 | -0.157 | -0.155 | -0.155 | -0.161 | -0.158 | -0.15 | -0.164 | -0.153 | -0.14 | -0.001 |
| 2013-06-01 00:00:00 | 0.123 | 0.086 | 0.072 | 0.075 | 0.083 | 0.063 | 0.063 | 0.072 | 0.051 | 0.028 | -0.095 |
| 2013-07-01 00:00:00 | 0.104 | 0.092 | 0.112 | 0.1 | 0.076 | 0.08 | 0.089 | 0.078 | 0.062 | 0.063 | -0.041 |
| 2013-08-01 00:00:00 | 0.076 | 0.053 | 0.052 | 0.053 | 0.059 | 0.043 | 0.056 | 0.049 | 0.056 | 0.054 | -0.021 |
| 2013-09-01 00:00:00 | -0.006 | -0.013 | -0.018 | -0.024 | -0.017 | -0.029 | -0.039 | -0.033 | -0.038 | -0.034 | -0.027 |
| 2013-10-01 00:00:00 | 0.131 | 0.128 | 0.111 | 0.086 | 0.097 | 0.083 | 0.076 | 0.068 | 0.055 | 0.044 | -0.087 |
| 2013-11-01 00:00:00 | -0.02 | -0.029 | -0.031 | -0.032 | -0.039 | -0.03 | -0.038 | -0.03 | -0.038 | -0.044 | -0.023 |
| 2013-12-01 00:00:00 | 0.035 | 0.062 | 0.024 | 0.01 | 0.031 | 0.046 | 0.007 | 0.035 | 0.004 | -0.031 | -0.066 |
| 2014-01-01 00:00:00 | 0.067 | 0.05 | 0.047 | 0.047 | 0.044 | 0.044 | 0.032 | 0.017 | 0.009 | -0.018 | -0.085 |
| 2014-02-01 00:00:00 | 0.025 | 0.003 | -0.013 | -0.021 | -0.033 | -0.037 | -0.042 | -0.043 | -0.043 | -0.036 | -0.061 |
| 2014-03-01 00:00:00 | 0.022 | 0.006 | -0.008 | -0.012 | -0.03 | -0.03 | -0.016 | -0.015 | -0.025 | -0.004 | -0.026 |
| 2014-04-01 00:00:00 | 0.115 | 0.055 | 0.048 | 0.027 | 0.036 | 0.032 | 0.037 | 0.022 | 0.02 | 0.008 | -0.107 |
| 2014-05-01 00:00:00 | 0.079 | 0.09 | 0.073 | 0.062 | 0.052 | 0.056 | 0.042 | 0.037 | 0.034 | 0.019 | -0.06 |
| 2014-06-01 00:00:00 | 0.104 | 0.075 | 0.075 | 0.083 | 0.077 | 0.069 | 0.072 | 0.072 | 0.066 | 0.077 | -0.027 |
| 2014-07-01 00:00:00 | 0.111 | 0.091 | 0.068 | 0.066 | 0.057 | 0.056 | 0.046 | 0.046 | 0.048 | 0.013 | -0.098 |
| 2014-08-01 00:00:00 | 0.211 | 0.191 | 0.158 | 0.146 | 0.146 | 0.122 | 0.12 | 0.12 | 0.104 | 0.066 | -0.145 |
| 2014-09-01 00:00:00 | 0.021 | 0.019 | 0.033 | 0.036 | 0.014 | 0.017 | 0.009 | 0.017 | 0.009 | 0.025 | 0.005 |
| 2014-10-01 00:00:00 | 0.069 | 0.075 | 0.047 | 0.064 | 0.054 | 0.07 | 0.037 | 0.048 | 0.062 | 0.109 | 0.04 |
| 2014-11-01 00:00:00 | -0.108 | -0.083 | -0.078 | -0.076 | -0.067 | -0.048 | -0.036 | 0.006 | 0.021 | 0.202 | 0.309 |
| 2014-12-01 00:00:00 | 0.116 | 0.106 | 0.112 | 0.104 | 0.09 | 0.099 | 0.074 | 0.076 | 0.075 | -0.001 | -0.116 |
| 2015-01-01 00:00:00 | 0.117 | 0.086 | 0.081 | 0.074 | 0.09 | 0.087 | 0.099 | 0.087 | 0.095 | 0.058 | -0.059 |
| 2015-02-01 00:00:00 | 0.271 | 0.243 | 0.243 | 0.251 | 0.24 | 0.242 | 0.224 | 0.225 | 0.201 | 0.153 | -0.118 |
| 2015-03-01 00:00:00 | 0.217 | 0.179 | 0.171 | 0.2 | 0.148 | 0.164 | 0.161 | 0.158 | 0.147 | 0.196 | -0.021 |
| 2015-04-01 00:00:00 | 0.373 | 0.317 | 0.294 | 0.284 | 0.276 | 0.256 | 0.253 | 0.203 | 0.158 | 0.059 | -0.314 |
| 2015-05-01 00:00:00 | -0.047 | -0.096 | -0.123 | -0.124 | -0.155 | -0.156 | -0.156 | -0.118 | -0.133 | -0.098 | -0.05 |
| 2015-06-01 00:00:00 | -0.161 | -0.178 | -0.209 | -0.209 | -0.203 | -0.19 | -0.179 | -0.152 | -0.159 | -0.164 | -0.003 |
| 2015-07-01 00:00:00 | -0.088 | -0.125 | -0.121 | -0.149 | -0.156 | -0.15 | -0.151 | -0.165 | -0.168 | -0.139 | -0.051 |
| 2015-08-01 00:00:00 | 0.004 | -0.005 | -0.003 | 0.009 | -0.011 | -0.011 | -0.01 | -0.034 | -0.046 | -0.061 | -0.065 |
| 2015-09-01 00:00:00 | 0.301 | 0.27 | 0.276 | 0.257 | 0.258 | 0.237 | 0.222 | 0.219 | 0.209 | 0.136 | -0.165 |
| 2015-10-01 00:00:00 | 0.203 | 0.193 | 0.173 | 0.148 | 0.128 | 0.111 | 0.081 | 0.061 | 0.045 | 0.013 | -0.19 |
| 2015-11-01 00:00:00 | 0.152 | 0.099 | 0.085 | 0.066 | 0.053 | 0.029 | 0.038 | 0.034 | 0.019 | 0.031 | -0.121 |
| 2015-12-01 00:00:00 | -0.303 | -0.296 | -0.309 | -0.31 | -0.306 | -0.311 | -0.305 | -0.298 | -0.301 | -0.25 | 0.053 |
| 2016-01-01 00:00:00 | 0.009 | -0.005 | -0.009 | -0.022 | -0.021 | -0.028 | -0.031 | -0.02 | -0.019 | -0.022 | -0.03 |
| 2016-02-01 00:00:00 | 0.257 | 0.223 | 0.22 | 0.201 | 0.208 | 0.214 | 0.187 | 0.179 | 0.169 | 0.137 | -0.12 |
| 2016-03-01 00:00:00 | 0.062 | 0.042 | 0.016 | 0.0 | -0.011 | -0.027 | -0.016 | -0.034 | -0.03 | -0.036 | -0.098 |
| 2016-04-01 00:00:00 | -0.035 | -0.029 | -0.023 | -0.011 | -0.01 | -0.007 | 0.003 | 0.002 | -0.005 | -0.004 | 0.031 |
| 2016-05-01 00:00:00 | 0.068 | 0.085 | 0.085 | 0.082 | 0.082 | 0.072 | 0.055 | 0.054 | 0.027 | 0.013 | -0.055 |
| 2016-06-01 00:00:00 | 0.002 | 0.001 | -0.009 | -0.014 | -0.02 | -0.02 | -0.026 | -0.011 | -0.003 | 0.034 | 0.032 |
| 2016-07-01 00:00:00 | 0.085 | 0.066 | 0.061 | 0.06 | 0.046 | 0.039 | 0.039 | 0.036 | 0.032 | 0.034 | -0.051 |
| 2016-08-01 00:00:00 | 0.057 | 0.016 | -0.005 | -0.019 | -0.014 | -0.021 | -0.031 | -0.026 | -0.031 | -0.032 | -0.089 |
| 2016-09-01 00:00:00 | 0.051 | 0.056 | 0.051 | 0.042 | 0.043 | 0.047 | 0.024 | 0.027 | 0.022 | 0.023 | -0.028 |
| 2016-10-01 00:00:00 | 0.062 | 0.055 | 0.036 | 0.025 | 0.026 | 0.021 | 0.016 | 0.016 | 0.021 | 0.044 | -0.019 |
| 2016-11-01 00:00:00 | 0.007 | -0.039 | -0.039 | -0.06 | -0.063 | -0.071 | -0.067 | -0.065 | -0.06 | -0.063 | -0.07 |
| 2016-12-01 00:00:00 | -0.043 | -0.037 | -0.043 | -0.04 | -0.037 | -0.034 | -0.03 | -0.029 | -0.021 | 0.012 | 0.055 |
| 2017-01-01 00:00:00 | 0.083 | 0.047 | 0.046 | 0.044 | 0.048 | 0.042 | 0.037 | 0.039 | 0.049 | 0.033 | -0.05 |
| 2017-02-01 00:00:00 | -0.031 | -0.022 | -0.021 | -0.024 | -0.018 | -0.019 | -0.02 | -0.011 | -0.012 | 0.005 | 0.036 |
| 2017-03-01 00:00:00 | -0.098 | -0.089 | -0.077 | -0.078 | -0.068 | -0.076 | -0.053 | -0.045 | -0.027 | -0.01 | 0.089 |
| 2017-04-01 00:00:00 | -0.095 | -0.093 | -0.091 | -0.083 | -0.085 | -0.081 | -0.076 | -0.068 | -0.067 | -0.02 | 0.076 |
| 2017-05-01 00:00:00 | 0.041 | 0.033 | 0.03 | 0.03 | 0.028 | 0.04 | 0.036 | 0.043 | 0.055 | 0.054 | 0.013 |
| 2017-06-01 00:00:00 | -0.048 | -0.034 | -0.018 | -0.018 | 0.0 | -0.003 | 0.004 | 0.008 | 0.027 | 0.017 | 0.065 |
| 2017-07-01 00:00:00 | 0.095 | 0.058 | 0.048 | 0.039 | 0.042 | 0.035 | 0.03 | 0.034 | 0.027 | 0.025 | -0.071 |
| 2017-08-01 00:00:00 | 0.019 | 0.02 | 0.023 | 0.011 | 0.014 | 0.017 | 0.013 | 0.016 | 0.011 | 0.003 | -0.016 |
| 2017-09-01 00:00:00 | -0.011 | -0.031 | -0.023 | -0.031 | -0.024 | -0.028 | -0.027 | -0.02 | -0.007 | 0.02 | 0.031 |
| 2017-10-01 00:00:00 | -0.086 | -0.099 | -0.097 | -0.085 | -0.081 | -0.073 | -0.057 | -0.057 | -0.044 | -0.028 | 0.058 |
| 2017-11-01 00:00:00 | -0.022 | -0.029 | -0.021 | -0.031 | -0.023 | -0.021 | -0.014 | -0.014 | -0.006 | -0.003 | 0.019 |
| 2017-12-01 00:00:00 | -0.05 | -0.041 | -0.046 | -0.05 | -0.04 | -0.034 | -0.029 | -0.023 | -0.005 | 0.025 | 0.075 |
| 2018-01-01 00:00:00 | -0.073 | -0.066 | -0.065 | -0.06 | -0.055 | -0.051 | -0.04 | -0.029 | -0.031 | -0.042 | 0.031 |
| 2018-02-01 00:00:00 | 0.133 | 0.099 | 0.092 | 0.065 | 0.057 | 0.052 | 0.038 | 0.03 | 0.011 | -0.013 | -0.146 |
| 2018-03-01 00:00:00 | -0.045 | -0.036 | -0.045 | -0.04 | -0.051 | -0.036 | -0.043 | -0.034 | -0.044 | -0.033 | 0.012 |
| 2018-04-01 00:00:00 | 0.014 | 0.019 | -0.015 | -0.021 | -0.025 | -0.011 | -0.013 | -0.019 | -0.007 | 0.014 | 0.0 |
| 2018-05-01 00:00:00 | -0.112 | -0.098 | -0.119 | -0.114 | -0.12 | -0.116 | -0.112 | -0.102 | -0.101 | -0.081 | 0.031 |
| 2018-06-01 00:00:00 | 0.028 | 0.018 | 0.002 | -0.008 | -0.016 | 0.002 | -0.015 | -0.009 | -0.001 | -0.003 | -0.03 |
| 2018-07-01 00:00:00 | -0.083 | -0.09 | -0.08 | -0.085 | -0.079 | -0.082 | -0.088 | -0.082 | -0.077 | -0.068 | 0.014 |
| 2018-08-01 00:00:00 | 0.013 | -0.002 | -0.013 | -0.01 | -0.014 | -0.013 | -0.002 | -0.018 | -0.001 | 0.015 | 0.001 |
| 2018-09-01 00:00:00 | -0.044 | -0.079 | -0.09 | -0.091 | -0.097 | -0.113 | -0.116 | -0.11 | -0.091 | -0.093 | -0.049 |
| 2018-10-01 00:00:00 | 0.089 | 0.067 | 0.077 | 0.064 | 0.069 | 0.061 | 0.054 | 0.045 | 0.032 | 0.013 | -0.076 |
| 2018-11-01 00:00:00 | -0.022 | -0.035 | -0.031 | -0.043 | -0.048 | -0.055 | -0.047 | -0.044 | -0.04 | -0.044 | -0.022 |
| 2018-12-01 00:00:00 | -0.046 | -0.04 | -0.039 | -0.038 | -0.03 | -0.019 | -0.02 | -0.018 | 0.008 | 0.026 | 0.071 |
| 2019-01-01 00:00:00 | 0.241 | 0.235 | 0.237 | 0.243 | 0.231 | 0.218 | 0.239 | 0.203 | 0.209 | 0.187 | -0.054 |
| 2019-02-01 00:00:00 | 0.122 | 0.11 | 0.112 | 0.11 | 0.104 | 0.104 | 0.111 | 0.102 | 0.103 | 0.07 | -0.053 |
| 2019-03-01 00:00:00 | -0.018 | -0.038 | -0.048 | -0.045 | -0.052 | -0.034 | -0.037 | -0.05 | -0.047 | -0.022 | -0.004 |
| 2019-04-01 00:00:00 | -0.012 | -0.031 | -0.033 | -0.051 | -0.055 | -0.045 | -0.06 | -0.067 | -0.066 | -0.067 | -0.055 |
| 2019-05-01 00:00:00 | 0.017 | 0.013 | 0.001 | -0.006 | -0.004 | -0.007 | -0.01 | 0.001 | 0.015 | 0.035 | 0.018 |
| 2019-06-01 00:00:00 | -0.011 | -0.016 | -0.03 | -0.028 | -0.023 | -0.032 | -0.016 | -0.022 | -0.005 | 0.005 | 0.016 |
| 2019-07-01 00:00:00 | -0.027 | -0.017 | -0.022 | -0.011 | -0.008 | -0.004 | -0.013 | -0.001 | -0.008 | -0.002 | 0.025 |
| 2019-08-01 00:00:00 | 0.018 | 0.023 | 0.027 | 0.019 | 0.014 | 0.01 | 0.008 | 0.015 | 0.009 | 0.01 | -0.008 |
| 2019-09-01 00:00:00 | -0.0 | -0.008 | -0.002 | -0.002 | -0.02 | -0.001 | -0.011 | -0.003 | -0.003 | 0.005 | 0.006 |
| 2019-10-01 00:00:00 | -0.015 | -0.022 | -0.026 | -0.023 | -0.033 | -0.023 | -0.029 | -0.023 | -0.011 | -0.005 | 0.01 |
| 2019-11-01 00:00:00 | 0.097 | 0.097 | 0.077 | 0.078 | 0.081 | 0.091 | 0.071 | 0.081 | 0.081 | 0.082 | -0.015 |
| 2019-12-01 00:00:00 | -0.023 | -0.014 | 0.002 | 0.005 | -0.001 | 0.013 | 0.01 | 0.027 | 0.014 | 0.001 | 0.025 |
+---------------------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+--------+
| Group | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Diff |
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+--------+
| Average | 0.031 | 0.019 | 0.015 | 0.014 | 0.011 | 0.011 | 0.008 | 0.009 | 0.008 | 0.008 | -0.023 |
| T-Test | 3.73 | 2.84 | 2.313 | 2.043 | 1.756 | 1.781 | 1.359 | 1.578 | 1.479 | 1.555 | -3.79 |
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+--------+
The second dataset contains below 30% stocks from 2000-01-01 to 2019-12-01. The size effect is significant since the t-test statistics is -3.79 whose absolute value is more than 2 corresponding to the significance level at 0.05. The monthly excess return is 2.3% and the annual excess return is about 27.6%.
# %% dataset 3
# select stocks whose size is among the up 30% stocks in each month and whose trading
# days are more than or equal to 10 days
test_data_3 = month_return[(month_return['cap']==True) & (month_return['Ndaytrd']>=10)]
# construct data for univariate analysis
test_data_3 = test_data_3[['emrwd', 'Msmvttl', 'Time']].dropna()
# time interval between 2000-01-01 to 2016-12-01
test_data_3 = test_data_3[(test_data_3['Time'] >= '2000-01-01') & (test_data_3['Time'] <= '2016-12-01')]
# analysis
uni_3 = Univariate(np.array(test_data_3), number=9)
uni_3.average_by_time()
uni_3.summary_and_test()
uni_3.print_summary_by_time()
uni_3.print_summary()
==========================================================================================================================
+---------------------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+
| Time | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | diff |
+---------------------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+
| 2000-01-01 00:00:00 | 0.124 | 0.144 | 0.126 | 0.129 | 0.1 | 0.129 | 0.095 | 0.103 | 0.114 | 0.135 | 0.011 |
| 2000-02-01 00:00:00 | 0.155 | 0.122 | 0.075 | 0.12 | 0.053 | 0.064 | 0.054 | 0.04 | 0.022 | 0.009 | -0.146 |
| 2000-03-01 00:00:00 | 0.007 | 0.022 | 0.012 | 0.01 | 0.004 | 0.002 | 0.016 | 0.015 | 0.017 | 0.033 | 0.026 |
| 2000-04-01 00:00:00 | 0.034 | 0.042 | 0.042 | 0.043 | 0.03 | 0.024 | 0.049 | 0.022 | 0.021 | 0.021 | -0.013 |
| 2000-05-01 00:00:00 | 0.008 | 0.041 | 0.046 | 0.015 | 0.029 | 0.022 | 0.007 | 0.03 | 0.044 | 0.021 | 0.013 |
| 2000-06-01 00:00:00 | 0.06 | 0.067 | 0.045 | 0.038 | 0.051 | 0.042 | 0.029 | 0.036 | 0.032 | 0.045 | -0.016 |
| 2000-07-01 00:00:00 | 0.017 | -0.003 | 0.003 | 0.001 | -0.013 | -0.008 | -0.014 | -0.003 | -0.012 | -0.028 | -0.045 |
| 2000-08-01 00:00:00 | -0.027 | -0.025 | -0.032 | -0.056 | -0.061 | -0.055 | -0.04 | -0.065 | -0.054 | -0.056 | -0.029 |
| 2000-09-01 00:00:00 | 0.038 | 0.049 | 0.034 | 0.034 | 0.038 | 0.022 | 0.031 | 0.015 | 0.013 | 0.002 | -0.036 |
| 2000-10-01 00:00:00 | 0.056 | 0.069 | 0.063 | 0.063 | 0.063 | 0.069 | 0.042 | 0.046 | 0.053 | 0.059 | 0.004 |
| 2000-11-01 00:00:00 | 0.009 | 0.013 | 0.011 | 0.008 | -0.002 | 0.014 | 0.01 | 0.0 | -0.012 | -0.024 | -0.033 |
| 2000-12-01 00:00:00 | 0.0 | -0.008 | -0.018 | -0.007 | -0.01 | -0.014 | 0.001 | -0.007 | -0.008 | -0.019 | -0.019 |
| 2001-01-01 00:00:00 | -0.077 | -0.058 | -0.067 | -0.064 | -0.053 | -0.055 | -0.063 | -0.055 | -0.048 | -0.05 | 0.027 |
| 2001-02-01 00:00:00 | 0.096 | 0.072 | 0.085 | 0.074 | 0.088 | 0.079 | 0.075 | 0.061 | 0.065 | 0.056 | -0.04 |
| 2001-03-01 00:00:00 | 0.015 | 0.009 | -0.01 | -0.001 | -0.007 | -0.011 | 0.001 | -0.012 | -0.009 | -0.017 | -0.032 |
| 2001-04-01 00:00:00 | 0.073 | 0.045 | 0.051 | 0.049 | 0.038 | 0.03 | 0.039 | 0.029 | 0.016 | 0.01 | -0.063 |
| 2001-05-01 00:00:00 | 0.018 | 0.01 | 0.012 | 0.012 | 0.019 | 0.002 | -0.005 | 0.015 | -0.01 | -0.002 | -0.02 |
| 2001-06-01 00:00:00 | -0.138 | -0.138 | -0.129 | -0.134 | -0.141 | -0.149 | -0.123 | -0.131 | -0.13 | -0.13 | 0.009 |
| 2001-07-01 00:00:00 | -0.031 | -0.035 | -0.034 | -0.039 | -0.038 | -0.041 | -0.04 | -0.03 | -0.034 | -0.049 | -0.018 |
| 2001-08-01 00:00:00 | -0.055 | -0.067 | -0.048 | -0.067 | -0.048 | -0.047 | -0.046 | -0.047 | -0.05 | -0.022 | 0.033 |
| 2001-09-01 00:00:00 | -0.062 | -0.054 | -0.052 | -0.057 | -0.056 | -0.066 | -0.053 | -0.046 | -0.053 | -0.028 | 0.034 |
| 2001-10-01 00:00:00 | 0.057 | 0.057 | 0.042 | 0.054 | 0.046 | 0.039 | 0.041 | 0.034 | 0.039 | 0.021 | -0.035 |
| 2001-11-01 00:00:00 | -0.067 | -0.082 | -0.069 | -0.078 | -0.067 | -0.063 | -0.067 | -0.058 | -0.05 | -0.047 | 0.021 |
| 2001-12-01 00:00:00 | -0.141 | -0.14 | -0.119 | -0.121 | -0.117 | -0.116 | -0.108 | -0.1 | -0.087 | -0.062 | 0.079 |
| 2002-01-01 00:00:00 | 0.035 | 0.044 | 0.043 | 0.036 | 0.03 | 0.032 | 0.028 | 0.025 | 0.016 | 0.011 | -0.024 |
| 2002-02-01 00:00:00 | 0.097 | 0.08 | 0.076 | 0.078 | 0.069 | 0.076 | 0.076 | 0.056 | 0.061 | 0.032 | -0.065 |
| 2002-03-01 00:00:00 | 0.057 | 0.059 | 0.048 | 0.037 | 0.053 | 0.042 | 0.028 | 0.037 | 0.031 | 0.033 | -0.025 |
| 2002-04-01 00:00:00 | -0.095 | -0.089 | -0.095 | -0.093 | -0.092 | -0.095 | -0.09 | -0.089 | -0.092 | -0.075 | 0.02 |
| 2002-05-01 00:00:00 | 0.116 | 0.115 | 0.11 | 0.113 | 0.122 | 0.114 | 0.142 | 0.123 | 0.152 | 0.158 | 0.042 |
| 2002-06-01 00:00:00 | -0.036 | -0.034 | -0.03 | -0.034 | -0.041 | -0.04 | -0.04 | -0.049 | -0.041 | -0.045 | -0.009 |
| 2002-07-01 00:00:00 | 0.011 | 0.004 | 0.005 | -0.0 | 0.009 | 0.008 | 0.007 | 0.011 | -0.003 | 0.005 | -0.006 |
| 2002-08-01 00:00:00 | -0.058 | -0.056 | -0.065 | -0.059 | -0.057 | -0.059 | -0.054 | -0.046 | -0.05 | -0.047 | 0.011 |
| 2002-09-01 00:00:00 | -0.073 | -0.06 | -0.059 | -0.053 | -0.049 | -0.057 | -0.045 | -0.045 | -0.049 | -0.044 | 0.028 |
| 2002-10-01 00:00:00 | -0.084 | -0.093 | -0.087 | -0.079 | -0.071 | -0.076 | -0.077 | -0.053 | -0.046 | -0.033 | 0.052 |
| 2002-11-01 00:00:00 | -0.059 | -0.055 | -0.056 | -0.058 | -0.051 | -0.062 | -0.05 | -0.05 | -0.05 | -0.045 | 0.013 |
| 2002-12-01 00:00:00 | 0.115 | 0.111 | 0.09 | 0.103 | 0.099 | 0.085 | 0.076 | 0.078 | 0.078 | 0.095 | -0.02 |
| 2003-01-01 00:00:00 | 0.015 | 0.012 | 0.019 | 0.01 | 0.01 | 0.012 | 0.014 | 0.012 | 0.004 | 0.006 | -0.009 |
| 2003-02-01 00:00:00 | -0.03 | -0.037 | -0.032 | -0.031 | -0.023 | -0.026 | -0.022 | -0.009 | -0.0 | 0.013 | 0.043 |
| 2003-03-01 00:00:00 | -0.07 | -0.041 | -0.05 | -0.048 | -0.037 | -0.02 | -0.023 | 0.002 | 0.002 | 0.033 | 0.104 |
| 2003-04-01 00:00:00 | 0.028 | 0.041 | 0.027 | 0.038 | 0.042 | 0.034 | 0.057 | 0.047 | 0.054 | 0.058 | 0.03 |
| 2003-05-01 00:00:00 | -0.067 | -0.063 | -0.074 | -0.07 | -0.079 | -0.072 | -0.082 | -0.056 | -0.06 | -0.065 | 0.002 |
| 2003-06-01 00:00:00 | -0.036 | -0.044 | -0.037 | -0.031 | -0.043 | -0.023 | -0.022 | -0.015 | 0.006 | 0.016 | 0.052 |
| 2003-07-01 00:00:00 | -0.02 | -0.016 | -0.027 | -0.041 | -0.029 | -0.037 | -0.032 | -0.025 | -0.029 | -0.043 | -0.022 |
| 2003-08-01 00:00:00 | -0.044 | -0.043 | -0.056 | -0.035 | -0.034 | -0.037 | -0.045 | -0.049 | -0.041 | -0.039 | 0.006 |
| 2003-09-01 00:00:00 | -0.081 | -0.077 | -0.073 | -0.066 | -0.062 | -0.064 | -0.042 | -0.032 | -0.023 | 0.011 | 0.092 |
| 2003-10-01 00:00:00 | 0.008 | 0.022 | 0.026 | 0.035 | 0.033 | 0.015 | 0.026 | 0.018 | 0.014 | 0.03 | 0.022 |
| 2003-11-01 00:00:00 | -0.019 | -0.021 | -0.028 | -0.016 | 0.01 | 0.013 | 0.022 | 0.022 | 0.035 | 0.088 | 0.106 |
| 2003-12-01 00:00:00 | 0.091 | 0.103 | 0.097 | 0.099 | 0.084 | 0.081 | 0.067 | 0.067 | 0.075 | 0.047 | -0.044 |
| 2004-01-01 00:00:00 | 0.122 | 0.097 | 0.083 | 0.093 | 0.11 | 0.081 | 0.077 | 0.074 | 0.071 | 0.051 | -0.072 |
| 2004-02-01 00:00:00 | 0.042 | 0.046 | 0.035 | 0.052 | 0.052 | 0.029 | 0.036 | 0.033 | 0.028 | 0.028 | -0.014 |
| 2004-03-01 00:00:00 | -0.103 | -0.086 | -0.1 | -0.1 | -0.091 | -0.093 | -0.083 | -0.101 | -0.086 | -0.116 | -0.013 |
| 2004-04-01 00:00:00 | -0.029 | -0.017 | -0.009 | -0.025 | -0.014 | -0.03 | -0.019 | -0.026 | -0.035 | -0.024 | 0.005 |
| 2004-05-01 00:00:00 | -0.128 | -0.131 | -0.135 | -0.134 | -0.132 | -0.126 | -0.114 | -0.124 | -0.111 | -0.085 | 0.043 |
| 2004-06-01 00:00:00 | -0.026 | -0.034 | -0.022 | -0.022 | 0.004 | 0.007 | 0.01 | 0.005 | 0.021 | 0.003 | 0.028 |
| 2004-07-01 00:00:00 | -0.049 | -0.046 | -0.052 | -0.057 | -0.058 | -0.059 | -0.062 | -0.066 | -0.042 | -0.036 | 0.013 |
| 2004-08-01 00:00:00 | 0.061 | 0.043 | 0.053 | 0.045 | 0.053 | 0.064 | 0.057 | 0.062 | 0.056 | 0.062 | 0.001 |
| 2004-09-01 00:00:00 | -0.075 | -0.053 | -0.076 | -0.048 | -0.057 | -0.066 | -0.061 | -0.03 | -0.018 | -0.053 | 0.022 |
| 2004-10-01 00:00:00 | 0.059 | 0.05 | 0.04 | 0.041 | 0.049 | 0.046 | 0.032 | 0.025 | 0.002 | -0.005 | -0.064 |
| 2004-11-01 00:00:00 | -0.078 | -0.08 | -0.086 | -0.079 | -0.09 | -0.093 | -0.077 | -0.066 | -0.076 | -0.048 | 0.03 |
| 2004-12-01 00:00:00 | -0.076 | -0.073 | -0.084 | -0.079 | -0.079 | -0.08 | -0.078 | -0.078 | -0.069 | -0.047 | 0.029 |
| 2005-01-01 00:00:00 | 0.112 | 0.11 | 0.107 | 0.102 | 0.116 | 0.115 | 0.117 | 0.095 | 0.093 | 0.093 | -0.019 |
| 2005-02-01 00:00:00 | -0.147 | -0.137 | -0.138 | -0.133 | -0.117 | -0.121 | -0.112 | -0.121 | -0.088 | -0.086 | 0.06 |
| 2005-03-01 00:00:00 | -0.107 | -0.076 | -0.084 | -0.049 | -0.067 | -0.05 | -0.041 | -0.037 | -0.008 | 0.012 | 0.119 |
| 2005-04-01 00:00:00 | -0.015 | -0.024 | -0.026 | -0.033 | -0.04 | -0.054 | -0.059 | -0.079 | -0.077 | -0.1 | -0.085 |
| 2005-05-01 00:00:00 | -0.001 | 0.001 | -0.001 | -0.003 | 0.003 | -0.011 | -0.004 | 0.011 | -0.005 | 0.037 | 0.038 |
| 2005-06-01 00:00:00 | -0.083 | -0.07 | -0.079 | -0.07 | -0.058 | -0.063 | -0.053 | -0.036 | -0.012 | 0.015 | 0.097 |
| 2005-07-01 00:00:00 | 0.169 | 0.184 | 0.163 | 0.159 | 0.131 | 0.132 | 0.127 | 0.139 | 0.073 | 0.048 | -0.121 |
| 2005-08-01 00:00:00 | 0.02 | 0.008 | 0.007 | 0.025 | 0.028 | 0.024 | 0.035 | 0.036 | 0.016 | -0.013 | -0.034 |
| 2005-09-01 00:00:00 | -0.071 | -0.05 | -0.067 | -0.043 | -0.062 | -0.055 | -0.056 | -0.042 | -0.057 | -0.053 | 0.019 |
| 2005-10-01 00:00:00 | 0.018 | 0.01 | 0.019 | 0.005 | 0.016 | 0.016 | -0.014 | -0.014 | -0.019 | -0.004 | -0.022 |
| 2005-11-01 00:00:00 | 0.016 | 0.01 | 0.018 | 0.022 | 0.033 | 0.043 | 0.047 | 0.067 | 0.062 | 0.079 | 0.063 |
| 2005-12-01 00:00:00 | 0.098 | 0.067 | 0.09 | 0.088 | 0.094 | 0.119 | 0.141 | 0.12 | 0.13 | 0.088 | -0.01 |
| 2006-01-01 00:00:00 | 0.034 | 0.026 | 0.023 | 0.019 | 0.021 | 0.017 | 0.017 | -0.007 | 0.022 | 0.046 | 0.012 |
| 2006-02-01 00:00:00 | -0.002 | 0.001 | 0.006 | 0.008 | 0.022 | 0.025 | 0.042 | 0.048 | 0.048 | 0.025 | 0.027 |
| 2006-03-01 00:00:00 | 0.093 | 0.106 | 0.101 | 0.089 | 0.122 | 0.118 | 0.133 | 0.145 | 0.16 | 0.127 | 0.034 |
| 2006-04-01 00:00:00 | 0.297 | 0.251 | 0.284 | 0.265 | 0.261 | 0.222 | 0.266 | 0.201 | 0.208 | 0.156 | -0.141 |
| 2006-05-01 00:00:00 | 0.065 | 0.091 | 0.067 | 0.052 | 0.058 | 0.04 | 0.048 | 0.045 | 0.013 | 0.02 | -0.045 |
| 2006-06-01 00:00:00 | -0.002 | -0.038 | -0.039 | -0.022 | -0.043 | -0.043 | -0.051 | -0.059 | -0.056 | -0.088 | -0.086 |
| 2006-07-01 00:00:00 | 0.029 | 0.016 | 0.042 | 0.028 | 0.042 | 0.029 | 0.057 | 0.031 | 0.04 | 0.024 | -0.005 |
| 2006-08-01 00:00:00 | 0.049 | 0.056 | 0.049 | 0.039 | 0.038 | 0.052 | 0.026 | 0.042 | 0.041 | 0.044 | -0.005 |
| 2006-09-01 00:00:00 | -0.011 | 0.01 | 0.016 | -0.013 | -0.029 | 0.004 | -0.01 | 0.029 | 0.014 | 0.034 | 0.045 |
| 2006-10-01 00:00:00 | 0.014 | 0.024 | 0.034 | 0.038 | 0.058 | 0.055 | 0.063 | 0.079 | 0.139 | 0.183 | 0.169 |
| 2006-11-01 00:00:00 | 0.055 | 0.032 | 0.036 | 0.043 | 0.072 | 0.061 | 0.088 | 0.097 | 0.099 | 0.17 | 0.115 |
| 2006-12-01 00:00:00 | 0.296 | 0.254 | 0.262 | 0.251 | 0.233 | 0.239 | 0.232 | 0.209 | 0.254 | 0.173 | -0.122 |
| 2007-01-01 00:00:00 | 0.254 | 0.179 | 0.218 | 0.187 | 0.26 | 0.177 | 0.139 | 0.162 | 0.128 | 0.066 | -0.188 |
| 2007-02-01 00:00:00 | 0.196 | 0.203 | 0.179 | 0.163 | 0.171 | 0.175 | 0.142 | 0.103 | 0.072 | 0.09 | -0.107 |
| 2007-03-01 00:00:00 | 0.389 | 0.32 | 0.358 | 0.298 | 0.342 | 0.341 | 0.329 | 0.362 | 0.337 | 0.262 | -0.127 |
| 2007-04-01 00:00:00 | 0.067 | 0.093 | 0.064 | 0.065 | 0.178 | 0.113 | 0.081 | 0.092 | 0.143 | 0.118 | 0.051 |
| 2007-05-01 00:00:00 | -0.205 | -0.205 | -0.177 | -0.162 | -0.144 | -0.171 | -0.121 | -0.109 | -0.064 | -0.028 | 0.176 |
| 2007-06-01 00:00:00 | 0.235 | 0.26 | 0.231 | 0.228 | 0.216 | 0.2 | 0.192 | 0.196 | 0.182 | 0.186 | -0.049 |
| 2007-07-01 00:00:00 | 0.093 | 0.095 | 0.108 | 0.086 | 0.133 | 0.093 | 0.108 | 0.131 | 0.161 | 0.183 | 0.09 |
| 2007-08-01 00:00:00 | 0.025 | 0.015 | 0.043 | 0.059 | 0.03 | 0.046 | 0.018 | 0.038 | 0.082 | 0.073 | 0.048 |
| 2007-09-01 00:00:00 | -0.113 | -0.135 | -0.115 | -0.099 | -0.099 | -0.115 | -0.093 | -0.091 | -0.072 | 0.016 | 0.129 |
| 2007-10-01 00:00:00 | -0.038 | -0.058 | -0.05 | -0.084 | -0.048 | -0.112 | -0.091 | -0.13 | -0.163 | -0.184 | -0.147 |
| 2007-11-01 00:00:00 | 0.207 | 0.201 | 0.219 | 0.213 | 0.218 | 0.209 | 0.23 | 0.192 | 0.192 | 0.135 | -0.073 |
| 2007-12-01 00:00:00 | -0.061 | -0.058 | -0.075 | -0.052 | -0.058 | -0.06 | -0.065 | -0.078 | -0.079 | -0.141 | -0.081 |
| 2008-01-01 00:00:00 | 0.11 | 0.096 | 0.1 | 0.089 | 0.083 | 0.068 | 0.063 | 0.05 | 0.03 | 0.012 | -0.097 |
| 2008-02-01 00:00:00 | -0.188 | -0.189 | -0.196 | -0.202 | -0.204 | -0.199 | -0.214 | -0.211 | -0.233 | -0.212 | -0.023 |
| 2008-03-01 00:00:00 | -0.061 | -0.091 | -0.055 | -0.055 | -0.048 | -0.038 | -0.013 | 0.003 | 0.03 | 0.057 | 0.118 |
| 2008-04-01 00:00:00 | 0.002 | -0.017 | -0.03 | -0.039 | -0.035 | -0.039 | -0.053 | -0.045 | -0.054 | -0.089 | -0.091 |
| 2008-05-01 00:00:00 | -0.275 | -0.261 | -0.249 | -0.262 | -0.252 | -0.239 | -0.247 | -0.242 | -0.227 | -0.215 | 0.06 |
| 2008-06-01 00:00:00 | 0.114 | 0.102 | 0.107 | 0.105 | 0.081 | 0.074 | 0.08 | 0.05 | 0.044 | -0.005 | -0.119 |
| 2008-07-01 00:00:00 | -0.244 | -0.214 | -0.223 | -0.248 | -0.229 | -0.235 | -0.253 | -0.226 | -0.239 | -0.169 | 0.075 |
| 2008-08-01 00:00:00 | -0.101 | -0.085 | -0.112 | -0.075 | -0.082 | -0.084 | -0.064 | -0.046 | -0.041 | -0.016 | 0.085 |
| 2008-09-01 00:00:00 | -0.261 | -0.263 | -0.251 | -0.261 | -0.271 | -0.265 | -0.26 | -0.273 | -0.261 | -0.257 | 0.003 |
| 2008-10-01 00:00:00 | 0.233 | 0.211 | 0.233 | 0.211 | 0.202 | 0.175 | 0.162 | 0.166 | 0.15 | 0.12 | -0.112 |
| 2008-11-01 00:00:00 | 0.116 | 0.053 | 0.073 | 0.073 | 0.043 | 0.054 | 0.064 | 0.052 | 0.041 | -0.002 | -0.118 |
| 2008-12-01 00:00:00 | 0.157 | 0.155 | 0.167 | 0.186 | 0.17 | 0.175 | 0.167 | 0.161 | 0.147 | 0.104 | -0.053 |
| 2009-01-01 00:00:00 | 0.091 | 0.081 | 0.091 | 0.093 | 0.073 | 0.084 | 0.077 | 0.064 | 0.06 | 0.06 | -0.031 |
| 2009-02-01 00:00:00 | 0.244 | 0.249 | 0.213 | 0.229 | 0.205 | 0.217 | 0.209 | 0.187 | 0.213 | 0.178 | -0.066 |
| 2009-03-01 00:00:00 | 0.07 | 0.076 | 0.085 | 0.074 | 0.049 | 0.039 | 0.078 | 0.025 | 0.065 | 0.046 | -0.025 |
| 2009-04-01 00:00:00 | 0.078 | 0.071 | 0.085 | 0.075 | 0.045 | 0.054 | 0.051 | 0.038 | 0.062 | 0.046 | -0.031 |
| 2009-05-01 00:00:00 | 0.038 | 0.035 | 0.049 | 0.052 | 0.037 | 0.052 | 0.049 | 0.081 | 0.072 | 0.145 | 0.107 |
| 2009-06-01 00:00:00 | 0.138 | 0.163 | 0.12 | 0.155 | 0.136 | 0.13 | 0.166 | 0.167 | 0.179 | 0.195 | 0.057 |
| 2009-07-01 00:00:00 | -0.155 | -0.136 | -0.135 | -0.147 | -0.146 | -0.168 | -0.171 | -0.177 | -0.194 | -0.245 | -0.09 |
| 2009-08-01 00:00:00 | 0.022 | 0.022 | 0.049 | 0.02 | 0.032 | 0.035 | 0.036 | 0.046 | 0.045 | 0.049 | 0.028 |
| 2009-09-01 00:00:00 | 0.125 | 0.117 | 0.133 | 0.126 | 0.133 | 0.115 | 0.108 | 0.11 | 0.107 | 0.085 | -0.039 |
| 2009-10-01 00:00:00 | 0.16 | 0.155 | 0.174 | 0.175 | 0.151 | 0.147 | 0.142 | 0.112 | 0.103 | 0.078 | -0.082 |
| 2009-11-01 00:00:00 | 0.038 | 0.027 | 0.03 | 0.029 | 0.024 | 0.001 | 0.005 | -0.001 | -0.006 | 0.008 | -0.03 |
| 2009-12-01 00:00:00 | -0.02 | -0.026 | -0.024 | -0.042 | -0.012 | -0.019 | -0.038 | -0.04 | -0.075 | -0.103 | -0.084 |
| 2010-01-01 00:00:00 | 0.068 | 0.062 | 0.059 | 0.073 | 0.055 | 0.057 | 0.058 | 0.047 | 0.039 | 0.021 | -0.048 |
| 2010-02-01 00:00:00 | 0.055 | 0.037 | 0.043 | 0.043 | 0.053 | 0.043 | 0.009 | 0.01 | 0.016 | 0.015 | -0.04 |
| 2010-03-01 00:00:00 | -0.085 | -0.067 | -0.082 | -0.071 | -0.059 | -0.083 | -0.078 | -0.053 | -0.067 | -0.081 | 0.004 |
| 2010-04-01 00:00:00 | -0.088 | -0.092 | -0.095 | -0.075 | -0.067 | -0.079 | -0.072 | -0.071 | -0.081 | -0.094 | -0.006 |
| 2010-05-01 00:00:00 | -0.081 | -0.097 | -0.083 | -0.099 | -0.092 | -0.103 | -0.099 | -0.098 | -0.097 | -0.077 | 0.005 |
| 2010-06-01 00:00:00 | 0.147 | 0.149 | 0.151 | 0.17 | 0.148 | 0.142 | 0.132 | 0.133 | 0.135 | 0.131 | -0.016 |
| 2010-07-01 00:00:00 | 0.108 | 0.112 | 0.098 | 0.094 | 0.081 | 0.085 | 0.122 | 0.079 | 0.059 | 0.019 | -0.089 |
| 2010-08-01 00:00:00 | -0.004 | 0.009 | 0.012 | -0.004 | -0.016 | 0.008 | 0.013 | 0.015 | 0.019 | 0.017 | 0.021 |
| 2010-09-01 00:00:00 | 0.108 | 0.074 | 0.085 | 0.097 | 0.08 | 0.103 | 0.105 | 0.092 | 0.148 | 0.155 | 0.047 |
| 2010-10-01 00:00:00 | 0.036 | 0.021 | 0.002 | 0.015 | 0.01 | 0.019 | 0.02 | -0.001 | -0.035 | -0.066 | -0.102 |
| 2010-11-01 00:00:00 | -0.024 | -0.025 | -0.031 | -0.036 | -0.026 | -0.035 | -0.034 | -0.02 | -0.006 | 0.006 | 0.03 |
| 2010-12-01 00:00:00 | -0.058 | -0.061 | -0.059 | -0.05 | -0.074 | -0.064 | -0.068 | -0.067 | -0.051 | -0.018 | 0.04 |
| 2011-01-01 00:00:00 | 0.098 | 0.093 | 0.11 | 0.096 | 0.105 | 0.103 | 0.101 | 0.097 | 0.069 | 0.052 | -0.046 |
| 2011-02-01 00:00:00 | 0.004 | -0.018 | -0.023 | -0.017 | -0.026 | -0.038 | -0.023 | -0.027 | -0.033 | -0.02 | -0.024 |
| 2011-03-01 00:00:00 | -0.054 | -0.036 | -0.052 | -0.05 | -0.027 | -0.035 | -0.039 | -0.039 | -0.02 | -0.022 | 0.032 |
| 2011-04-01 00:00:00 | -0.081 | -0.067 | -0.055 | -0.083 | -0.082 | -0.076 | -0.084 | -0.085 | -0.077 | -0.066 | 0.016 |
| 2011-05-01 00:00:00 | 0.034 | 0.031 | 0.042 | 0.023 | 0.041 | 0.032 | 0.031 | 0.036 | 0.03 | 0.03 | -0.004 |
| 2011-06-01 00:00:00 | 0.033 | 0.026 | 0.038 | 0.021 | 0.017 | 0.022 | 0.024 | 0.016 | -0.0 | -0.017 | -0.05 |
| 2011-07-01 00:00:00 | -0.017 | -0.032 | -0.026 | -0.032 | -0.036 | -0.034 | -0.034 | -0.047 | -0.041 | -0.054 | -0.036 |
| 2011-08-01 00:00:00 | -0.123 | -0.115 | -0.124 | -0.131 | -0.136 | -0.128 | -0.141 | -0.125 | -0.111 | -0.093 | 0.029 |
| 2011-09-01 00:00:00 | 0.041 | 0.045 | 0.046 | 0.041 | 0.047 | 0.026 | 0.052 | 0.045 | 0.036 | 0.034 | -0.006 |
| 2011-10-01 00:00:00 | -0.045 | -0.038 | -0.029 | -0.04 | -0.041 | -0.042 | -0.045 | -0.049 | -0.056 | -0.069 | -0.024 |
| 2011-11-01 00:00:00 | -0.17 | -0.17 | -0.174 | -0.151 | -0.164 | -0.159 | -0.137 | -0.13 | -0.102 | -0.082 | 0.087 |
| 2011-12-01 00:00:00 | -0.016 | -0.018 | -0.006 | -0.018 | -0.018 | 0.003 | -0.013 | -0.0 | -0.002 | 0.045 | 0.062 |
| 2012-01-01 00:00:00 | 0.143 | 0.138 | 0.135 | 0.136 | 0.129 | 0.128 | 0.131 | 0.119 | 0.109 | 0.072 | -0.071 |
| 2012-02-01 00:00:00 | -0.081 | -0.061 | -0.075 | -0.08 | -0.077 | -0.078 | -0.073 | -0.079 | -0.071 | -0.074 | 0.007 |
| 2012-03-01 00:00:00 | 0.088 | 0.069 | 0.064 | 0.073 | 0.07 | 0.064 | 0.063 | 0.053 | 0.063 | 0.072 | -0.016 |
| 2012-04-01 00:00:00 | 0.022 | 0.024 | 0.025 | 0.017 | 0.017 | 0.033 | 0.024 | 0.028 | 0.038 | 0.008 | -0.014 |
| 2012-05-01 00:00:00 | -0.06 | -0.06 | -0.061 | -0.073 | -0.067 | -0.066 | -0.071 | -0.071 | -0.058 | -0.057 | 0.003 |
| 2012-06-01 00:00:00 | -0.11 | -0.094 | -0.092 | -0.103 | -0.099 | -0.089 | -0.087 | -0.082 | -0.075 | -0.054 | 0.057 |
| 2012-07-01 00:00:00 | 0.042 | 0.045 | 0.033 | 0.026 | 0.033 | 0.0 | 0.01 | -0.022 | -0.034 | -0.056 | -0.098 |
| 2012-08-01 00:00:00 | 0.003 | 0.004 | 0.002 | -0.005 | 0.004 | 0.002 | 0.022 | 0.007 | 0.029 | 0.044 | 0.04 |
| 2012-09-01 00:00:00 | -0.004 | 0.002 | 0.008 | -0.0 | -0.015 | 0.0 | -0.012 | -0.02 | -0.017 | -0.016 | -0.012 |
| 2012-10-01 00:00:00 | -0.119 | -0.121 | -0.125 | -0.113 | -0.124 | -0.113 | -0.123 | -0.103 | -0.097 | -0.059 | 0.06 |
| 2012-11-01 00:00:00 | 0.164 | 0.178 | 0.184 | 0.163 | 0.163 | 0.182 | 0.181 | 0.166 | 0.171 | 0.172 | 0.008 |
| 2012-12-01 00:00:00 | 0.07 | 0.072 | 0.066 | 0.069 | 0.065 | 0.054 | 0.065 | 0.061 | 0.049 | 0.057 | -0.013 |
| 2013-01-01 00:00:00 | 0.044 | 0.033 | 0.036 | 0.037 | 0.038 | 0.043 | 0.042 | 0.039 | 0.024 | -0.004 | -0.047 |
| 2013-02-01 00:00:00 | -0.032 | -0.024 | -0.031 | -0.027 | -0.047 | -0.041 | -0.047 | -0.057 | -0.04 | -0.05 | -0.018 |
| 2013-03-01 00:00:00 | -0.032 | -0.032 | -0.025 | -0.026 | -0.031 | -0.027 | -0.019 | -0.017 | -0.026 | -0.021 | 0.011 |
| 2013-04-01 00:00:00 | 0.158 | 0.154 | 0.147 | 0.142 | 0.152 | 0.156 | 0.15 | 0.125 | 0.125 | 0.067 | -0.091 |
| 2013-05-01 00:00:00 | -0.16 | -0.157 | -0.157 | -0.157 | -0.154 | -0.154 | -0.164 | -0.151 | -0.154 | -0.136 | 0.024 |
| 2013-06-01 00:00:00 | 0.073 | 0.084 | 0.079 | 0.069 | 0.054 | 0.07 | 0.073 | 0.045 | 0.062 | 0.014 | -0.058 |
| 2013-07-01 00:00:00 | 0.102 | 0.093 | 0.076 | 0.064 | 0.102 | 0.072 | 0.082 | 0.063 | 0.069 | 0.058 | -0.045 |
| 2013-08-01 00:00:00 | 0.053 | 0.064 | 0.046 | 0.045 | 0.048 | 0.061 | 0.043 | 0.051 | 0.07 | 0.047 | -0.006 |
| 2013-09-01 00:00:00 | -0.025 | -0.023 | -0.016 | -0.035 | -0.039 | -0.033 | -0.034 | -0.029 | -0.034 | -0.04 | -0.014 |
| 2013-10-01 00:00:00 | 0.092 | 0.095 | 0.083 | 0.083 | 0.084 | 0.083 | 0.055 | 0.063 | 0.052 | 0.039 | -0.054 |
| 2013-11-01 00:00:00 | -0.034 | -0.029 | -0.038 | -0.032 | -0.045 | -0.027 | -0.028 | -0.047 | -0.033 | -0.046 | -0.012 |
| 2013-12-01 00:00:00 | 0.001 | 0.017 | 0.038 | 0.057 | 0.027 | 0.002 | 0.036 | 0.002 | 0.012 | -0.052 | -0.053 |
| 2014-01-01 00:00:00 | 0.047 | 0.042 | 0.044 | 0.044 | 0.045 | 0.015 | 0.023 | 0.016 | -0.003 | -0.021 | -0.068 |
| 2014-02-01 00:00:00 | -0.023 | -0.02 | -0.04 | -0.038 | -0.039 | -0.039 | -0.043 | -0.051 | -0.041 | -0.028 | -0.005 |
| 2014-03-01 00:00:00 | -0.009 | -0.027 | -0.031 | -0.028 | -0.026 | -0.012 | -0.018 | -0.026 | -0.009 | -0.005 | 0.005 |
| 2014-04-01 00:00:00 | 0.027 | 0.035 | 0.034 | 0.028 | 0.05 | 0.025 | 0.02 | 0.022 | 0.018 | 0.002 | -0.024 |
| 2014-05-01 00:00:00 | 0.064 | 0.059 | 0.046 | 0.054 | 0.055 | 0.031 | 0.037 | 0.038 | 0.026 | 0.019 | -0.045 |
| 2014-06-01 00:00:00 | 0.09 | 0.076 | 0.076 | 0.068 | 0.06 | 0.082 | 0.075 | 0.067 | 0.065 | 0.079 | -0.012 |
| 2014-07-01 00:00:00 | 0.065 | 0.06 | 0.06 | 0.054 | 0.044 | 0.057 | 0.038 | 0.053 | 0.041 | 0.004 | -0.061 |
| 2014-08-01 00:00:00 | 0.152 | 0.141 | 0.143 | 0.124 | 0.119 | 0.114 | 0.127 | 0.101 | 0.09 | 0.064 | -0.089 |
| 2014-09-01 00:00:00 | 0.044 | 0.018 | 0.014 | 0.017 | 0.014 | 0.013 | 0.014 | 0.004 | 0.015 | 0.029 | -0.015 |
| 2014-10-01 00:00:00 | 0.067 | 0.049 | 0.062 | 0.07 | 0.045 | 0.04 | 0.048 | 0.055 | 0.076 | 0.123 | 0.056 |
| 2014-11-01 00:00:00 | -0.08 | -0.069 | -0.055 | -0.049 | -0.046 | -0.022 | 0.002 | -0.004 | 0.074 | 0.246 | 0.327 |
| 2014-12-01 00:00:00 | 0.108 | 0.105 | 0.094 | 0.097 | 0.087 | 0.068 | 0.077 | 0.082 | 0.062 | -0.026 | -0.135 |
| 2015-01-01 00:00:00 | 0.078 | 0.077 | 0.09 | 0.087 | 0.094 | 0.099 | 0.088 | 0.104 | 0.073 | 0.052 | -0.026 |
| 2015-02-01 00:00:00 | 0.259 | 0.235 | 0.248 | 0.252 | 0.229 | 0.214 | 0.228 | 0.209 | 0.184 | 0.142 | -0.116 |
| 2015-03-01 00:00:00 | 0.213 | 0.168 | 0.14 | 0.166 | 0.162 | 0.168 | 0.155 | 0.153 | 0.154 | 0.203 | -0.01 |
| 2015-04-01 00:00:00 | 0.302 | 0.264 | 0.261 | 0.253 | 0.252 | 0.252 | 0.204 | 0.182 | 0.119 | 0.036 | -0.266 |
| 2015-05-01 00:00:00 | -0.114 | -0.147 | -0.155 | -0.158 | -0.149 | -0.145 | -0.119 | -0.144 | -0.133 | -0.079 | 0.035 |
| 2015-06-01 00:00:00 | -0.212 | -0.204 | -0.201 | -0.192 | -0.177 | -0.176 | -0.15 | -0.17 | -0.154 | -0.159 | 0.052 |
| 2015-07-01 00:00:00 | -0.151 | -0.156 | -0.145 | -0.149 | -0.161 | -0.136 | -0.177 | -0.177 | -0.15 | -0.133 | 0.018 |
| 2015-08-01 00:00:00 | 0.012 | 0.0 | -0.017 | -0.004 | -0.016 | -0.022 | -0.028 | -0.045 | -0.062 | -0.053 | -0.065 |
| 2015-09-01 00:00:00 | 0.257 | 0.252 | 0.26 | 0.243 | 0.206 | 0.236 | 0.222 | 0.21 | 0.186 | 0.123 | -0.134 |
| 2015-10-01 00:00:00 | 0.152 | 0.146 | 0.116 | 0.116 | 0.096 | 0.063 | 0.069 | 0.049 | 0.024 | 0.009 | -0.143 |
| 2015-11-01 00:00:00 | 0.07 | 0.065 | 0.038 | 0.03 | 0.049 | 0.026 | 0.034 | 0.018 | 0.024 | 0.032 | -0.038 |
| 2015-12-01 00:00:00 | -0.309 | -0.309 | -0.31 | -0.31 | -0.311 | -0.295 | -0.301 | -0.308 | -0.278 | -0.243 | 0.066 |
| 2016-01-01 00:00:00 | -0.012 | -0.031 | -0.023 | -0.032 | -0.028 | -0.021 | -0.021 | -0.025 | -0.013 | -0.025 | -0.013 |
| 2016-02-01 00:00:00 | 0.204 | 0.21 | 0.204 | 0.209 | 0.196 | 0.19 | 0.172 | 0.171 | 0.162 | 0.132 | -0.072 |
| 2016-03-01 00:00:00 | 0.002 | -0.007 | -0.012 | -0.034 | -0.013 | -0.019 | -0.035 | -0.032 | -0.032 | -0.036 | -0.038 |
| 2016-04-01 00:00:00 | -0.017 | -0.009 | -0.006 | -0.012 | 0.0 | 0.007 | 0.002 | -0.01 | -0.005 | 0.001 | 0.018 |
| 2016-05-01 00:00:00 | 0.077 | 0.092 | 0.074 | 0.082 | 0.051 | 0.058 | 0.051 | 0.033 | 0.02 | 0.01 | -0.067 |
| 2016-06-01 00:00:00 | -0.012 | -0.011 | -0.029 | -0.014 | -0.022 | -0.033 | -0.007 | -0.017 | 0.031 | 0.028 | 0.041 |
| 2016-07-01 00:00:00 | 0.064 | 0.052 | 0.043 | 0.035 | 0.034 | 0.045 | 0.037 | 0.035 | 0.033 | 0.031 | -0.033 |
| 2016-08-01 00:00:00 | -0.025 | -0.015 | -0.015 | -0.021 | -0.028 | -0.028 | -0.026 | -0.029 | -0.03 | -0.034 | -0.009 |
| 2016-09-01 00:00:00 | 0.04 | 0.038 | 0.05 | 0.046 | 0.037 | 0.023 | 0.026 | 0.026 | 0.018 | 0.024 | -0.016 |
| 2016-10-01 00:00:00 | 0.03 | 0.016 | 0.029 | 0.025 | 0.014 | 0.015 | 0.016 | 0.014 | 0.036 | 0.045 | 0.015 |
| 2016-11-01 00:00:00 | -0.057 | -0.059 | -0.065 | -0.076 | -0.059 | -0.07 | -0.067 | -0.061 | -0.062 | -0.063 | -0.006 |
| 2016-12-01 00:00:00 | -0.037 | -0.036 | -0.041 | -0.035 | -0.032 | -0.03 | -0.03 | -0.018 | -0.008 | 0.012 | 0.049 |
+---------------------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+--------+
| Group | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Diff |
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+--------+
| Average | 0.018 | 0.016 | 0.015 | 0.014 | 0.014 | 0.011 | 0.012 | 0.009 | 0.011 | 0.009 | -0.01 |
| T-Test | 2.397 | 2.178 | 2.063 | 1.907 | 1.945 | 1.614 | 1.8 | 1.441 | 1.72 | 1.434 | -2.028 |
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+--------+
The third dataset excludes below 30% stocks from 2000-01-01 to 2016-12-01. The size effect is significant since the t-test statistics is -2.028 whose absolute value is more than 2 corresponding to the significance level at 0.05. The monthly excess return is 1.0% and the annual excess return is about 12.0%.
# %% dataset 4
# select stocks whose trading days are more than or equal to 10 days
test_data_4 = month_return[month_return['Ndaytrd']>=10]
# construct data for univariate analysis
test_data_4 = test_data_4[['emrwd', 'Msmvttl', 'Time']].dropna()
# time interval between 2000-01-01 to 2016-12-01
test_data_4 = test_data_4[(test_data_4['Time'] >= '2000-01-01') & (test_data_4['Time'] <= '2016-12-01')]
# analysis
uni_4 = Univariate(np.array(test_data_4), number=9)
uni_4.average_by_time()
uni_4.summary_and_test()
uni_4.print_summary_by_time()
uni_4.print_summary()
==========================================================================================================================
+---------------------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+
| Time | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | diff |
+---------------------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+
| 2000-01-01 00:00:00 | 0.164 | 0.167 | 0.126 | 0.139 | 0.131 | 0.12 | 0.118 | 0.094 | 0.113 | 0.125 | -0.039 |
| 2000-02-01 00:00:00 | 0.208 | 0.203 | 0.128 | 0.151 | 0.085 | 0.113 | 0.052 | 0.053 | 0.044 | 0.002 | -0.206 |
| 2000-03-01 00:00:00 | 0.001 | 0.035 | 0.019 | 0.006 | 0.024 | 0.012 | -0.008 | 0.017 | 0.014 | 0.032 | 0.032 |
| 2000-04-01 00:00:00 | 0.056 | 0.06 | 0.052 | 0.038 | 0.047 | 0.034 | 0.028 | 0.039 | 0.025 | 0.021 | -0.035 |
| 2000-05-01 00:00:00 | 0.019 | 0.021 | 0.032 | 0.02 | 0.044 | 0.019 | 0.024 | 0.014 | 0.031 | 0.034 | 0.015 |
| 2000-06-01 00:00:00 | 0.108 | 0.057 | 0.056 | 0.062 | 0.047 | 0.047 | 0.05 | 0.029 | 0.035 | 0.041 | -0.067 |
| 2000-07-01 00:00:00 | 0.053 | 0.039 | 0.023 | 0.009 | -0.001 | -0.002 | -0.006 | -0.015 | -0.007 | -0.021 | -0.074 |
| 2000-08-01 00:00:00 | 0.016 | -0.027 | -0.033 | -0.022 | -0.038 | -0.053 | -0.059 | -0.045 | -0.059 | -0.056 | -0.072 |
| 2000-09-01 00:00:00 | 0.065 | 0.058 | 0.049 | 0.048 | 0.034 | 0.035 | 0.026 | 0.029 | 0.014 | 0.007 | -0.057 |
| 2000-10-01 00:00:00 | 0.073 | 0.063 | 0.064 | 0.059 | 0.066 | 0.064 | 0.062 | 0.053 | 0.051 | 0.054 | -0.019 |
| 2000-11-01 00:00:00 | -0.002 | 0.028 | 0.025 | 0.008 | 0.014 | 0.005 | 0.006 | 0.011 | -0.003 | -0.024 | -0.023 |
| 2000-12-01 00:00:00 | -0.024 | -0.019 | -0.012 | -0.006 | -0.012 | -0.006 | -0.014 | -0.003 | -0.003 | -0.02 | 0.003 |
| 2001-01-01 00:00:00 | -0.098 | -0.062 | -0.067 | -0.072 | -0.062 | -0.062 | -0.052 | -0.064 | -0.051 | -0.049 | 0.05 |
| 2001-02-01 00:00:00 | 0.114 | 0.103 | 0.088 | 0.088 | 0.079 | 0.084 | 0.079 | 0.076 | 0.062 | 0.058 | -0.056 |
| 2001-03-01 00:00:00 | 0.04 | 0.019 | 0.001 | 0.012 | -0.005 | -0.003 | -0.009 | 0.002 | -0.014 | -0.015 | -0.055 |
| 2001-04-01 00:00:00 | 0.096 | 0.087 | 0.084 | 0.066 | 0.047 | 0.048 | 0.031 | 0.036 | 0.025 | 0.012 | -0.084 |
| 2001-05-01 00:00:00 | 0.016 | 0.007 | 0.017 | 0.016 | 0.01 | 0.013 | 0.011 | -0.001 | 0.005 | -0.006 | -0.022 |
| 2001-06-01 00:00:00 | -0.133 | -0.143 | -0.135 | -0.135 | -0.133 | -0.138 | -0.143 | -0.129 | -0.127 | -0.134 | -0.002 |
| 2001-07-01 00:00:00 | -0.001 | -0.013 | -0.021 | -0.03 | -0.037 | -0.037 | -0.041 | -0.04 | -0.032 | -0.043 | -0.042 |
| 2001-08-01 00:00:00 | -0.087 | -0.059 | -0.069 | -0.065 | -0.053 | -0.062 | -0.048 | -0.043 | -0.047 | -0.032 | 0.055 |
| 2001-09-01 00:00:00 | -0.057 | -0.064 | -0.059 | -0.058 | -0.056 | -0.057 | -0.065 | -0.046 | -0.056 | -0.033 | 0.024 |
| 2001-10-01 00:00:00 | 0.079 | 0.066 | 0.064 | 0.057 | 0.048 | 0.051 | 0.039 | 0.042 | 0.035 | 0.027 | -0.052 |
| 2001-11-01 00:00:00 | -0.09 | -0.083 | -0.077 | -0.073 | -0.072 | -0.075 | -0.064 | -0.067 | -0.054 | -0.047 | 0.044 |
| 2001-12-01 00:00:00 | -0.166 | -0.135 | -0.149 | -0.142 | -0.126 | -0.123 | -0.115 | -0.109 | -0.095 | -0.067 | 0.099 |
| 2002-01-01 00:00:00 | 0.095 | 0.052 | 0.041 | 0.038 | 0.044 | 0.036 | 0.029 | 0.03 | 0.018 | 0.014 | -0.081 |
| 2002-02-01 00:00:00 | 0.102 | 0.099 | 0.09 | 0.089 | 0.081 | 0.075 | 0.072 | 0.073 | 0.062 | 0.037 | -0.065 |
| 2002-03-01 00:00:00 | 0.081 | 0.067 | 0.054 | 0.057 | 0.055 | 0.041 | 0.045 | 0.032 | 0.037 | 0.031 | -0.049 |
| 2002-04-01 00:00:00 | -0.077 | -0.083 | -0.082 | -0.092 | -0.094 | -0.092 | -0.092 | -0.089 | -0.091 | -0.081 | -0.004 |
| 2002-05-01 00:00:00 | 0.091 | 0.091 | 0.106 | 0.113 | 0.114 | 0.116 | 0.118 | 0.136 | 0.133 | 0.156 | 0.065 |
| 2002-06-01 00:00:00 | -0.026 | -0.032 | -0.034 | -0.033 | -0.034 | -0.036 | -0.043 | -0.04 | -0.047 | -0.042 | -0.016 |
| 2002-07-01 00:00:00 | 0.023 | 0.014 | 0.011 | 0.01 | 0.001 | 0.003 | 0.008 | 0.009 | 0.003 | 0.004 | -0.019 |
| 2002-08-01 00:00:00 | -0.063 | -0.06 | -0.055 | -0.059 | -0.06 | -0.062 | -0.057 | -0.053 | -0.047 | -0.049 | 0.014 |
| 2002-09-01 00:00:00 | -0.051 | -0.071 | -0.06 | -0.074 | -0.057 | -0.047 | -0.054 | -0.05 | -0.044 | -0.048 | 0.004 |
| 2002-10-01 00:00:00 | -0.097 | -0.091 | -0.09 | -0.089 | -0.085 | -0.08 | -0.073 | -0.076 | -0.05 | -0.038 | 0.059 |
| 2002-11-01 00:00:00 | -0.029 | -0.053 | -0.052 | -0.056 | -0.056 | -0.054 | -0.057 | -0.054 | -0.05 | -0.047 | -0.018 |
| 2002-12-01 00:00:00 | 0.134 | 0.123 | 0.113 | 0.114 | 0.098 | 0.101 | 0.092 | 0.08 | 0.075 | 0.09 | -0.044 |
| 2003-01-01 00:00:00 | 0.018 | 0.022 | 0.023 | 0.015 | 0.016 | 0.01 | 0.013 | 0.013 | 0.009 | 0.005 | -0.013 |
| 2003-02-01 00:00:00 | -0.042 | -0.031 | -0.042 | -0.034 | -0.033 | -0.033 | -0.021 | -0.022 | -0.007 | 0.01 | 0.052 |
| 2003-03-01 00:00:00 | -0.094 | -0.067 | -0.081 | -0.067 | -0.038 | -0.051 | -0.035 | -0.011 | 0.005 | 0.021 | 0.115 |
| 2003-04-01 00:00:00 | 0.037 | 0.039 | 0.028 | 0.032 | 0.034 | 0.037 | 0.038 | 0.049 | 0.054 | 0.055 | 0.018 |
| 2003-05-01 00:00:00 | -0.055 | -0.061 | -0.068 | -0.066 | -0.07 | -0.072 | -0.075 | -0.079 | -0.057 | -0.065 | -0.01 |
| 2003-06-01 00:00:00 | -0.05 | -0.049 | -0.041 | -0.039 | -0.037 | -0.036 | -0.03 | -0.023 | -0.007 | 0.013 | 0.063 |
| 2003-07-01 00:00:00 | -0.001 | -0.014 | -0.016 | -0.017 | -0.023 | -0.037 | -0.034 | -0.033 | -0.021 | -0.043 | -0.042 |
| 2003-08-01 00:00:00 | -0.054 | -0.056 | -0.053 | -0.043 | -0.051 | -0.037 | -0.035 | -0.046 | -0.047 | -0.037 | 0.017 |
| 2003-09-01 00:00:00 | -0.114 | -0.096 | -0.086 | -0.08 | -0.075 | -0.065 | -0.066 | -0.044 | -0.028 | 0.003 | 0.117 |
| 2003-10-01 00:00:00 | 0.002 | 0.003 | 0.009 | 0.012 | 0.024 | 0.029 | 0.028 | 0.026 | 0.014 | 0.024 | 0.022 |
| 2003-11-01 00:00:00 | -0.069 | -0.038 | -0.033 | -0.016 | -0.034 | -0.006 | 0.004 | 0.025 | 0.032 | 0.07 | 0.138 |
| 2003-12-01 00:00:00 | 0.111 | 0.105 | 0.102 | 0.096 | 0.099 | 0.097 | 0.084 | 0.068 | 0.073 | 0.052 | -0.058 |
| 2004-01-01 00:00:00 | 0.145 | 0.125 | 0.102 | 0.12 | 0.08 | 0.104 | 0.091 | 0.076 | 0.074 | 0.056 | -0.089 |
| 2004-02-01 00:00:00 | 0.048 | 0.055 | 0.054 | 0.044 | 0.035 | 0.055 | 0.038 | 0.033 | 0.034 | 0.026 | -0.022 |
| 2004-03-01 00:00:00 | -0.115 | -0.124 | -0.105 | -0.098 | -0.093 | -0.098 | -0.095 | -0.084 | -0.096 | -0.107 | 0.008 |
| 2004-04-01 00:00:00 | 0.017 | -0.013 | -0.009 | -0.03 | -0.003 | -0.025 | -0.021 | -0.025 | -0.023 | -0.033 | -0.049 |
| 2004-05-01 00:00:00 | -0.139 | -0.132 | -0.13 | -0.128 | -0.134 | -0.132 | -0.13 | -0.116 | -0.122 | -0.091 | 0.048 |
| 2004-06-01 00:00:00 | -0.072 | -0.059 | -0.054 | -0.025 | -0.027 | -0.023 | 0.01 | 0.005 | 0.014 | 0.008 | 0.08 |
| 2004-07-01 00:00:00 | -0.066 | -0.061 | -0.053 | -0.05 | -0.047 | -0.055 | -0.061 | -0.064 | -0.061 | -0.032 | 0.034 |
| 2004-08-01 00:00:00 | 0.031 | 0.051 | 0.053 | 0.056 | 0.048 | 0.051 | 0.056 | 0.057 | 0.06 | 0.059 | 0.028 |
| 2004-09-01 00:00:00 | -0.129 | -0.091 | -0.081 | -0.067 | -0.066 | -0.053 | -0.064 | -0.058 | -0.028 | -0.04 | 0.089 |
| 2004-10-01 00:00:00 | 0.109 | 0.063 | 0.06 | 0.056 | 0.047 | 0.048 | 0.037 | 0.041 | 0.01 | -0.001 | -0.11 |
| 2004-11-01 00:00:00 | -0.089 | -0.092 | -0.093 | -0.077 | -0.086 | -0.08 | -0.091 | -0.08 | -0.07 | -0.056 | 0.033 |
| 2004-12-01 00:00:00 | -0.045 | -0.062 | -0.084 | -0.077 | -0.081 | -0.075 | -0.084 | -0.076 | -0.078 | -0.052 | -0.006 |
| 2005-01-01 00:00:00 | 0.114 | 0.105 | 0.112 | 0.113 | 0.109 | 0.102 | 0.118 | 0.115 | 0.094 | 0.092 | -0.022 |
| 2005-02-01 00:00:00 | -0.137 | -0.14 | -0.132 | -0.142 | -0.136 | -0.136 | -0.12 | -0.113 | -0.108 | -0.086 | 0.05 |
| 2005-03-01 00:00:00 | -0.14 | -0.125 | -0.092 | -0.096 | -0.081 | -0.053 | -0.065 | -0.037 | -0.026 | 0.004 | 0.144 |
| 2005-04-01 00:00:00 | 0.019 | -0.013 | -0.023 | -0.02 | -0.023 | -0.032 | -0.052 | -0.055 | -0.081 | -0.094 | -0.112 |
| 2005-05-01 00:00:00 | 0.001 | 0.0 | -0.001 | 0.004 | -0.003 | -0.001 | -0.006 | -0.001 | -0.002 | 0.029 | 0.028 |
| 2005-06-01 00:00:00 | -0.1 | -0.1 | -0.083 | -0.08 | -0.073 | -0.068 | -0.064 | -0.054 | -0.028 | 0.011 | 0.111 |
| 2005-07-01 00:00:00 | 0.258 | 0.196 | 0.192 | 0.174 | 0.173 | 0.152 | 0.136 | 0.124 | 0.119 | 0.05 | -0.208 |
| 2005-08-01 00:00:00 | 0.081 | 0.027 | 0.031 | 0.025 | -0.002 | 0.027 | 0.029 | 0.029 | 0.027 | -0.004 | -0.085 |
| 2005-09-01 00:00:00 | -0.083 | -0.056 | -0.06 | -0.067 | -0.058 | -0.052 | -0.056 | -0.056 | -0.048 | -0.052 | 0.031 |
| 2005-10-01 00:00:00 | 0.032 | 0.028 | 0.037 | 0.017 | 0.015 | 0.01 | 0.013 | -0.003 | -0.014 | -0.012 | -0.044 |
| 2005-11-01 00:00:00 | -0.011 | -0.005 | 0.001 | 0.017 | 0.012 | 0.023 | 0.032 | 0.053 | 0.067 | 0.073 | 0.085 |
| 2005-12-01 00:00:00 | -0.008 | 0.056 | 0.076 | 0.09 | 0.078 | 0.091 | 0.11 | 0.13 | 0.127 | 0.096 | 0.104 |
| 2006-01-01 00:00:00 | 0.094 | 0.047 | 0.026 | 0.032 | 0.021 | 0.022 | 0.017 | 0.019 | -0.001 | 0.043 | -0.051 |
| 2006-02-01 00:00:00 | -0.037 | -0.008 | -0.004 | -0.002 | 0.004 | 0.006 | 0.031 | 0.028 | 0.057 | 0.027 | 0.064 |
| 2006-03-01 00:00:00 | 0.139 | 0.007 | 0.082 | 0.08 | 0.099 | 0.113 | 0.105 | 0.133 | 0.139 | 0.151 | 0.011 |
| 2006-04-01 00:00:00 | 1.07 | 0.313 | 0.307 | 0.308 | 0.274 | 0.269 | 0.258 | 0.237 | 0.213 | 0.164 | -0.906 |
| 2006-05-01 00:00:00 | 0.07 | 0.079 | 0.066 | 0.083 | 0.065 | 0.071 | 0.039 | 0.053 | 0.024 | 0.021 | -0.049 |
| 2006-06-01 00:00:00 | 0.001 | 0.005 | -0.014 | -0.012 | -0.037 | -0.028 | -0.041 | -0.059 | -0.047 | -0.084 | -0.085 |
| 2006-07-01 00:00:00 | 0.022 | 0.03 | 0.025 | 0.023 | 0.032 | 0.033 | 0.035 | 0.045 | 0.04 | 0.027 | 0.005 |
| 2006-08-01 00:00:00 | 0.113 | 0.065 | 0.062 | 0.049 | 0.052 | 0.041 | 0.046 | 0.036 | 0.037 | 0.043 | -0.07 |
| 2006-09-01 00:00:00 | -0.01 | -0.013 | -0.018 | -0.002 | 0.016 | -0.017 | -0.011 | -0.0 | 0.019 | 0.029 | 0.039 |
| 2006-10-01 00:00:00 | -0.011 | -0.007 | -0.003 | 0.022 | 0.025 | 0.035 | 0.063 | 0.059 | 0.105 | 0.171 | 0.182 |
| 2006-11-01 00:00:00 | 0.011 | 0.036 | 0.035 | 0.05 | 0.035 | 0.042 | 0.069 | 0.085 | 0.095 | 0.153 | 0.141 |
| 2006-12-01 00:00:00 | 0.305 | 0.269 | 0.26 | 0.286 | 0.257 | 0.25 | 0.224 | 0.234 | 0.241 | 0.19 | -0.115 |
| 2007-01-01 00:00:00 | 0.257 | 0.244 | 0.241 | 0.223 | 0.217 | 0.186 | 0.245 | 0.136 | 0.15 | 0.083 | -0.175 |
| 2007-02-01 00:00:00 | 0.272 | 0.261 | 0.216 | 0.204 | 0.191 | 0.164 | 0.175 | 0.143 | 0.085 | 0.087 | -0.185 |
| 2007-03-01 00:00:00 | 0.332 | 0.329 | 0.343 | 0.363 | 0.339 | 0.322 | 0.336 | 0.348 | 0.347 | 0.283 | -0.049 |
| 2007-04-01 00:00:00 | 0.199 | 0.088 | 0.089 | 0.081 | 0.071 | 0.131 | 0.111 | 0.079 | 0.106 | 0.135 | -0.064 |
| 2007-05-01 00:00:00 | -0.22 | -0.23 | -0.216 | -0.211 | -0.189 | -0.155 | -0.159 | -0.13 | -0.092 | -0.04 | 0.181 |
| 2007-06-01 00:00:00 | 0.296 | 0.287 | 0.278 | 0.244 | 0.236 | 0.236 | 0.212 | 0.186 | 0.189 | 0.185 | -0.111 |
| 2007-07-01 00:00:00 | 0.198 | 0.127 | 0.104 | 0.099 | 0.094 | 0.096 | 0.115 | 0.108 | 0.143 | 0.18 | -0.018 |
| 2007-08-01 00:00:00 | 0.046 | 0.016 | 0.018 | 0.025 | 0.035 | 0.042 | 0.029 | 0.04 | 0.054 | 0.075 | 0.029 |
| 2007-09-01 00:00:00 | -0.124 | -0.139 | -0.115 | -0.117 | -0.121 | -0.099 | -0.117 | -0.097 | -0.084 | -0.007 | 0.117 |
| 2007-10-01 00:00:00 | 0.009 | -0.013 | -0.019 | -0.052 | -0.049 | -0.075 | -0.08 | -0.1 | -0.134 | -0.187 | -0.196 |
| 2007-11-01 00:00:00 | 0.184 | 0.205 | 0.204 | 0.208 | 0.21 | 0.21 | 0.22 | 0.216 | 0.2 | 0.148 | -0.036 |
| 2007-12-01 00:00:00 | -0.054 | -0.06 | -0.063 | -0.051 | -0.077 | -0.047 | -0.059 | -0.069 | -0.084 | -0.12 | -0.067 |
| 2008-01-01 00:00:00 | 0.116 | 0.109 | 0.117 | 0.107 | 0.101 | 0.083 | 0.076 | 0.065 | 0.043 | 0.017 | -0.099 |
| 2008-02-01 00:00:00 | -0.174 | -0.171 | -0.181 | -0.182 | -0.199 | -0.201 | -0.199 | -0.217 | -0.224 | -0.212 | -0.039 |
| 2008-03-01 00:00:00 | -0.087 | -0.091 | -0.077 | -0.075 | -0.069 | -0.051 | -0.049 | -0.006 | 0.017 | 0.043 | 0.13 |
| 2008-04-01 00:00:00 | 0.006 | -0.007 | -0.008 | -0.003 | -0.026 | -0.039 | -0.027 | -0.059 | -0.048 | -0.078 | -0.084 |
| 2008-05-01 00:00:00 | -0.239 | -0.234 | -0.266 | -0.275 | -0.249 | -0.26 | -0.239 | -0.25 | -0.234 | -0.221 | 0.018 |
| 2008-06-01 00:00:00 | 0.137 | 0.118 | 0.116 | 0.111 | 0.108 | 0.103 | 0.072 | 0.076 | 0.052 | 0.005 | -0.132 |
| 2008-07-01 00:00:00 | -0.207 | -0.224 | -0.227 | -0.233 | -0.223 | -0.238 | -0.241 | -0.238 | -0.229 | -0.194 | 0.013 |
| 2008-08-01 00:00:00 | -0.117 | -0.104 | -0.09 | -0.098 | -0.101 | -0.08 | -0.085 | -0.061 | -0.044 | -0.026 | 0.09 |
| 2008-09-01 00:00:00 | -0.225 | -0.232 | -0.249 | -0.265 | -0.247 | -0.266 | -0.272 | -0.262 | -0.275 | -0.248 | -0.023 |
| 2008-10-01 00:00:00 | 0.231 | 0.215 | 0.219 | 0.221 | 0.225 | 0.223 | 0.185 | 0.161 | 0.157 | 0.131 | -0.101 |
| 2008-11-01 00:00:00 | 0.155 | 0.13 | 0.094 | 0.097 | 0.061 | 0.068 | 0.053 | 0.065 | 0.041 | 0.013 | -0.142 |
| 2008-12-01 00:00:00 | 0.149 | 0.161 | 0.163 | 0.159 | 0.162 | 0.187 | 0.162 | 0.169 | 0.158 | 0.119 | -0.03 |
| 2009-01-01 00:00:00 | 0.124 | 0.116 | 0.094 | 0.084 | 0.092 | 0.09 | 0.073 | 0.081 | 0.057 | 0.063 | -0.061 |
| 2009-02-01 00:00:00 | 0.255 | 0.254 | 0.235 | 0.246 | 0.226 | 0.224 | 0.21 | 0.209 | 0.198 | 0.186 | -0.069 |
| 2009-03-01 00:00:00 | 0.102 | 0.11 | 0.078 | 0.074 | 0.081 | 0.073 | 0.038 | 0.066 | 0.041 | 0.05 | -0.052 |
| 2009-04-01 00:00:00 | 0.096 | 0.092 | 0.106 | 0.07 | 0.085 | 0.062 | 0.057 | 0.047 | 0.045 | 0.056 | -0.041 |
| 2009-05-01 00:00:00 | 0.112 | 0.081 | 0.061 | 0.039 | 0.04 | 0.055 | 0.039 | 0.053 | 0.078 | 0.124 | 0.012 |
| 2009-06-01 00:00:00 | 0.134 | 0.125 | 0.133 | 0.136 | 0.143 | 0.155 | 0.129 | 0.153 | 0.182 | 0.183 | 0.05 |
| 2009-07-01 00:00:00 | -0.124 | -0.141 | -0.151 | -0.144 | -0.147 | -0.139 | -0.155 | -0.171 | -0.18 | -0.236 | -0.112 |
| 2009-08-01 00:00:00 | 0.055 | 0.041 | 0.044 | 0.024 | 0.03 | 0.037 | 0.032 | 0.035 | 0.04 | 0.052 | -0.003 |
| 2009-09-01 00:00:00 | 0.124 | 0.133 | 0.129 | 0.128 | 0.12 | 0.132 | 0.12 | 0.112 | 0.108 | 0.092 | -0.032 |
| 2009-10-01 00:00:00 | 0.167 | 0.173 | 0.153 | 0.158 | 0.163 | 0.178 | 0.144 | 0.142 | 0.109 | 0.084 | -0.083 |
| 2009-11-01 00:00:00 | 0.052 | 0.039 | 0.035 | 0.029 | 0.035 | 0.032 | 0.006 | 0.005 | -0.005 | 0.004 | -0.048 |
| 2009-12-01 00:00:00 | -0.016 | -0.011 | -0.033 | -0.026 | -0.018 | -0.031 | -0.019 | -0.035 | -0.049 | -0.1 | -0.084 |
| 2010-01-01 00:00:00 | 0.09 | 0.082 | 0.078 | 0.064 | 0.061 | 0.068 | 0.059 | 0.057 | 0.043 | 0.025 | -0.065 |
| 2010-02-01 00:00:00 | 0.086 | 0.067 | 0.064 | 0.053 | 0.039 | 0.042 | 0.046 | 0.017 | 0.017 | 0.011 | -0.075 |
| 2010-03-01 00:00:00 | -0.056 | -0.063 | -0.082 | -0.084 | -0.072 | -0.068 | -0.07 | -0.078 | -0.063 | -0.073 | -0.017 |
| 2010-04-01 00:00:00 | -0.088 | -0.08 | -0.073 | -0.088 | -0.094 | -0.077 | -0.08 | -0.065 | -0.078 | -0.089 | -0.0 |
| 2010-05-01 00:00:00 | -0.082 | -0.083 | -0.087 | -0.083 | -0.091 | -0.094 | -0.099 | -0.101 | -0.098 | -0.081 | 0.001 |
| 2010-06-01 00:00:00 | 0.168 | 0.164 | 0.153 | 0.149 | 0.149 | 0.164 | 0.143 | 0.138 | 0.133 | 0.13 | -0.038 |
| 2010-07-01 00:00:00 | 0.107 | 0.106 | 0.09 | 0.113 | 0.097 | 0.096 | 0.084 | 0.109 | 0.075 | 0.027 | -0.08 |
| 2010-08-01 00:00:00 | 0.025 | -0.012 | -0.007 | 0.002 | 0.007 | -0.004 | -0.008 | 0.016 | 0.02 | 0.016 | -0.009 |
| 2010-09-01 00:00:00 | 0.062 | 0.078 | 0.074 | 0.098 | 0.082 | 0.091 | 0.093 | 0.098 | 0.114 | 0.156 | 0.094 |
| 2010-10-01 00:00:00 | 0.039 | 0.036 | 0.04 | 0.028 | 0.014 | 0.012 | 0.016 | 0.018 | -0.015 | -0.06 | -0.099 |
| 2010-11-01 00:00:00 | -0.007 | -0.023 | -0.015 | -0.024 | -0.029 | -0.035 | -0.027 | -0.034 | -0.018 | 0.007 | 0.014 |
| 2010-12-01 00:00:00 | -0.031 | -0.055 | -0.053 | -0.059 | -0.06 | -0.058 | -0.067 | -0.065 | -0.065 | -0.025 | 0.006 |
| 2011-01-01 00:00:00 | 0.099 | 0.104 | 0.101 | 0.093 | 0.106 | 0.096 | 0.105 | 0.102 | 0.085 | 0.059 | -0.04 |
| 2011-02-01 00:00:00 | 0.034 | 0.004 | -0.008 | -0.001 | -0.019 | -0.024 | -0.036 | -0.022 | -0.027 | -0.027 | -0.06 |
| 2011-03-01 00:00:00 | -0.029 | -0.04 | -0.039 | -0.051 | -0.046 | -0.046 | -0.029 | -0.037 | -0.034 | -0.019 | 0.01 |
| 2011-04-01 00:00:00 | -0.062 | -0.074 | -0.068 | -0.075 | -0.06 | -0.081 | -0.081 | -0.081 | -0.083 | -0.067 | -0.005 |
| 2011-05-01 00:00:00 | 0.044 | 0.045 | 0.035 | 0.03 | 0.046 | 0.025 | 0.034 | 0.032 | 0.036 | 0.029 | -0.015 |
| 2011-06-01 00:00:00 | 0.04 | 0.029 | 0.03 | 0.033 | 0.033 | 0.021 | 0.016 | 0.024 | 0.011 | -0.012 | -0.052 |
| 2011-07-01 00:00:00 | 0.008 | -0.009 | -0.014 | -0.019 | -0.031 | -0.031 | -0.035 | -0.033 | -0.047 | -0.052 | -0.06 |
| 2011-08-01 00:00:00 | -0.109 | -0.117 | -0.122 | -0.119 | -0.121 | -0.133 | -0.13 | -0.137 | -0.122 | -0.096 | 0.013 |
| 2011-09-01 00:00:00 | 0.054 | 0.044 | 0.046 | 0.04 | 0.046 | 0.044 | 0.039 | 0.046 | 0.039 | 0.035 | -0.019 |
| 2011-10-01 00:00:00 | -0.03 | -0.022 | -0.042 | -0.048 | -0.027 | -0.038 | -0.045 | -0.04 | -0.055 | -0.065 | -0.035 |
| 2011-11-01 00:00:00 | -0.177 | -0.178 | -0.169 | -0.171 | -0.172 | -0.152 | -0.164 | -0.142 | -0.12 | -0.085 | 0.092 |
| 2011-12-01 00:00:00 | 0.01 | -0.007 | -0.021 | -0.023 | -0.007 | -0.014 | -0.009 | -0.007 | -0.004 | 0.035 | 0.025 |
| 2012-01-01 00:00:00 | 0.16 | 0.155 | 0.149 | 0.142 | 0.137 | 0.136 | 0.127 | 0.127 | 0.117 | 0.082 | -0.078 |
| 2012-02-01 00:00:00 | -0.079 | -0.081 | -0.073 | -0.07 | -0.076 | -0.077 | -0.076 | -0.078 | -0.073 | -0.074 | 0.004 |
| 2012-03-01 00:00:00 | 0.061 | 0.064 | 0.069 | 0.084 | 0.065 | 0.068 | 0.072 | 0.06 | 0.057 | 0.069 | 0.008 |
| 2012-04-01 00:00:00 | 0.04 | 0.029 | 0.012 | 0.023 | 0.023 | 0.02 | 0.023 | 0.031 | 0.032 | 0.013 | -0.028 |
| 2012-05-01 00:00:00 | -0.018 | -0.035 | -0.055 | -0.058 | -0.061 | -0.07 | -0.068 | -0.071 | -0.062 | -0.061 | -0.043 |
| 2012-06-01 00:00:00 | -0.125 | -0.108 | -0.095 | -0.101 | -0.097 | -0.102 | -0.093 | -0.087 | -0.081 | -0.057 | 0.068 |
| 2012-07-01 00:00:00 | 0.068 | 0.064 | 0.055 | 0.047 | 0.032 | 0.033 | 0.013 | 0.005 | -0.023 | -0.053 | -0.121 |
| 2012-08-01 00:00:00 | 0.014 | 0.016 | -0.007 | 0.004 | 0.004 | -0.001 | -0.001 | 0.018 | 0.017 | 0.039 | 0.026 |
| 2012-09-01 00:00:00 | 0.012 | 0.01 | 0.004 | -0.001 | 0.003 | -0.0 | -0.01 | -0.008 | -0.018 | -0.016 | -0.028 |
| 2012-10-01 00:00:00 | -0.095 | -0.12 | -0.115 | -0.12 | -0.122 | -0.116 | -0.124 | -0.116 | -0.105 | -0.066 | 0.029 |
| 2012-11-01 00:00:00 | 0.167 | 0.175 | 0.165 | 0.169 | 0.181 | 0.164 | 0.174 | 0.179 | 0.166 | 0.175 | 0.008 |
| 2012-12-01 00:00:00 | 0.062 | 0.057 | 0.073 | 0.071 | 0.071 | 0.064 | 0.059 | 0.065 | 0.056 | 0.054 | -0.008 |
| 2013-01-01 00:00:00 | 0.06 | 0.041 | 0.041 | 0.041 | 0.037 | 0.034 | 0.039 | 0.041 | 0.036 | 0.005 | -0.055 |
| 2013-02-01 00:00:00 | -0.025 | -0.026 | -0.017 | -0.03 | -0.03 | -0.025 | -0.048 | -0.045 | -0.047 | -0.053 | -0.028 |
| 2013-03-01 00:00:00 | -0.023 | -0.048 | -0.04 | -0.031 | -0.032 | -0.027 | -0.027 | -0.019 | -0.021 | -0.022 | 0.002 |
| 2013-04-01 00:00:00 | 0.177 | 0.155 | 0.157 | 0.153 | 0.153 | 0.146 | 0.151 | 0.152 | 0.132 | 0.076 | -0.102 |
| 2013-05-01 00:00:00 | -0.139 | -0.157 | -0.155 | -0.155 | -0.161 | -0.158 | -0.15 | -0.164 | -0.153 | -0.14 | -0.001 |
| 2013-06-01 00:00:00 | 0.123 | 0.086 | 0.072 | 0.075 | 0.083 | 0.063 | 0.063 | 0.072 | 0.051 | 0.028 | -0.095 |
| 2013-07-01 00:00:00 | 0.104 | 0.092 | 0.112 | 0.1 | 0.076 | 0.08 | 0.089 | 0.078 | 0.062 | 0.063 | -0.041 |
| 2013-08-01 00:00:00 | 0.076 | 0.053 | 0.052 | 0.053 | 0.059 | 0.043 | 0.056 | 0.049 | 0.056 | 0.054 | -0.021 |
| 2013-09-01 00:00:00 | -0.006 | -0.013 | -0.018 | -0.024 | -0.017 | -0.029 | -0.039 | -0.033 | -0.038 | -0.034 | -0.027 |
| 2013-10-01 00:00:00 | 0.131 | 0.128 | 0.111 | 0.086 | 0.097 | 0.083 | 0.076 | 0.068 | 0.055 | 0.044 | -0.087 |
| 2013-11-01 00:00:00 | -0.02 | -0.029 | -0.031 | -0.032 | -0.039 | -0.03 | -0.038 | -0.03 | -0.038 | -0.044 | -0.023 |
| 2013-12-01 00:00:00 | 0.035 | 0.062 | 0.024 | 0.01 | 0.031 | 0.046 | 0.007 | 0.035 | 0.004 | -0.031 | -0.066 |
| 2014-01-01 00:00:00 | 0.067 | 0.05 | 0.047 | 0.047 | 0.044 | 0.044 | 0.032 | 0.017 | 0.009 | -0.018 | -0.085 |
| 2014-02-01 00:00:00 | 0.025 | 0.003 | -0.013 | -0.021 | -0.033 | -0.037 | -0.042 | -0.043 | -0.043 | -0.036 | -0.061 |
| 2014-03-01 00:00:00 | 0.022 | 0.006 | -0.008 | -0.012 | -0.03 | -0.03 | -0.016 | -0.015 | -0.025 | -0.004 | -0.026 |
| 2014-04-01 00:00:00 | 0.115 | 0.055 | 0.048 | 0.027 | 0.036 | 0.032 | 0.037 | 0.022 | 0.02 | 0.008 | -0.107 |
| 2014-05-01 00:00:00 | 0.079 | 0.09 | 0.073 | 0.062 | 0.052 | 0.056 | 0.042 | 0.037 | 0.034 | 0.019 | -0.06 |
| 2014-06-01 00:00:00 | 0.104 | 0.075 | 0.075 | 0.083 | 0.077 | 0.069 | 0.072 | 0.072 | 0.066 | 0.077 | -0.027 |
| 2014-07-01 00:00:00 | 0.111 | 0.091 | 0.068 | 0.066 | 0.057 | 0.056 | 0.046 | 0.046 | 0.048 | 0.013 | -0.098 |
| 2014-08-01 00:00:00 | 0.211 | 0.191 | 0.158 | 0.146 | 0.146 | 0.122 | 0.12 | 0.12 | 0.104 | 0.066 | -0.145 |
| 2014-09-01 00:00:00 | 0.021 | 0.019 | 0.033 | 0.036 | 0.014 | 0.017 | 0.009 | 0.017 | 0.009 | 0.025 | 0.005 |
| 2014-10-01 00:00:00 | 0.069 | 0.075 | 0.047 | 0.064 | 0.054 | 0.07 | 0.037 | 0.048 | 0.062 | 0.109 | 0.04 |
| 2014-11-01 00:00:00 | -0.108 | -0.083 | -0.078 | -0.076 | -0.067 | -0.048 | -0.036 | 0.006 | 0.021 | 0.202 | 0.309 |
| 2014-12-01 00:00:00 | 0.116 | 0.106 | 0.112 | 0.104 | 0.09 | 0.099 | 0.074 | 0.076 | 0.075 | -0.001 | -0.116 |
| 2015-01-01 00:00:00 | 0.117 | 0.086 | 0.081 | 0.074 | 0.09 | 0.087 | 0.099 | 0.087 | 0.095 | 0.058 | -0.059 |
| 2015-02-01 00:00:00 | 0.271 | 0.243 | 0.243 | 0.251 | 0.24 | 0.242 | 0.224 | 0.225 | 0.201 | 0.153 | -0.118 |
| 2015-03-01 00:00:00 | 0.217 | 0.179 | 0.171 | 0.2 | 0.148 | 0.164 | 0.161 | 0.158 | 0.147 | 0.196 | -0.021 |
| 2015-04-01 00:00:00 | 0.373 | 0.317 | 0.294 | 0.284 | 0.276 | 0.256 | 0.253 | 0.203 | 0.158 | 0.059 | -0.314 |
| 2015-05-01 00:00:00 | -0.047 | -0.096 | -0.123 | -0.124 | -0.155 | -0.156 | -0.156 | -0.118 | -0.133 | -0.098 | -0.05 |
| 2015-06-01 00:00:00 | -0.161 | -0.178 | -0.209 | -0.209 | -0.203 | -0.19 | -0.179 | -0.152 | -0.159 | -0.164 | -0.003 |
| 2015-07-01 00:00:00 | -0.088 | -0.125 | -0.121 | -0.149 | -0.156 | -0.15 | -0.151 | -0.165 | -0.168 | -0.139 | -0.051 |
| 2015-08-01 00:00:00 | 0.004 | -0.005 | -0.003 | 0.009 | -0.011 | -0.011 | -0.01 | -0.034 | -0.046 | -0.061 | -0.065 |
| 2015-09-01 00:00:00 | 0.301 | 0.27 | 0.276 | 0.257 | 0.258 | 0.237 | 0.222 | 0.219 | 0.209 | 0.136 | -0.165 |
| 2015-10-01 00:00:00 | 0.203 | 0.193 | 0.173 | 0.148 | 0.128 | 0.111 | 0.081 | 0.061 | 0.045 | 0.013 | -0.19 |
| 2015-11-01 00:00:00 | 0.152 | 0.099 | 0.085 | 0.066 | 0.053 | 0.029 | 0.038 | 0.034 | 0.019 | 0.031 | -0.121 |
| 2015-12-01 00:00:00 | -0.303 | -0.296 | -0.309 | -0.31 | -0.306 | -0.311 | -0.305 | -0.298 | -0.301 | -0.25 | 0.053 |
| 2016-01-01 00:00:00 | 0.009 | -0.005 | -0.009 | -0.022 | -0.021 | -0.028 | -0.031 | -0.02 | -0.019 | -0.022 | -0.03 |
| 2016-02-01 00:00:00 | 0.257 | 0.223 | 0.22 | 0.201 | 0.208 | 0.214 | 0.187 | 0.179 | 0.169 | 0.137 | -0.12 |
| 2016-03-01 00:00:00 | 0.062 | 0.042 | 0.016 | 0.0 | -0.011 | -0.027 | -0.016 | -0.034 | -0.03 | -0.036 | -0.098 |
| 2016-04-01 00:00:00 | -0.035 | -0.029 | -0.023 | -0.011 | -0.01 | -0.007 | 0.003 | 0.002 | -0.005 | -0.004 | 0.031 |
| 2016-05-01 00:00:00 | 0.068 | 0.085 | 0.085 | 0.082 | 0.082 | 0.072 | 0.055 | 0.054 | 0.027 | 0.013 | -0.055 |
| 2016-06-01 00:00:00 | 0.002 | 0.001 | -0.009 | -0.014 | -0.02 | -0.02 | -0.026 | -0.011 | -0.003 | 0.034 | 0.032 |
| 2016-07-01 00:00:00 | 0.085 | 0.066 | 0.061 | 0.06 | 0.046 | 0.039 | 0.039 | 0.036 | 0.032 | 0.034 | -0.051 |
| 2016-08-01 00:00:00 | 0.057 | 0.016 | -0.005 | -0.019 | -0.014 | -0.021 | -0.031 | -0.026 | -0.031 | -0.032 | -0.089 |
| 2016-09-01 00:00:00 | 0.051 | 0.056 | 0.051 | 0.042 | 0.043 | 0.047 | 0.024 | 0.027 | 0.022 | 0.023 | -0.028 |
| 2016-10-01 00:00:00 | 0.062 | 0.055 | 0.036 | 0.025 | 0.026 | 0.021 | 0.016 | 0.016 | 0.021 | 0.044 | -0.019 |
| 2016-11-01 00:00:00 | 0.007 | -0.039 | -0.039 | -0.06 | -0.063 | -0.071 | -0.067 | -0.065 | -0.06 | -0.063 | -0.07 |
| 2016-12-01 00:00:00 | -0.043 | -0.037 | -0.043 | -0.04 | -0.037 | -0.034 | -0.03 | -0.029 | -0.021 | 0.012 | 0.055 |
+---------------------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+--------+
| Group | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Diff |
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+--------+
| Average | 0.036 | 0.024 | 0.019 | 0.018 | 0.015 | 0.015 | 0.011 | 0.012 | 0.01 | 0.009 | -0.027 |
| T-Test | 3.823 | 3.07 | 2.584 | 2.358 | 2.08 | 2.044 | 1.619 | 1.796 | 1.566 | 1.508 | -3.949 |
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+--------+
The fourth dataset includes below 30% stocks from 2000-01-01 to 2016-12-01. The size effect is significant since the t-test statistics is -3.949 whose absolute value is more than 2 corresponding to the significance level at 0.05. The monthly excess return is 2.7% and the annual excess return is about 32.4%.
The size effect provides 0.6% excess return a month in U.S. market.
Value Effect
The value effect was discovered since 1980s and became famous since the research by Fama and French (1993). The value factor, as one of systematic factors, is constructed by the variable, book to market ratio (BM). The positive correlation between the BM and the future return is widely tested by literatures (Fama and French, 1993, 1995; Stattman, 1980; Barber and Lyon, 1997). Other than BM, some value-related variables are also taken into consideration, and the most common one is earnings to price ratio, EP (Basu, 1983). Aras and Yilmaz (2008) and Cakici et al. (2013) discovered the value effect is existing in 12 and 18 emerging markets, respectively.
As for the value effect in China market, Liu et al. (2019) argue that EP is more suitable than BM, through which they construct the value factor in China market. In this demo, the BM and EP are both tested, while some adjustment are attached to these variables, and precisely the reverse form of theses two variables are used respectively named, price to earnings ratio (PE) and price to book ratio (PB). Thus, the relation between the variables and the future return is negative.
Following the conventions, stocks are grouped by two variables, market value (size) and value variables, independently and formed a 5*5 portfolio matrix. The dataset contains monthly China A share stock between 2000-01-01 to 2021-12-31 from the CSMAR dataset. WARNING: Do Not use dataset in this demo for any commercial purpose.
import pandas as pd
import sys, os
sys.path.append(os.path.abspath(".."))
# %% import data
# Monthly return of stocks in China security market
month_return = pd.read_hdf('.\data\month_return.h5', key='month_return')
company_data = pd.read_hdf('.\data\last_filter_pe.h5', key='data')
Data need some preprocessing.
# %% preprocessing data
# forward the monthly return for each stock
# emrwd is the return including dividend
month_return['emrwd'] = month_return.groupby(['Stkcd'])['Mretwd'].shift(-1)
# emrnd is the return including no dividend
month_return['emrnd'] = month_return.groupby(['Stkcd'])['Mretnd'].shift(-1)
# select the A share stock
month_return = month_return[month_return['Markettype'].isin([1, 4, 16])]
# % distinguish the stocks whose size is among the up 30% stocks in each month
def percentile(stocks) :
return stocks >= stocks.quantile(q=.3)
month_return['cap'] = month_return.groupby(['Trdmnt'])['Msmvttl'].apply(percentile)
# %% merge data
from pandas.tseries.offsets import *
month_return['Stkcd_merge'] = month_return['Stkcd'].astype(dtype='string')
month_return['Date_merge'] = pd.to_datetime(month_return['Trdmnt'])
#month_return['Date_merge'] += MonthEnd()
company_data['Stkcd_merge'] = company_data['Symbol'].dropna().astype(dtype='int').astype(dtype='string')
company_data['Date_merge'] = pd.to_datetime(company_data['TradingDate'])
company_data['Date_merge'] += MonthBegin()
Consistent with the size effect, the dataset starts from 2000-01.
# %% dataset starts from '2000-01'
company_data = company_data[company_data['Date_merge'] >= '2000-01']
month_return = month_return[month_return['Date_merge'] >= '2000-01']
return_company = pd.merge(company_data, month_return, on=['Stkcd_merge', 'Date_merge'])
Four datasets are tested. Due to specific requirement of the IPO, some dominant company would purchase a small listed company and join the A share market. Thus, in the research by Liu et al. (2016), the stocks whose size is below the 30% are abandoned. The PE and PB are both tested.
# %% construct test_data for bivariate analysis
# dataset 1 : PE
from portfolio_analysis import Bivariate
import numpy as np
# select stocks whose size is among the up 30% stocks in each month and whose trading
# days are more than or equal to 10 days
test_data_1 = return_company[(return_company['cap']==True) & (return_company['Ndaytrd']>=10)]
test_data_1 = test_data_1[['emrwd', 'Msmvttl', 'PE1A', 'Date_merge']].dropna()
test_data_1 = test_data_1[(test_data_1['Date_merge'] >= '2000-01-01') & (test_data_1['Date_merge'] <= '2019-12-01')]
# Independent-sort Bivariate Analysis
bi_1 = Bivariate(np.array(test_data_1), number=4)
bi_1.average_by_time()
bi_1.summary_and_test()
bi_1.print_summary_by_time()
bi_1.print_summary()
===============================================================
+-------+--------+--------+--------+--------+--------+--------+
| Group | 1 | 2 | 3 | 4 | 5 | Diff |
+-------+--------+--------+--------+--------+--------+--------+
| 1 | 0.019 | 0.017 | 0.013 | 0.013 | 0.01 | -0.009 |
| | 3.024 | 2.693 | 2.003 | 1.89 | 1.472 | -3.551 |
| 2 | 0.014 | 0.015 | 0.011 | 0.011 | 0.009 | -0.005 |
| | 2.25 | 2.415 | 1.779 | 1.658 | 1.374 | -1.947 |
| 3 | 0.014 | 0.01 | 0.009 | 0.009 | 0.005 | -0.009 |
| | 2.298 | 1.648 | 1.478 | 1.36 | 0.778 | -3.19 |
| 4 | 0.011 | 0.011 | 0.009 | 0.009 | 0.005 | -0.006 |
| | 1.901 | 1.871 | 1.507 | 1.431 | 0.799 | -1.98 |
| 5 | 0.013 | 0.009 | 0.007 | 0.006 | 0.002 | -0.011 |
| | 2.204 | 1.678 | 1.258 | 0.988 | 0.331 | -2.984 |
| Diff | -0.007 | -0.008 | -0.006 | -0.007 | -0.008 | -0.001 |
| | -1.876 | -2.628 | -1.819 | -2.117 | -2.389 | -0.446 |
+-------+--------+--------+--------+--------+--------+--------+
# Risk-adjustment Using Market factor
risk_model = risk_premium['MKT']
risk_model = risk_model['2000':'2019']
bi_1.factor_adjustment(risk_model)
bi_1.print_summary()
===============================================================
+-------+--------+--------+--------+--------+--------+--------+
| Group | 1 | 2 | 3 | 4 | 5 | Diff |
+-------+--------+--------+--------+--------+--------+--------+
| 1 | 0.019 | 0.017 | 0.013 | 0.013 | 0.01 | -0.009 |
| | 3.024 | 2.693 | 2.003 | 1.89 | 1.472 | -3.551 |
| alpha | 0.017 | 0.015 | 0.011 | 0.01 | 0.008 | -0.009 |
| | 2.53 | 2.294 | 1.723 | 1.579 | 1.064 | -3.467 |
| 2 | 0.014 | 0.015 | 0.011 | 0.011 | 0.009 | -0.005 |
| | 2.25 | 2.415 | 1.779 | 1.658 | 1.374 | -1.947 |
| alpha | 0.012 | 0.013 | 0.009 | 0.009 | 0.007 | -0.004 |
| | 1.888 | 1.955 | 1.356 | 1.358 | 1.031 | -2.071 |
| 3 | 0.014 | 0.01 | 0.009 | 0.009 | 0.005 | -0.009 |
| | 2.298 | 1.648 | 1.478 | 1.36 | 0.778 | -3.19 |
| alpha | 0.012 | 0.008 | 0.007 | 0.006 | 0.003 | -0.009 |
| | 1.824 | 1.293 | 1.145 | 1.044 | 0.444 | -3.508 |
| 4 | 0.011 | 0.011 | 0.009 | 0.009 | 0.005 | -0.006 |
| | 1.901 | 1.871 | 1.507 | 1.431 | 0.799 | -1.98 |
| alpha | 0.01 | 0.009 | 0.007 | 0.007 | 0.004 | -0.006 |
| | 1.476 | 1.421 | 1.124 | 1.067 | 0.599 | -2.197 |
| 5 | 0.013 | 0.009 | 0.007 | 0.006 | 0.002 | -0.011 |
| | 2.204 | 1.678 | 1.258 | 0.988 | 0.331 | -2.984 |
| alpha | 0.011 | 0.008 | 0.005 | 0.004 | 0.0 | -0.011 |
| | 1.726 | 1.252 | 0.873 | 0.68 | 0.042 | -3.074 |
| Diff | -0.007 | -0.008 | -0.006 | -0.007 | -0.008 | -0.001 |
| | -1.876 | -2.628 | -1.819 | -2.117 | -2.389 | -0.446 |
| alpha | -0.005 | -0.007 | -0.005 | -0.006 | -0.007 | -0.002 |
| | -1.847 | -2.257 | -1.383 | -1.603 | -1.851 | -0.792 |
+-------+--------+--------+--------+--------+--------+--------+
===============================================================
# Dependent-sort Bivariate Analysis
bi_1_de = Bivariate(test_data_1, number=4)
bi_1_de.fit(conditional=True)
bi_1_de.print_summary()
==================================================================
+----------+--------+--------+--------+--------+--------+--------+
| Group | PE1A1 | PE1A2 | PE1A3 | PE1A4 | PE1A5 | Diff |
+----------+--------+--------+--------+--------+--------+--------+
| Msmvttl1 | 0.018 | 0.015 | 0.013 | 0.011 | 0.01 | -0.008 |
| | 2.94 | 2.257 | 2.027 | 1.687 | 1.445 | -3.787 |
| Msmvttl2 | 0.014 | 0.013 | 0.012 | 0.009 | 0.01 | -0.004 |
| | 2.225 | 2.182 | 1.955 | 1.369 | 1.45 | -1.617 |
| Msmvttl3 | 0.013 | 0.01 | 0.009 | 0.009 | 0.005 | -0.008 |
| | 2.187 | 1.668 | 1.44 | 1.413 | 0.748 | -3.215 |
| Msmvttl4 | 0.011 | 0.011 | 0.009 | 0.008 | 0.006 | -0.005 |
| | 1.822 | 1.866 | 1.571 | 1.372 | 0.932 | -1.674 |
| Msmvttl5 | 0.013 | 0.012 | 0.008 | 0.006 | 0.004 | -0.009 |
| | 2.261 | 2.163 | 1.545 | 1.067 | 0.732 | -2.473 |
| Diff | -0.005 | -0.002 | -0.005 | -0.006 | -0.006 | -0.001 |
| | -1.349 | -0.641 | -1.334 | -1.534 | -1.665 | -0.17 |
+----------+--------+--------+--------+--------+--------+--------+
==================================================================
# Risk-adjustment
bi_1_de.factor_adjustment(risk_model)
bi_1_de.print_summary()
==================================================================
+----------+--------+--------+--------+--------+--------+--------+
| Group | PE1A1 | PE1A2 | PE1A3 | PE1A4 | PE1A5 | Diff |
+----------+--------+--------+--------+--------+--------+--------+
| Msmvttl1 | 0.018 | 0.015 | 0.013 | 0.011 | 0.01 | -0.008 |
| | 2.94 | 2.257 | 2.027 | 1.687 | 1.445 | -3.787 |
| alpha | 0.016 | 0.012 | 0.011 | 0.009 | 0.008 | -0.008 |
| | 2.529 | 1.873 | 1.769 | 1.29 | 1.061 | -3.959 |
| Msmvttl2 | 0.014 | 0.013 | 0.012 | 0.009 | 0.01 | -0.004 |
| | 2.225 | 2.182 | 1.955 | 1.369 | 1.45 | -1.617 |
| alpha | 0.012 | 0.011 | 0.01 | 0.007 | 0.008 | -0.004 |
| | 1.861 | 1.741 | 1.521 | 1.109 | 1.086 | -1.971 |
| Msmvttl3 | 0.013 | 0.01 | 0.009 | 0.009 | 0.005 | -0.008 |
| | 2.187 | 1.668 | 1.44 | 1.413 | 0.748 | -3.215 |
| alpha | 0.011 | 0.008 | 0.007 | 0.007 | 0.003 | -0.008 |
| | 1.719 | 1.352 | 1.096 | 1.056 | 0.441 | -3.324 |
| Msmvttl4 | 0.011 | 0.011 | 0.009 | 0.008 | 0.006 | -0.005 |
| | 1.822 | 1.866 | 1.571 | 1.372 | 0.932 | -1.674 |
| alpha | 0.009 | 0.009 | 0.007 | 0.006 | 0.005 | -0.005 |
| | 1.393 | 1.525 | 1.16 | 0.991 | 0.7 | -1.788 |
| Msmvttl5 | 0.013 | 0.012 | 0.008 | 0.006 | 0.004 | -0.009 |
| | 2.261 | 2.163 | 1.545 | 1.067 | 0.732 | -2.473 |
| alpha | 0.012 | 0.011 | 0.007 | 0.004 | 0.003 | -0.009 |
| | 1.83 | 1.628 | 1.169 | 0.718 | 0.406 | -2.612 |
| Diff | -0.005 | -0.002 | -0.005 | -0.006 | -0.006 | -0.001 |
| | -1.349 | -0.641 | -1.334 | -1.534 | -1.665 | -0.17 |
| alpha | -0.004 | -0.002 | -0.004 | -0.004 | -0.005 | -0.001 |
| | -1.315 | -0.431 | -0.939 | -1.031 | -1.407 | -0.297 |
+----------+--------+--------+--------+--------+--------+--------+
The first dataset contains no tail 30% stocks from 2000-01-01 to 2019-12-01 and the value factor is PE. The value effect is significant since the t-test statistics for differenced portfolio are -3.551, -1.947, -3.19, -1.98, -2.984, respectively, whose absolute values are generally more than 2 corresponding to the significance level at 0.05. The factor adjustment tends to strengthen the portfolio excess return; while the dependent-sort bivariate tends to weaken the portfolio excess return.
# %% construct test_data for bivariate analysis
# dataset 2 : PB
from portfolio_analysis import Bivariate
import numpy as np
# select stocks whose size is among the up 30% stocks in each month and whose trading
# days are more than or equal to 10 days
test_data_2 = return_company[(return_company['cap']==True) & (return_company['Ndaytrd']>=10)]
test_data_2 = test_data_2[['emrwd', 'Msmvttl', 'PBV1A', 'Date_merge']].dropna()
test_data_2 = test_data_2[(test_data_2['Date_merge'] >= '2000-01-01') & (test_data_2['Date_merge'] <= '2019-12-01')]
# Independent-sort Bivariate analysis
bi_2 = Bivariate(np.array(test_data_2), number=4)
bi_2.average_by_time()
bi_2.summary_and_test()
bi_2.print_summary_by_time()
bi_2.print_summary()
===============================================================
+-------+--------+--------+--------+--------+--------+--------+
| Group | 1 | 2 | 3 | 4 | 5 | Diff |
+-------+--------+--------+--------+--------+--------+--------+
| 1 | 0.016 | 0.015 | 0.012 | 0.014 | 0.008 | -0.008 |
| | 2.41 | 2.321 | 1.904 | 1.969 | 1.135 | -2.467 |
| 2 | 0.013 | 0.012 | 0.012 | 0.011 | 0.006 | -0.007 |
| | 2.075 | 1.87 | 1.877 | 1.645 | 0.955 | -1.902 |
| 3 | 0.012 | 0.009 | 0.008 | 0.01 | 0.007 | -0.005 |
| | 1.898 | 1.479 | 1.302 | 1.571 | 1.075 | -1.492 |
| 4 | 0.012 | 0.011 | 0.008 | 0.006 | 0.008 | -0.004 |
| | 1.911 | 1.804 | 1.284 | 0.996 | 1.266 | -1.075 |
| 5 | 0.011 | 0.011 | 0.008 | 0.007 | 0.006 | -0.005 |
| | 1.975 | 1.995 | 1.423 | 1.282 | 1.111 | -1.185 |
| Diff | -0.004 | -0.004 | -0.004 | -0.006 | -0.002 | 0.003 |
| | -1.301 | -1.127 | -1.38 | -1.726 | -0.418 | 0.785 |
+-------+--------+--------+--------+--------+--------+--------+
===============================================================
# Risk adjustment
risk_model = risk_premium['MKT']
risk_model = risk_model['2000':'2019']
bi_2.factor_adjustment(risk_model)
bi_2.print_summary()
===============================================================
+-------+--------+--------+--------+--------+--------+--------+
| Group | 1 | 2 | 3 | 4 | 5 | Diff |
+-------+--------+--------+--------+--------+--------+--------+
| 1 | 0.016 | 0.015 | 0.012 | 0.014 | 0.008 | -0.008 |
| | 2.41 | 2.321 | 1.904 | 1.969 | 1.135 | -2.467 |
| alpha | 0.013 | 0.013 | 0.01 | 0.011 | 0.005 | -0.008 |
| | 2.1 | 1.901 | 1.522 | 1.521 | 0.804 | -2.722 |
| 2 | 0.013 | 0.012 | 0.012 | 0.011 | 0.006 | -0.007 |
| | 2.075 | 1.87 | 1.877 | 1.645 | 0.955 | -1.902 |
| alpha | 0.011 | 0.01 | 0.01 | 0.009 | 0.004 | -0.007 |
| | 1.663 | 1.515 | 1.54 | 1.295 | 0.632 | -2.229 |
| 3 | 0.012 | 0.009 | 0.008 | 0.01 | 0.007 | -0.005 |
| | 1.898 | 1.479 | 1.302 | 1.571 | 1.075 | -1.492 |
| alpha | 0.01 | 0.007 | 0.006 | 0.008 | 0.005 | -0.005 |
| | 1.522 | 1.102 | 0.982 | 1.183 | 0.73 | -1.719 |
| 4 | 0.012 | 0.011 | 0.008 | 0.006 | 0.008 | -0.004 |
| | 1.911 | 1.804 | 1.284 | 0.996 | 1.266 | -1.075 |
| alpha | 0.01 | 0.009 | 0.006 | 0.004 | 0.006 | -0.004 |
| | 1.496 | 1.382 | 0.954 | 0.72 | 0.938 | -1.243 |
| 5 | 0.011 | 0.011 | 0.008 | 0.007 | 0.006 | -0.005 |
| | 1.975 | 1.995 | 1.423 | 1.282 | 1.111 | -1.185 |
| alpha | 0.01 | 0.01 | 0.007 | 0.006 | 0.005 | -0.005 |
| | 1.53 | 1.621 | 1.036 | 0.878 | 0.741 | -1.268 |
| Diff | -0.004 | -0.004 | -0.004 | -0.006 | -0.002 | 0.003 |
| | -1.301 | -1.127 | -1.38 | -1.726 | -0.418 | 0.785 |
| alpha | -0.004 | -0.002 | -0.003 | -0.005 | -0.0 | 0.003 |
| | -1.193 | -0.745 | -0.989 | -1.195 | -0.091 | 0.785 |
+-------+--------+--------+--------+--------+--------+--------+
===============================================================
# Dependent-sort Bivariate Analysis
bi_2_de = Bivariate(test_data_2, number=4)
bi_2_de.fit(conditional=True)
bi_2_de.print_summary()
==================================================================
+----------+--------+--------+--------+--------+--------+--------+
| Group | PBV1A1 | PBV1A2 | PBV1A3 | PBV1A4 | PBV1A5 | Diff |
+----------+--------+--------+--------+--------+--------+--------+
| Msmvttl1 | 0.016 | 0.015 | 0.013 | 0.014 | 0.009 | -0.007 |
| | 2.43 | 2.21 | 1.929 | 2.014 | 1.253 | -2.267 |
| Msmvttl2 | 0.013 | 0.012 | 0.013 | 0.011 | 0.006 | -0.006 |
| | 1.994 | 1.876 | 1.993 | 1.723 | 0.987 | -1.857 |
| Msmvttl3 | 0.011 | 0.009 | 0.008 | 0.01 | 0.007 | -0.004 |
| | 1.838 | 1.499 | 1.289 | 1.588 | 1.116 | -1.35 |
| Msmvttl4 | 0.012 | 0.01 | 0.007 | 0.006 | 0.008 | -0.004 |
| | 1.975 | 1.618 | 1.173 | 1.077 | 1.276 | -1.179 |
| Msmvttl5 | 0.012 | 0.01 | 0.009 | 0.005 | 0.007 | -0.005 |
| | 2.131 | 1.83 | 1.558 | 0.946 | 1.195 | -1.206 |
| Diff | -0.004 | -0.004 | -0.004 | -0.008 | -0.002 | 0.002 |
| | -1.006 | -1.135 | -1.07 | -2.332 | -0.519 | 0.432 |
+----------+--------+--------+--------+--------+--------+--------+
==================================================================
# Risk Adjustment
bi_2_de.factor_adjustment(risk_model)
bi_2_de.print_summary()
==================================================================
+----------+--------+--------+--------+--------+--------+--------+
| Group | PBV1A1 | PBV1A2 | PBV1A3 | PBV1A4 | PBV1A5 | Diff |
+----------+--------+--------+--------+--------+--------+--------+
| Msmvttl1 | 0.016 | 0.015 | 0.013 | 0.014 | 0.009 | -0.007 |
| | 2.43 | 2.21 | 1.929 | 2.014 | 1.253 | -2.267 |
| alpha | 0.013 | 0.012 | 0.01 | 0.011 | 0.006 | -0.007 |
| | 2.097 | 1.822 | 1.514 | 1.583 | 0.883 | -2.449 |
| Msmvttl2 | 0.013 | 0.012 | 0.013 | 0.011 | 0.006 | -0.006 |
| | 1.994 | 1.876 | 1.993 | 1.723 | 0.987 | -1.857 |
| alpha | 0.01 | 0.01 | 0.011 | 0.01 | 0.004 | -0.006 |
| | 1.585 | 1.55 | 1.62 | 1.402 | 0.647 | -2.206 |
| Msmvttl3 | 0.011 | 0.009 | 0.008 | 0.01 | 0.007 | -0.004 |
| | 1.838 | 1.499 | 1.289 | 1.588 | 1.116 | -1.35 |
| alpha | 0.009 | 0.007 | 0.006 | 0.008 | 0.005 | -0.004 |
| | 1.454 | 1.167 | 0.938 | 1.212 | 0.765 | -1.554 |
| Msmvttl4 | 0.012 | 0.01 | 0.007 | 0.006 | 0.008 | -0.004 |
| | 1.975 | 1.618 | 1.173 | 1.077 | 1.276 | -1.179 |
| alpha | 0.01 | 0.008 | 0.006 | 0.005 | 0.006 | -0.004 |
| | 1.531 | 1.256 | 0.887 | 0.784 | 0.953 | -1.34 |
| Msmvttl5 | 0.012 | 0.01 | 0.009 | 0.005 | 0.007 | -0.005 |
| | 2.131 | 1.83 | 1.558 | 0.946 | 1.195 | -1.206 |
| alpha | 0.011 | 0.009 | 0.008 | 0.004 | 0.005 | -0.005 |
| | 1.652 | 1.435 | 1.212 | 0.608 | 0.805 | -1.34 |
| Diff | -0.004 | -0.004 | -0.004 | -0.008 | -0.002 | 0.002 |
| | -1.006 | -1.135 | -1.07 | -2.332 | -0.519 | 0.432 |
| alpha | -0.003 | -0.003 | -0.002 | -0.007 | -0.001 | 0.002 |
| | -0.818 | -0.957 | -0.724 | -1.678 | -0.162 | 0.488 |
+----------+--------+--------+--------+--------+--------+--------+
The second dataset contains no tail 30% stocks and the value variable is PB from 2000-01-01 to 2019-12-01. The value effect is partly significant since the t-test statistics for differenced portfolio are -2.467, -1.902, -1.492, -1.075, -1.185, respectively, whose absolute values are generally no more than 2 corresponding to the significance level at 0.05. The factor adjustment tends to strengthen the portfolio excess return; while the dependent-sort bivariate tends to weaken the portfolio excess return.
# %% construct test_data for bivariate analysis
# dataset 3 : PE
from portfolio_analysis import Bivariate
import numpy as np
# select stocks whose size is among the up 30% stocks in each month and whose trading
# days are more than or equal to 10 days
test_data_3 = return_company[return_company['Ndaytrd']>=10]
test_data_3 = test_data_3[['emrwd', 'Msmvttl', 'PE1A', 'Date_merge']].dropna()
test_data_3 = test_data_3[(test_data_3['Date_merge'] >= '2000-01-01') & (test_data_3['Date_merge'] <= '2019-12-01')]
# Independent-sort Bivariate analysis
bi_3 = Bivariate(np.array(test_data_3), number=4)
bi_3.average_by_time()
bi_3.summary_and_test()
bi_3.print_summary_by_time()
bi_3.print_summary()
===============================================================
+-------+--------+--------+--------+--------+--------+--------+
| Group | 1 | 2 | 3 | 4 | 5 | Diff |
+-------+--------+--------+--------+--------+--------+--------+
| 1 | 0.023 | 0.023 | 0.022 | 0.022 | 0.022 | -0.001 |
| | 3.492 | 3.471 | 3.239 | 3.107 | 3.043 | -0.664 |
| 2 | 0.019 | 0.017 | 0.014 | 0.013 | 0.011 | -0.008 |
| | 3.04 | 2.619 | 2.163 | 1.915 | 1.635 | -3.531 |
| 3 | 0.014 | 0.013 | 0.011 | 0.01 | 0.009 | -0.005 |
| | 2.296 | 2.181 | 1.723 | 1.57 | 1.338 | -2.334 |
| 4 | 0.013 | 0.009 | 0.009 | 0.007 | 0.005 | -0.008 |
| | 2.159 | 1.626 | 1.519 | 1.138 | 0.69 | -3.141 |
| 5 | 0.012 | 0.009 | 0.007 | 0.006 | 0.003 | -0.009 |
| | 2.098 | 1.648 | 1.273 | 0.992 | 0.521 | -2.597 |
| Diff | -0.011 | -0.014 | -0.015 | -0.016 | -0.018 | -0.007 |
| | -2.816 | -3.834 | -4.025 | -4.372 | -5.071 | -2.236 |
+-------+--------+--------+--------+--------+--------+--------+
===============================================================
# Risk Adjustment
risk_model = risk_premium['MKT']
risk_model = risk_model['2000':'2019']
bi_3.factor_adjustment(risk_model)
bi_3.print_summary()
===============================================================
+-------+--------+--------+--------+--------+--------+--------+
| Group | 1 | 2 | 3 | 4 | 5 | Diff |
+-------+--------+--------+--------+--------+--------+--------+
| 1 | 0.023 | 0.023 | 0.022 | 0.022 | 0.022 | -0.001 |
| | 3.492 | 3.471 | 3.239 | 3.107 | 3.043 | -0.664 |
| alpha | 0.021 | 0.02 | 0.019 | 0.019 | 0.019 | -0.002 |
| | 2.983 | 2.997 | 2.683 | 2.628 | 2.494 | -1.041 |
| 2 | 0.019 | 0.017 | 0.014 | 0.013 | 0.011 | -0.008 |
| | 3.04 | 2.619 | 2.163 | 1.915 | 1.635 | -3.531 |
| alpha | 0.016 | 0.014 | 0.012 | 0.011 | 0.009 | -0.008 |
| | 2.644 | 2.218 | 1.844 | 1.564 | 1.25 | -3.46 |
| 3 | 0.014 | 0.013 | 0.011 | 0.01 | 0.009 | -0.005 |
| | 2.296 | 2.181 | 1.723 | 1.57 | 1.338 | -2.334 |
| alpha | 0.012 | 0.011 | 0.009 | 0.008 | 0.007 | -0.005 |
| | 1.914 | 1.779 | 1.344 | 1.262 | 0.98 | -2.709 |
| 4 | 0.013 | 0.009 | 0.009 | 0.007 | 0.005 | -0.008 |
| | 2.159 | 1.626 | 1.519 | 1.138 | 0.69 | -3.141 |
| alpha | 0.011 | 0.008 | 0.007 | 0.005 | 0.003 | -0.008 |
| | 1.731 | 1.28 | 1.127 | 0.862 | 0.409 | -3.648 |
| 5 | 0.012 | 0.009 | 0.007 | 0.006 | 0.003 | -0.009 |
| | 2.098 | 1.648 | 1.273 | 0.992 | 0.521 | -2.597 |
| alpha | 0.01 | 0.007 | 0.005 | 0.004 | 0.002 | -0.009 |
| | 1.598 | 1.193 | 0.874 | 0.647 | 0.277 | -2.897 |
| Diff | -0.011 | -0.014 | -0.015 | -0.016 | -0.018 | -0.007 |
| | -2.816 | -3.834 | -4.025 | -4.372 | -5.071 | -2.236 |
| alpha | -0.01 | -0.013 | -0.014 | -0.014 | -0.017 | -0.007 |
| | -2.534 | -2.77 | -2.761 | -3.106 | -3.862 | -2.331 |
+-------+--------+--------+--------+--------+--------+--------+
===============================================================
# Dependent-sort Bivariate Analysis
bi_3_de = Bivariate(test_data_3, number=4)
bi_3_de.fit(conditional=True)
bi_3_de.print_summary()
==================================================================
+----------+--------+--------+--------+--------+--------+--------+
| Group | PE1A1 | PE1A2 | PE1A3 | PE1A4 | PE1A5 | Diff |
+----------+--------+--------+--------+--------+--------+--------+
| Msmvttl1 | 0.023 | 0.023 | 0.022 | 0.022 | 0.022 | -0.001 |
| | 3.463 | 3.313 | 3.113 | 3.161 | 2.992 | -0.499 |
| Msmvttl2 | 0.018 | 0.016 | 0.014 | 0.013 | 0.012 | -0.006 |
| | 2.855 | 2.461 | 2.072 | 1.85 | 1.68 | -3.032 |
| Msmvttl3 | 0.014 | 0.013 | 0.011 | 0.01 | 0.009 | -0.005 |
| | 2.217 | 2.197 | 1.768 | 1.557 | 1.284 | -2.425 |
| Msmvttl4 | 0.012 | 0.011 | 0.009 | 0.009 | 0.004 | -0.008 |
| | 2.049 | 1.896 | 1.45 | 1.427 | 0.633 | -3.034 |
| Msmvttl5 | 0.013 | 0.011 | 0.008 | 0.006 | 0.005 | -0.008 |
| | 2.282 | 1.894 | 1.584 | 1.19 | 0.839 | -2.33 |
| Diff | -0.009 | -0.012 | -0.013 | -0.016 | -0.017 | -0.007 |
| | -2.064 | -2.804 | -3.221 | -4.152 | -4.434 | -1.881 |
+----------+--------+--------+--------+--------+--------+--------+
==================================================================
# Risk Adjustment
bi_3_de.factor_adjustment(risk_model)
bi_3_de.print_summary()
==================================================================
+----------+--------+--------+--------+--------+--------+--------+
| Group | PE1A1 | PE1A2 | PE1A3 | PE1A4 | PE1A5 | Diff |
+----------+--------+--------+--------+--------+--------+--------+
| Msmvttl1 | 0.023 | 0.023 | 0.022 | 0.022 | 0.022 | -0.001 |
| | 3.463 | 3.313 | 3.113 | 3.161 | 2.992 | -0.499 |
| alpha | 0.02 | 0.02 | 0.019 | 0.019 | 0.019 | -0.001 |
| | 2.95 | 2.71 | 2.691 | 2.621 | 2.434 | -0.798 |
| Msmvttl2 | 0.018 | 0.016 | 0.014 | 0.013 | 0.012 | -0.006 |
| | 2.855 | 2.461 | 2.072 | 1.85 | 1.68 | -3.032 |
| alpha | 0.015 | 0.013 | 0.012 | 0.01 | 0.009 | -0.006 |
| | 2.456 | 2.057 | 1.812 | 1.473 | 1.279 | -3.127 |
| Msmvttl3 | 0.014 | 0.013 | 0.011 | 0.01 | 0.009 | -0.005 |
| | 2.217 | 2.197 | 1.768 | 1.557 | 1.284 | -2.425 |
| alpha | 0.012 | 0.012 | 0.009 | 0.008 | 0.007 | -0.005 |
| | 1.831 | 1.775 | 1.413 | 1.236 | 0.938 | -2.902 |
| Msmvttl4 | 0.012 | 0.011 | 0.009 | 0.009 | 0.004 | -0.008 |
| | 2.049 | 1.896 | 1.45 | 1.427 | 0.633 | -3.034 |
| alpha | 0.01 | 0.009 | 0.007 | 0.007 | 0.002 | -0.008 |
| | 1.64 | 1.541 | 1.089 | 1.109 | 0.365 | -3.268 |
| Msmvttl5 | 0.013 | 0.011 | 0.008 | 0.006 | 0.005 | -0.008 |
| | 2.282 | 1.894 | 1.584 | 1.19 | 0.839 | -2.33 |
| alpha | 0.012 | 0.009 | 0.007 | 0.005 | 0.003 | -0.008 |
| | 1.774 | 1.438 | 1.165 | 0.803 | 0.501 | -2.625 |
| Diff | -0.009 | -0.012 | -0.013 | -0.016 | -0.017 | -0.007 |
| | -2.064 | -2.804 | -3.221 | -4.152 | -4.434 | -1.881 |
| alpha | -0.008 | -0.011 | -0.012 | -0.014 | -0.015 | -0.007 |
| | -1.82 | -1.909 | -2.355 | -2.986 | -3.436 | -1.972 |
+----------+--------+--------+--------+--------+--------+--------+
The third dataset contains tail 30% stocks and the value variable is PE from 2000-01-01 to 2019-12-01. The value effect is partly significant since the t-test statistics for differenced portfolio are -0.664, -3.531, -2.334, -3.141, -2.597, respectively, whose absolute values are generally more than 2 corresponding to the significance level at 0.05. The factor adjustment tends to strengthen the portfolio excess return; while the dependent-sort bivariate tends to weaken the portfolio excess return.
# %% construct test_data for bivariate analysis
# dataset 4 : PB
from portfolio_analysis import Bivariate
import numpy as np
# select stocks whose size is among the up 30% stocks in each month and whose trading
# days are more than or equal to 10 days
test_data_4 = return_company[(return_company['Ndaytrd']>=10)]
test_data_4 = test_data_4[['emrwd', 'Msmvttl', 'PBV1A', 'Date_merge']].dropna()
test_data_4 = test_data_4[(test_data_4['Date_merge'] >= '2000-01-01') & (test_data_4['Date_merge'] <= '2019-12-01')]
# analysis
bi_4 = Bivariate(np.array(test_data_4), number=4)
bi_4.average_by_time()
bi_4.summary_and_test()
bi_4.print_summary_by_time()
bi_4.print_summary()
===============================================================
+-------+--------+--------+--------+--------+--------+--------+
| Group | 1 | 2 | 3 | 4 | 5 | Diff |
+-------+--------+--------+--------+--------+--------+--------+
| 1 | 0.022 | 0.024 | 0.025 | 0.022 | 0.02 | -0.002 |
| | 3.342 | 3.475 | 3.554 | 3.054 | 2.714 | -0.905 |
| 2 | 0.017 | 0.016 | 0.013 | 0.015 | 0.009 | -0.008 |
| | 2.632 | 2.365 | 1.939 | 2.239 | 1.337 | -2.653 |
| 3 | 0.013 | 0.013 | 0.012 | 0.01 | 0.007 | -0.006 |
| | 2.045 | 2.071 | 1.9 | 1.616 | 1.051 | -1.827 |
| 4 | 0.011 | 0.01 | 0.009 | 0.008 | 0.007 | -0.004 |
| | 1.783 | 1.592 | 1.416 | 1.299 | 1.167 | -1.093 |
| 5 | 0.011 | 0.011 | 0.008 | 0.007 | 0.006 | -0.006 |
| | 1.975 | 1.914 | 1.382 | 1.174 | 0.997 | -1.392 |
| Diff | -0.011 | -0.013 | -0.017 | -0.015 | -0.015 | -0.004 |
| | -2.803 | -3.498 | -4.532 | -3.934 | -3.144 | -0.891 |
+-------+--------+--------+--------+--------+--------+--------+
===============================================================
# Risk Adjustment
risk_model = risk_premium['MKT']
risk_model = risk_model['2000':'2019']
bi_4.factor_adjustment(risk_model)
bi_4.print_summary()
===============================================================
+-------+--------+--------+--------+--------+--------+--------+
| Group | 1 | 2 | 3 | 4 | 5 | Diff |
+-------+--------+--------+--------+--------+--------+--------+
| 1 | 0.022 | 0.024 | 0.025 | 0.022 | 0.02 | -0.002 |
| | 3.342 | 3.475 | 3.554 | 3.054 | 2.714 | -0.905 |
| alpha | 0.02 | 0.021 | 0.022 | 0.019 | 0.017 | -0.003 |
| | 2.773 | 2.872 | 3.019 | 2.511 | 2.226 | -1.715 |
| 2 | 0.017 | 0.016 | 0.013 | 0.015 | 0.009 | -0.008 |
| | 2.632 | 2.365 | 1.939 | 2.239 | 1.337 | -2.653 |
| alpha | 0.015 | 0.013 | 0.011 | 0.013 | 0.007 | -0.008 |
| | 2.23 | 1.957 | 1.572 | 1.744 | 1.032 | -2.8 |
| 3 | 0.013 | 0.013 | 0.012 | 0.01 | 0.007 | -0.006 |
| | 2.045 | 2.071 | 1.9 | 1.616 | 1.051 | -1.827 |
| alpha | 0.011 | 0.011 | 0.01 | 0.008 | 0.005 | -0.006 |
| | 1.65 | 1.702 | 1.531 | 1.274 | 0.729 | -2.156 |
| 4 | 0.011 | 0.01 | 0.009 | 0.008 | 0.007 | -0.004 |
| | 1.783 | 1.592 | 1.416 | 1.299 | 1.167 | -1.093 |
| alpha | 0.009 | 0.008 | 0.007 | 0.006 | 0.005 | -0.004 |
| | 1.409 | 1.203 | 1.036 | 0.994 | 0.806 | -1.155 |
| 5 | 0.011 | 0.011 | 0.008 | 0.007 | 0.006 | -0.006 |
| | 1.975 | 1.914 | 1.382 | 1.174 | 0.997 | -1.392 |
| alpha | 0.01 | 0.01 | 0.006 | 0.005 | 0.004 | -0.006 |
| | 1.507 | 1.496 | 0.991 | 0.815 | 0.632 | -1.592 |
| Diff | -0.011 | -0.013 | -0.017 | -0.015 | -0.015 | -0.004 |
| | -2.803 | -3.498 | -4.532 | -3.934 | -3.144 | -0.891 |
| alpha | -0.01 | -0.011 | -0.016 | -0.014 | -0.013 | -0.003 |
| | -2.266 | -2.591 | -3.095 | -2.767 | -2.484 | -0.71 |
+-------+--------+--------+--------+--------+--------+--------+
===============================================================
# Dependent-sort Bivariate Analysis
bi_4_de = Bivariate(test_data_4, number=4)
bi_4_de.fit(conditional=True)
bi_4_de.print_summary()
==================================================================
+----------+--------+--------+--------+--------+--------+--------+
| Group | PBV1A1 | PBV1A2 | PBV1A3 | PBV1A4 | PBV1A5 | Diff |
+----------+--------+--------+--------+--------+--------+--------+
| Msmvttl1 | 0.023 | 0.024 | 0.025 | 0.022 | 0.02 | -0.003 |
| | 3.364 | 3.478 | 3.614 | 3.142 | 2.629 | -1.141 |
| Msmvttl2 | 0.017 | 0.016 | 0.013 | 0.015 | 0.01 | -0.007 |
| | 2.585 | 2.424 | 2.012 | 2.226 | 1.476 | -2.287 |
| Msmvttl3 | 0.013 | 0.013 | 0.012 | 0.011 | 0.007 | -0.006 |
| | 2.07 | 1.977 | 1.916 | 1.762 | 1.075 | -1.91 |
| Msmvttl4 | 0.011 | 0.009 | 0.008 | 0.008 | 0.007 | -0.004 |
| | 1.858 | 1.481 | 1.344 | 1.359 | 1.179 | -1.239 |
| Msmvttl5 | 0.012 | 0.01 | 0.008 | 0.006 | 0.006 | -0.006 |
| | 2.08 | 1.785 | 1.453 | 0.977 | 1.055 | -1.371 |
| Diff | -0.011 | -0.014 | -0.017 | -0.017 | -0.014 | -0.003 |
| | -2.615 | -3.36 | -4.379 | -4.139 | -2.871 | -0.726 |
+----------+--------+--------+--------+--------+--------+--------+
==================================================================
# Risk Adjustment
bi_4_de.factor_adjustment(risk_model)
bi_4_de.print_summary()
==================================================================
+----------+--------+--------+--------+--------+--------+--------+
| Group | PBV1A1 | PBV1A2 | PBV1A3 | PBV1A4 | PBV1A5 | Diff |
+----------+--------+--------+--------+--------+--------+--------+
| Msmvttl1 | 0.023 | 0.024 | 0.025 | 0.022 | 0.02 | -0.003 |
| | 3.364 | 3.478 | 3.614 | 3.142 | 2.629 | -1.141 |
| alpha | 0.02 | 0.021 | 0.023 | 0.02 | 0.016 | -0.004 |
| | 2.733 | 2.943 | 3.024 | 2.582 | 2.165 | -1.794 |
| Msmvttl2 | 0.017 | 0.016 | 0.013 | 0.015 | 0.01 | -0.007 |
| | 2.585 | 2.424 | 2.012 | 2.226 | 1.476 | -2.287 |
| alpha | 0.014 | 0.014 | 0.011 | 0.013 | 0.008 | -0.007 |
| | 2.196 | 2.031 | 1.594 | 1.76 | 1.122 | -2.375 |
| Msmvttl3 | 0.013 | 0.013 | 0.012 | 0.011 | 0.007 | -0.006 |
| | 2.07 | 1.977 | 1.916 | 1.762 | 1.075 | -1.91 |
| alpha | 0.011 | 0.011 | 0.01 | 0.01 | 0.005 | -0.006 |
| | 1.677 | 1.64 | 1.517 | 1.45 | 0.736 | -2.243 |
| Msmvttl4 | 0.011 | 0.009 | 0.008 | 0.008 | 0.007 | -0.004 |
| | 1.858 | 1.481 | 1.344 | 1.359 | 1.179 | -1.239 |
| alpha | 0.009 | 0.007 | 0.006 | 0.006 | 0.005 | -0.004 |
| | 1.463 | 1.134 | 1.005 | 1.028 | 0.83 | -1.352 |
| Msmvttl5 | 0.012 | 0.01 | 0.008 | 0.006 | 0.006 | -0.006 |
| | 2.08 | 1.785 | 1.453 | 0.977 | 1.055 | -1.371 |
| alpha | 0.01 | 0.009 | 0.007 | 0.004 | 0.004 | -0.006 |
| | 1.594 | 1.395 | 1.087 | 0.647 | 0.7 | -1.633 |
| Diff | -0.011 | -0.014 | -0.017 | -0.017 | -0.014 | -0.003 |
| | -2.615 | -3.36 | -4.379 | -4.139 | -2.871 | -0.726 |
| alpha | -0.01 | -0.012 | -0.016 | -0.015 | -0.012 | -0.002 |
| | -2.109 | -2.55 | -3.328 | -2.861 | -2.408 | -0.629 |
+----------+--------+--------+--------+--------+--------+--------+
The fourth dataset contains tail 30% stocks and the value variable is PB from 2000-01-01 to 2019-12-01. The value effect is partly significant since the t-test statistics for differenced portfolio are -0.905, -2.653, -1.827, -1.093, -1.392, respectively, whose absolute values are generally no more than 2 corresponding to the significance level at 0.05. The factor adjustment tends to strengthen the portfolio excess return; while the dependent-sort bivariate tends to weaken the portfolio excess return.
Profitability Factor
The relation of profitability and future return is more discussed in literature (Fama and French, 2015; Hou et al., 2015), through which the profitability factor is constituted and included in two main asset pricing model, Fama-French 5 factor model and HXZ's model. There are many proxy variables for profitability factor. These variables are highly correlated and the most common one is return on equity (ROE). Besides the ROE, ROA is supported by several literatures (Novy-Marx, 2013; Ball et al., 2015). Another substitution is return on tangible capital (ROTC), which is proposed by Greenblatt (2006, 2010). Through empirical evidence, it is suggested that profitability is positively related with future return in American stock market, while in China stock market the relation needs further discussion.
In this demo, the ROE(TTM) is used as the proxy variable for profitability factor. The dataset starts from Jan, 2004 and is collected from CSMAR dataset. WARNING: Do Not use dataset in this demo for any commercial purpose.
# %% import package
import pandas as pd
import sys, os
sys.path.append(os.path.abspath(".."))
# %% import data
# Monthly return of stocks in China security market
month_return = pd.read_hdf('.\data\month_return.h5', key='month_return')
company_data = pd.read_hdf('.\data\last_filter_pe.h5', key='data')
The data needs some preprocessing.
# %% preprocessing data
# forward the monthly return for each stock
# emrwd is the return including dividend
month_return['emrwd'] = month_return.groupby(['Stkcd'])['Mretwd'].shift(-1)
# emrnd is the return including no dividend
month_return['emrnd'] = month_return.groupby(['Stkcd'])['Mretnd'].shift(-1)
# select the A share stock
month_return = month_return[month_return['Markettype'].isin([1, 4, 16])]
# % distinguish the stocks whose size is among the up 30% stocks in each month
def percentile(stocks) :
return stocks >= stocks.quantile(q=.3)
month_return['cap'] = month_return.groupby(['Trdmnt'])['Msmvttl'].apply(percentile)
# %% prepare merge data
from pandas.tseries.offsets import *
month_return['Stkcd_merge'] = month_return['Stkcd'].astype(dtype='string')
month_return['Date_merge'] = pd.to_datetime(month_return['Trdmnt'])
month_return['Yearmonth'] = month_return['Date_merge'].map(lambda x : 1000*x.year + x.month)
#month_return['Date_merge'] += MonthEnd()
# in this demo, the ROE(TTM) are used
# ROE(TTM) = PBV1B/PE(TTM)
company_data['ROE(TTM)'] = company_data['PBV1B']/company_data['PE1TTM']
company_data['Stkcd_merge'] = company_data['Symbol'].dropna().astype(dtype='int').astype(dtype='string')
company_data['Date_merge'] = pd.to_datetime(company_data['TradingDate'])
company_data['Yearmonth'] = company_data['Date_merge'].map(lambda x : 1000*x.year + x.month)
company_data['Date_merge'] += MonthBegin()
# %% dataset starts from '2000-01'
company_data = company_data[company_data['Date_merge'] >= '2000-01']
month_return = month_return[month_return['Date_merge'] >= '2000-01']
return_company = pd.merge(company_data, month_return, on=['Stkcd_merge', 'Date_merge'])
Two datasets are constituted. One includes tail 30% stock, while one includes not. Univariate analysis and Bivariate analysis are attached.
# %% construct test_data for bivariate analysis
# dataset 1 : no tail stocks & ROE Bivariate
from portfolio_analysis import Bivariate, Univariate
import numpy as np
# select stocks whose size is among the up 30% stocks in each month and whose trading
# days are more than or equal to 10 days
test_data_1 = return_company[(return_company['cap']==True) & (return_company['Ndaytrd']>=10)]
test_data_1 = test_data_1[['emrwd', 'Msmvttl', 'ROE(TTM)', 'Date_merge']].dropna()
test_data_1 = test_data_1[(test_data_1['Date_merge'] >= '2004-01-01') & (test_data_1['Date_merge'] <= '2019-12-01')]
# Univariate analysis
uni_1 = Univariate(np.array(test_data_1[['emrwd', 'ROE(TTM)', 'Date_merge']]), number=9)
uni_1.summary_and_test()
uni_1.print_summary_by_time()
uni_1.print_summary()
====================================================================================================
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+
| Group | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Diff |
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+
| Average | 0.012 | 0.011 | 0.013 | 0.013 | 0.013 | 0.015 | 0.016 | 0.015 | 0.017 | 0.017 | 0.005 |
| T-Test | 1.465 | 1.372 | 1.648 | 1.826 | 1.884 | 2.048 | 2.354 | 2.3 | 2.548 | 2.494 | 1.473 |
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+
====================================================================================================
# Bivariate analysis
bi_1 = Bivariate(np.array(test_data_1), number=4)
bi_1.average_by_time()
bi_1.summary_and_test()
bi_1.print_summary_by_time()
bi_1.print_summary()
===============================================================
+-------+--------+--------+--------+--------+--------+-------+
| Group | 1 | 2 | 3 | 4 | 5 | Diff |
+-------+--------+--------+--------+--------+--------+-------+
| 1 | 0.014 | 0.017 | 0.021 | 0.023 | 0.02 | 0.006 |
| | 1.683 | 2.197 | 2.712 | 3.026 | 2.519 | 2.308 |
| 2 | 0.014 | 0.015 | 0.017 | 0.018 | 0.019 | 0.005 |
| | 1.702 | 1.895 | 2.228 | 2.604 | 2.567 | 1.699 |
| 3 | 0.008 | 0.011 | 0.012 | 0.016 | 0.018 | 0.01 |
| | 1.091 | 1.373 | 1.712 | 2.246 | 2.624 | 3.775 |
| 4 | 0.008 | 0.011 | 0.01 | 0.014 | 0.016 | 0.008 |
| | 1.002 | 1.442 | 1.468 | 2.109 | 2.305 | 2.41 |
| 5 | 0.004 | 0.009 | 0.008 | 0.01 | 0.016 | 0.012 |
| | 0.565 | 1.271 | 1.257 | 1.613 | 2.417 | 3.234 |
| Diff | -0.009 | -0.008 | -0.012 | -0.013 | -0.004 | 0.005 |
| | -2.446 | -2.151 | -3.025 | -3.231 | -0.917 | 1.502 |
+-------+--------+--------+--------+--------+--------+-------+
===============================================================
# Risk adjustment
risk_model = risk_premium[['MKT', 'SMB', 'HML']]
risk_model = risk_model['2004':'2019']
bi_1.factor_adjustment(risk_model)
bi_1.print_summary()
==============================================================
+-------+--------+--------+--------+--------+--------+-------+
| Group | 1 | 2 | 3 | 4 | 5 | Diff |
+-------+--------+--------+--------+--------+--------+-------+
| 1 | 0.014 | 0.017 | 0.021 | 0.023 | 0.02 | 0.006 |
| | 1.683 | 2.197 | 2.712 | 3.026 | 2.519 | 2.308 |
| alpha | 0.013 | 0.016 | 0.019 | 0.022 | 0.02 | 0.007 |
| | 1.546 | 2.033 | 2.438 | 2.492 | 2.237 | 2.902 |
| 2 | 0.014 | 0.015 | 0.017 | 0.018 | 0.019 | 0.005 |
| | 1.702 | 1.895 | 2.228 | 2.604 | 2.567 | 1.699 |
| alpha | 0.013 | 0.014 | 0.017 | 0.018 | 0.018 | 0.004 |
| | 1.517 | 1.709 | 2.014 | 2.326 | 2.36 | 1.449 |
| 3 | 0.008 | 0.011 | 0.012 | 0.016 | 0.018 | 0.01 |
| | 1.091 | 1.373 | 1.712 | 2.246 | 2.624 | 3.775 |
| alpha | 0.008 | 0.01 | 0.012 | 0.015 | 0.017 | 0.009 |
| | 0.958 | 1.19 | 1.461 | 1.997 | 2.162 | 3.132 |
| 4 | 0.008 | 0.011 | 0.01 | 0.014 | 0.016 | 0.008 |
| | 1.002 | 1.442 | 1.468 | 2.109 | 2.305 | 2.41 |
| alpha | 0.009 | 0.01 | 0.009 | 0.015 | 0.015 | 0.006 |
| | 0.913 | 1.339 | 1.162 | 1.937 | 1.833 | 2.256 |
| 5 | 0.004 | 0.009 | 0.008 | 0.01 | 0.016 | 0.012 |
| | 0.565 | 1.271 | 1.257 | 1.613 | 2.417 | 3.234 |
| alpha | 0.004 | 0.008 | 0.009 | 0.009 | 0.015 | 0.011 |
| | 0.444 | 0.909 | 1.106 | 1.215 | 1.803 | 2.872 |
| Diff | -0.009 | -0.008 | -0.012 | -0.013 | -0.004 | 0.005 |
| | -2.446 | -2.151 | -3.025 | -3.231 | -0.917 | 1.502 |
| alpha | -0.008 | -0.008 | -0.01 | -0.012 | -0.005 | 0.004 |
| | -1.86 | -2.15 | -2.315 | -2.652 | -0.856 | 0.91 |
+-------+--------+--------+--------+--------+--------+-------+
==============================================================
# Dependent-sort Bivariate Analysis
bi_1_de = Bivariate(test_data_1, number=4)
bi_1_de.fit(conditional=True)
bi_1_de.print_summary()
================================================================================
+----------+-----------+-----------+-----------+-----------+-----------+-------+
| Group | ROE(TTM)1 | ROE(TTM)2 | ROE(TTM)3 | ROE(TTM)4 | ROE(TTM)5 | Diff |
+----------+-----------+-----------+-----------+-----------+-----------+-------+
| Msmvttl1 | 0.013 | 0.016 | 0.017 | 0.022 | 0.021 | 0.008 |
| | 1.64 | 1.96 | 2.155 | 2.927 | 2.753 | 3.698 |
| Msmvttl2 | 0.015 | 0.013 | 0.016 | 0.018 | 0.018 | 0.004 |
| | 1.766 | 1.699 | 2.074 | 2.483 | 2.57 | 1.215 |
| Msmvttl3 | 0.009 | 0.009 | 0.013 | 0.015 | 0.018 | 0.009 |
| | 1.123 | 1.188 | 1.827 | 2.13 | 2.591 | 3.573 |
| Msmvttl4 | 0.009 | 0.01 | 0.012 | 0.014 | 0.016 | 0.007 |
| | 1.181 | 1.41 | 1.645 | 2.174 | 2.327 | 2.27 |
| Msmvttl5 | 0.007 | 0.008 | 0.011 | 0.015 | 0.016 | 0.01 |
| | 0.945 | 1.245 | 1.728 | 2.323 | 2.456 | 2.956 |
| Diff | -0.007 | -0.008 | -0.006 | -0.007 | -0.005 | 0.002 |
| | -1.82 | -1.737 | -1.313 | -1.625 | -1.073 | 0.578 |
+----------+-----------+-----------+-----------+-----------+-----------+-------+
================================================================================
# Risk Adjustment
bi_1_de.factor_adjustment(risk_model)
bi_1_de.print_summary()
================================================================================
+----------+-----------+-----------+-----------+-----------+-----------+-------+
| Group | ROE(TTM)1 | ROE(TTM)2 | ROE(TTM)3 | ROE(TTM)4 | ROE(TTM)5 | Diff |
+----------+-----------+-----------+-----------+-----------+-----------+-------+
| Msmvttl1 | 0.013 | 0.016 | 0.017 | 0.022 | 0.021 | 0.008 |
| | 1.64 | 1.96 | 2.155 | 2.927 | 2.753 | 3.698 |
| alpha | 0.012 | 0.015 | 0.016 | 0.021 | 0.02 | 0.008 |
| | 1.496 | 1.808 | 2.008 | 2.632 | 2.33 | 3.948 |
| Msmvttl2 | 0.015 | 0.013 | 0.016 | 0.018 | 0.018 | 0.004 |
| | 1.766 | 1.699 | 2.074 | 2.483 | 2.57 | 1.215 |
| alpha | 0.014 | 0.013 | 0.015 | 0.018 | 0.018 | 0.004 |
| | 1.539 | 1.618 | 1.816 | 2.228 | 2.324 | 1.164 |
| Msmvttl3 | 0.009 | 0.009 | 0.013 | 0.015 | 0.018 | 0.009 |
| | 1.123 | 1.188 | 1.827 | 2.13 | 2.591 | 3.573 |
| alpha | 0.008 | 0.008 | 0.013 | 0.014 | 0.017 | 0.008 |
| | 0.995 | 1.031 | 1.537 | 1.904 | 2.15 | 3.126 |
| Msmvttl4 | 0.009 | 0.01 | 0.012 | 0.014 | 0.016 | 0.007 |
| | 1.181 | 1.41 | 1.645 | 2.174 | 2.327 | 2.27 |
| alpha | 0.009 | 0.009 | 0.011 | 0.015 | 0.015 | 0.006 |
| | 1.079 | 1.154 | 1.389 | 1.954 | 1.851 | 2.01 |
| Msmvttl5 | 0.007 | 0.008 | 0.011 | 0.015 | 0.016 | 0.01 |
| | 0.945 | 1.245 | 1.728 | 2.323 | 2.456 | 2.956 |
| alpha | 0.006 | 0.009 | 0.01 | 0.015 | 0.016 | 0.01 |
| | 0.723 | 1.063 | 1.249 | 1.677 | 1.9 | 2.797 |
| Diff | -0.007 | -0.008 | -0.006 | -0.007 | -0.005 | 0.002 |
| | -1.82 | -1.737 | -1.313 | -1.625 | -1.073 | 0.578 |
| alpha | -0.006 | -0.006 | -0.006 | -0.006 | -0.004 | 0.002 |
| | -1.624 | -1.401 | -1.333 | -1.174 | -0.782 | 0.528 |
+----------+-----------+-----------+-----------+-----------+-----------+-------+
The result from dataset #1 is interesting that in univariate analysis the differenced return is not significant since the t-value is below 2.3, while in bivariate analysis the differenced return in most part is significant since the t-value is greater than 2.3, suggesting that profitability factor provides excess return. The factor adjustment tends to weaken the portfolio excess return; while the dependent-sort bivariate tends to weaken the portfolio excess return.
# %% construct test_data for bivariate analysis
# dataset 2 : tail stocks & ROE Bivariate
from portfolio_analysis import Bivariate
import numpy as np
# select stocks whose size is among the up 30% stocks in each month and whose trading
# days are more than or equal to 10 days
test_data_2 = return_company[return_company['Ndaytrd']>=10]
test_data_2 = test_data_2[['emrwd', 'Msmvttl', 'ROE(TTM)', 'Date_merge']].dropna()
test_data_2 = test_data_2[(test_data_2['Date_merge'] >= '2004-01-01') & (test_data_2['Date_merge'] <= '2019-12-01')]
# Univariate analysis
uni_2 = Univariate(np.array(test_data_2[['emrwd', 'ROE(TTM)', 'Date_merge']]), number=9)
uni_2.summary_and_test()
uni_2.print_summary_by_time()
uni_2.print_summary()
====================================================================================================
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+
| Group | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Diff |
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+
| Average | 0.017 | 0.016 | 0.016 | 0.017 | 0.017 | 0.016 | 0.017 | 0.017 | 0.017 | 0.017 | 0.0 |
| T-Test | 2.132 | 2.032 | 2.037 | 2.2 | 2.298 | 2.293 | 2.392 | 2.549 | 2.586 | 2.572 | 0.019 |
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+
====================================================================================================
# Independent-sort Bivariate Analysis
bi_2 = Bivariate(np.array(test_data_2), number=4)
bi_2.average_by_time()
bi_2.summary_and_test()
bi_2.print_summary_by_time()
bi_2.print_summary()
================================================================
+-------+--------+--------+--------+--------+--------+--------+
| Group | 1 | 2 | 3 | 4 | 5 | Diff |
+-------+--------+--------+--------+--------+--------+--------+
| 1 | 0.025 | 0.026 | 0.026 | 0.028 | 0.024 | -0.001 |
| | 3.043 | 3.195 | 3.306 | 3.489 | 2.874 | -0.434 |
| 2 | 0.015 | 0.018 | 0.019 | 0.023 | 0.021 | 0.006 |
| | 1.833 | 2.238 | 2.488 | 3.105 | 2.701 | 2.495 |
| 3 | 0.013 | 0.011 | 0.016 | 0.017 | 0.019 | 0.006 |
| | 1.626 | 1.466 | 2.135 | 2.38 | 2.65 | 2.073 |
| 4 | 0.009 | 0.011 | 0.012 | 0.015 | 0.016 | 0.008 |
| | 1.086 | 1.359 | 1.656 | 2.101 | 2.394 | 2.546 |
| 5 | 0.006 | 0.008 | 0.009 | 0.01 | 0.015 | 0.01 |
| | 0.748 | 1.091 | 1.321 | 1.638 | 2.377 | 2.831 |
| Diff | -0.019 | -0.018 | -0.017 | -0.018 | -0.009 | 0.011 |
| | -4.676 | -4.202 | -3.963 | -3.927 | -1.68 | 2.951 |
+-------+--------+--------+--------+--------+--------+--------+
================================================================
# Risk adjustment
risk_model = risk_premium[['MKT', 'SMB', 'HML']]
risk_model = risk_model['2004':'2019']
bi_2.factor_adjustment(risk_model)
bi_2.print_summary()
===============================================================
+-------+--------+--------+--------+--------+--------+--------+
| Group | 1 | 2 | 3 | 4 | 5 | Diff |
+-------+--------+--------+--------+--------+--------+--------+
| 1 | 0.025 | 0.026 | 0.026 | 0.028 | 0.024 | -0.001 |
| | 3.043 | 3.195 | 3.306 | 3.489 | 2.874 | -0.434 |
| alpha | 0.023 | 0.024 | 0.025 | 0.026 | 0.022 | -0.002 |
| | 2.593 | 2.772 | 2.93 | 2.984 | 2.345 | -0.956 |
| 2 | 0.015 | 0.018 | 0.019 | 0.023 | 0.021 | 0.006 |
| | 1.833 | 2.238 | 2.488 | 3.105 | 2.701 | 2.495 |
| alpha | 0.014 | 0.017 | 0.018 | 0.022 | 0.02 | 0.006 |
| | 1.678 | 2.1 | 2.214 | 2.738 | 2.328 | 3.018 |
| 3 | 0.013 | 0.011 | 0.016 | 0.017 | 0.019 | 0.006 |
| | 1.626 | 1.466 | 2.135 | 2.38 | 2.65 | 2.073 |
| alpha | 0.012 | 0.011 | 0.016 | 0.017 | 0.018 | 0.005 |
| | 1.409 | 1.372 | 1.886 | 2.153 | 2.315 | 1.971 |
| 4 | 0.009 | 0.011 | 0.012 | 0.015 | 0.016 | 0.008 |
| | 1.086 | 1.359 | 1.656 | 2.101 | 2.394 | 2.546 |
| alpha | 0.008 | 0.01 | 0.011 | 0.014 | 0.016 | 0.007 |
| | 0.96 | 1.256 | 1.36 | 1.874 | 2.001 | 2.724 |
| 5 | 0.006 | 0.008 | 0.009 | 0.01 | 0.015 | 0.01 |
| | 0.748 | 1.091 | 1.321 | 1.638 | 2.377 | 2.831 |
| alpha | 0.006 | 0.008 | 0.009 | 0.011 | 0.015 | 0.009 |
| | 0.664 | 0.894 | 1.037 | 1.338 | 1.788 | 2.208 |
| Diff | -0.019 | -0.018 | -0.017 | -0.018 | -0.009 | 0.011 |
| | -4.676 | -4.202 | -3.963 | -3.927 | -1.68 | 2.951 |
| alpha | -0.017 | -0.016 | -0.016 | -0.016 | -0.007 | 0.011 |
| | -3.328 | -2.902 | -2.865 | -3.026 | -1.07 | 3.015 |
+-------+--------+--------+--------+--------+--------+--------+
===============================================================
# Dependent-sort Bivariate Analysis
bi_2_de = Bivariate(test_data_2, number=4)
bi_2_de.fit(conditional=True)
bi_2_de.print_summary()
================================================================================
+----------+-----------+-----------+-----------+-----------+-----------+-------+
| Group | ROE(TTM)1 | ROE(TTM)2 | ROE(TTM)3 | ROE(TTM)4 | ROE(TTM)5 | Diff |
+----------+-----------+-----------+-----------+-----------+-----------+-------+
| Msmvttl1 | 0.025 | 0.025 | 0.026 | 0.026 | 0.027 | 0.002 |
| | 2.985 | 3.104 | 3.202 | 3.343 | 3.293 | 0.789 |
| Msmvttl2 | 0.015 | 0.017 | 0.019 | 0.022 | 0.021 | 0.006 |
| | 1.848 | 2.086 | 2.381 | 2.846 | 2.805 | 3.2 |
| Msmvttl3 | 0.013 | 0.011 | 0.015 | 0.017 | 0.019 | 0.006 |
| | 1.61 | 1.48 | 1.981 | 2.366 | 2.628 | 2.01 |
| Msmvttl4 | 0.009 | 0.011 | 0.013 | 0.016 | 0.016 | 0.007 |
| | 1.158 | 1.433 | 1.824 | 2.249 | 2.4 | 2.495 |
| Msmvttl5 | 0.007 | 0.009 | 0.011 | 0.014 | 0.017 | 0.01 |
| | 1.014 | 1.267 | 1.783 | 2.22 | 2.512 | 3.116 |
| Diff | -0.018 | -0.017 | -0.014 | -0.012 | -0.01 | 0.008 |
| | -4.476 | -3.908 | -3.107 | -2.627 | -1.928 | 2.589 |
+----------+-----------+-----------+-----------+-----------+-----------+-------+
================================================================================
# Risk Adjustment
bi_2_de.factor_adjustment(risk_model)
bi_2_de.print_summary()
================================================================================
+----------+-----------+-----------+-----------+-----------+-----------+-------+
| Group | ROE(TTM)1 | ROE(TTM)2 | ROE(TTM)3 | ROE(TTM)4 | ROE(TTM)5 | Diff |
+----------+-----------+-----------+-----------+-----------+-----------+-------+
| Msmvttl1 | 0.025 | 0.025 | 0.026 | 0.026 | 0.027 | 0.002 |
| | 2.985 | 3.104 | 3.202 | 3.343 | 3.293 | 0.789 |
| alpha | 0.023 | 0.024 | 0.024 | 0.025 | 0.025 | 0.002 |
| | 2.543 | 2.662 | 2.829 | 2.943 | 2.768 | 0.991 |
| Msmvttl2 | 0.015 | 0.017 | 0.019 | 0.022 | 0.021 | 0.006 |
| | 1.848 | 2.086 | 2.381 | 2.846 | 2.805 | 3.2 |
| alpha | 0.014 | 0.016 | 0.018 | 0.02 | 0.02 | 0.006 |
| | 1.697 | 1.94 | 2.157 | 2.556 | 2.448 | 3.445 |
| Msmvttl3 | 0.013 | 0.011 | 0.015 | 0.017 | 0.019 | 0.006 |
| | 1.61 | 1.48 | 1.981 | 2.366 | 2.628 | 2.01 |
| alpha | 0.012 | 0.011 | 0.015 | 0.017 | 0.018 | 0.005 |
| | 1.386 | 1.41 | 1.74 | 2.145 | 2.316 | 2.062 |
| Msmvttl4 | 0.009 | 0.011 | 0.013 | 0.016 | 0.016 | 0.007 |
| | 1.158 | 1.433 | 1.824 | 2.249 | 2.4 | 2.495 |
| alpha | 0.009 | 0.01 | 0.013 | 0.015 | 0.016 | 0.006 |
| | 1.06 | 1.204 | 1.553 | 2.017 | 1.969 | 2.489 |
| Msmvttl5 | 0.007 | 0.009 | 0.011 | 0.014 | 0.017 | 0.01 |
| | 1.014 | 1.267 | 1.783 | 2.22 | 2.512 | 3.116 |
| alpha | 0.007 | 0.008 | 0.011 | 0.014 | 0.016 | 0.009 |
| | 0.847 | 1.03 | 1.345 | 1.644 | 1.942 | 2.518 |
| Diff | -0.018 | -0.017 | -0.014 | -0.012 | -0.01 | 0.008 |
| | -4.476 | -3.908 | -3.107 | -2.627 | -1.928 | 2.589 |
| alpha | -0.015 | -0.016 | -0.013 | -0.011 | -0.009 | 0.007 |
| | -3.209 | -3.128 | -2.502 | -1.789 | -1.311 | 2.075 |
+----------+-----------+-----------+-----------+-----------+-----------+-------+
The result from dataset #2 is interesting that in univariate analysis the differenced return is not significant since the t-value is below 2.3, while in bivariate analysis the differenced return in most part is significant since the t-value is greater than 2.3, suggesting that profitability factor provides excess return. The factor adjustment tends to weaken the portfolio excess return; while the dependent-sort bivariate tends to weaken the portfolio excess return.
Investment Factor
The investment factor gradually becomes popular since the introduction by Fama and French (2015). It is also included in the HXZ's model (2015) and Zhang (2017) expands it to ICAPM. Before its popularity, Titman et al. (2014) is among the early research of the factor, who use abnormal capital investment as proxy variable. However, in subsequent literature, most research uses asset growth rate as proxy variable, including Fama and French (2015) and Hou et al. (2015). In market of developed countries, investment factor is negatively correlated with future return, while in most developing country, the relation is much more tender. In China market, there exists no significant investment effect by most literatures (Guo et al., 2017; Qiao, 2019; Liu et al., 2019).
In this demo, annual asset growth rate is used as the proxy variable for profitability factor, which is calculated from the financial data and derivative ratios. The dataset starts from Jan, 2004 and is collected from CSMAR dataset. WARNING: Do Not use dataset in this demo for any commercial purpose.
# %% import package
from numpy import dtype
import pandas as pd
import sys, os
sys.path.append(os.path.abspath(".."))
# %% import data
# Monthly return of stocks in China security market
month_return = pd.read_hdf('.\data\month_return.h5', key='month_return')
company_data = pd.read_hdf('.\data\last_filter_pe.h5', key='data')
The data needs some preprocessing.
# %% preprocessing data
# forward the monthly return for each stock
# emrwd is the return including dividend
month_return['emrwd'] = month_return.groupby(['Stkcd'])['Mretwd'].shift(-1)
# emrnd is the return including no dividend
month_return['emrnd'] = month_return.groupby(['Stkcd'])['Mretnd'].shift(-1)
# select the A share stock
month_return = month_return[month_return['Markettype'].isin([1, 4, 16])]
# % distinguish the stocks whose size is among the up 30% stocks in each month
def percentile(stocks) :
return stocks >= stocks.quantile(q=.3)
month_return['cap'] = month_return.groupby(['Trdmnt'])['Msmvttl'].apply(percentile)
Annual asset growth rate is used as the proxy variable for profitability factor, which is calculated from the financial data and derivative ratios.
# %% calculate the total asset
# asset = debt + equity
# debt = company_value - market_value
# equity = market_value / PB
company_data['debt'] = company_data['EV1'] - company_data['MarketValue']
company_data['equity'] = company_data['MarketValue']/company_data['PBV1A']
company_data['asset'] = company_data['debt'] + company_data['equity']
# asset growth rate
company_data['asset_growth_rate'] = company_data['asset'].groupby(['Symbol']).diff(12)/company_data['asset']
Continue data preprocessing.
# %% prepare merge data
from pandas.tseries.offsets import *
month_return['Stkcd_merge'] = month_return['Stkcd'].astype(dtype='string')
month_return['Date_merge'] = pd.to_datetime(month_return['Trdmnt'])
#month_return['Yearmonth'] = month_return['Date_merge'].map(lambda x : 1000*x.year + x.month)
#month_return['Date_merge'] += MonthEnd()
company_data['Stkcd_merge'] = company_data['Symbol'].dropna().astype(dtype='int').astype(dtype='string')
company_data['Date_merge'] = pd.to_datetime(company_data['TradingDate'])
#company_data['Yearmonth'] = company_data['Date_merge'].map(lambda x : 1000*x.year + x.month)
company_data['Date_merge'] += MonthBegin()
# %% dataset starts from '2000-01'
company_data = company_data[company_data['Date_merge'] >= '2000-01']
month_return = month_return[month_return['Date_merge'] >= '2000-01']
return_company = pd.merge(company_data, month_return, on=['Stkcd_merge', 'Date_merge'])
Two datasets are constituted. One includes tail 30% stock, while one includes not. Univariate analysis and Bivariate analysis are attached.
# %% construct test_data for bivariate analysis
# dataset 1 : no tail stocks & ROE Bivariate
from portfolio_analysis import Bivariate, Univariate
import numpy as np
# select stocks whose size is among the up 30% stocks in each month and whose trading
# days are more than or equal to 10 days
test_data_1 = return_company[(return_company['cap']==True) & (return_company['Ndaytrd']>=10)]
test_data_1 = test_data_1[['emrwd', 'Msmvttl', 'asset_growth_rate', 'Date_merge']].dropna()
test_data_1 = test_data_1[(test_data_1['Date_merge'] >= '2004-01-01') & (test_data_1['Date_merge'] <= '2019-12-01')]
# Univariate analysis
uni_1 = Univariate(np.array(test_data_1[['emrwd', 'asset_growth_rate', 'Date_merge']]), number=9)
uni_1.summary_and_test()
uni_1.print_summary_by_time()
uni_1.print_summary()
====================================================================================================
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+
| Group | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Diff |
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+
| Average | 0.011 | 0.012 | 0.013 | 0.013 | 0.015 | 0.014 | 0.013 | 0.015 | 0.015 | 0.016 | 0.005 |
| T-Test | 1.393 | 1.655 | 1.783 | 1.879 | 2.054 | 1.985 | 1.955 | 2.162 | 2.064 | 2.152 | 1.907 |
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+
====================================================================================================
# Bivariate analysis
bi_1 = Bivariate(np.array(test_data_1), number=4)
bi_1.average_by_time()
bi_1.summary_and_test()
bi_1.print_summary_by_time()
bi_1.print_summary()
==============================================================
+-------+--------+--------+--------+--------+--------+-------+
| Group | 1 | 2 | 3 | 4 | 5 | Diff |
+-------+--------+--------+--------+--------+--------+-------+
| 1 | 0.015 | 0.017 | 0.018 | 0.018 | 0.02 | 0.005 |
| | 1.848 | 2.119 | 2.336 | 2.404 | 2.482 | 1.985 |
| 2 | 0.012 | 0.014 | 0.017 | 0.015 | 0.019 | 0.007 |
| | 1.509 | 1.784 | 2.301 | 1.984 | 2.434 | 2.8 |
| 3 | 0.01 | 0.012 | 0.015 | 0.014 | 0.014 | 0.004 |
| | 1.314 | 1.695 | 2.026 | 1.884 | 1.912 | 1.862 |
| 4 | 0.009 | 0.01 | 0.011 | 0.013 | 0.015 | 0.006 |
| | 1.194 | 1.507 | 1.579 | 1.831 | 2.009 | 2.45 |
| 5 | 0.007 | 0.01 | 0.011 | 0.014 | 0.012 | 0.005 |
| | 1.03 | 1.517 | 1.685 | 2.106 | 1.749 | 1.7 |
| Diff | -0.008 | -0.007 | -0.008 | -0.005 | -0.007 | 0.0 |
| | -1.902 | -1.646 | -1.897 | -1.213 | -1.771 | 0.088 |
+-------+--------+--------+--------+--------+--------+-------+
==============================================================
# Factor adjustment
# Fama French 3 factors model adjust
# risk factor model
risk_model = risk_factor['2004':'2019'][['MKT', 'SMB','HML']]
bi_1.factor_adjustment(risk_model)
bi_1.print_summary()
=============================================================================================================================
+----------+--------------------+--------------------+--------------------+--------------------+--------------------+-------+
| Group | asset_growth_rate1 | asset_growth_rate2 | asset_growth_rate3 | asset_growth_rate4 | asset_growth_rate5 | Diff |
+----------+--------------------+--------------------+--------------------+--------------------+--------------------+-------+
| Msmvttl1 | 0.015 | 0.017 | 0.018 | 0.018 | 0.02 | 0.005 |
| | 1.848 | 2.119 | 2.336 | 2.404 | 2.482 | 1.985 |
| alpha | 0.014 | 0.016 | 0.017 | 0.017 | 0.019 | 0.005 |
| | 1.655 | 1.951 | 2.203 | 2.159 | 2.157 | 1.959 |
| Msmvttl2 | 0.012 | 0.014 | 0.017 | 0.015 | 0.019 | 0.007 |
| | 1.509 | 1.784 | 2.301 | 1.984 | 2.434 | 2.8 |
| alpha | 0.011 | 0.014 | 0.017 | 0.015 | 0.017 | 0.006 |
| | 1.309 | 1.671 | 2.117 | 1.902 | 1.996 | 3.213 |
| Msmvttl3 | 0.01 | 0.012 | 0.015 | 0.014 | 0.014 | 0.004 |
| | 1.314 | 1.695 | 2.026 | 1.884 | 1.912 | 1.862 |
| alpha | 0.009 | 0.011 | 0.015 | 0.013 | 0.013 | 0.004 |
| | 1.134 | 1.451 | 1.814 | 1.713 | 1.54 | 1.349 |
| Msmvttl4 | 0.009 | 0.01 | 0.011 | 0.013 | 0.015 | 0.006 |
| | 1.194 | 1.507 | 1.579 | 1.831 | 2.009 | 2.45 |
| alpha | 0.009 | 0.01 | 0.01 | 0.012 | 0.014 | 0.005 |
| | 1.097 | 1.37 | 1.327 | 1.512 | 1.674 | 3.089 |
| Msmvttl5 | 0.007 | 0.01 | 0.011 | 0.014 | 0.012 | 0.005 |
| | 1.03 | 1.517 | 1.685 | 2.106 | 1.749 | 1.7 |
| alpha | 0.007 | 0.009 | 0.01 | 0.013 | 0.012 | 0.005 |
| | 0.871 | 1.241 | 1.281 | 1.599 | 1.382 | 1.714 |
| Diff | -0.008 | -0.007 | -0.008 | -0.005 | -0.007 | 0.0 |
| | -1.902 | -1.646 | -1.897 | -1.213 | -1.771 | 0.088 |
| alpha | -0.007 | -0.006 | -0.007 | -0.004 | -0.007 | 0.0 |
| | -1.97 | -1.449 | -1.592 | -0.834 | -1.414 | 0.12 |
+----------+--------------------+--------------------+--------------------+--------------------+--------------------+-------+
=============================================================================================================================
# Dependent-sort Bivariate Analysis
bi_1_de = Bivariate(test_data_1, number=4)
bi_1_de.fit(conditional=True)
bi_1_de.print_summary()
==============================================================================================================================
+----------+--------------------+--------------------+--------------------+--------------------+--------------------+--------+
| Group | asset_growth_rate1 | asset_growth_rate2 | asset_growth_rate3 | asset_growth_rate4 | asset_growth_rate5 | Diff |
+----------+--------------------+--------------------+--------------------+--------------------+--------------------+--------+
| Msmvttl1 | 0.014 | 0.017 | 0.017 | 0.019 | 0.018 | 0.005 |
| | 1.727 | 2.106 | 2.18 | 2.503 | 2.352 | 2.072 |
| Msmvttl2 | 0.012 | 0.014 | 0.016 | 0.015 | 0.019 | 0.007 |
| | 1.505 | 1.765 | 2.081 | 1.946 | 2.464 | 2.831 |
| Msmvttl3 | 0.01 | 0.012 | 0.014 | 0.014 | 0.014 | 0.004 |
| | 1.371 | 1.637 | 1.974 | 1.92 | 1.918 | 1.7 |
| Msmvttl4 | 0.009 | 0.011 | 0.011 | 0.013 | 0.015 | 0.007 |
| | 1.249 | 1.533 | 1.602 | 1.821 | 2.054 | 2.6 |
| Msmvttl5 | 0.009 | 0.01 | 0.011 | 0.014 | 0.013 | 0.004 |
| | 1.29 | 1.625 | 1.715 | 2.176 | 1.794 | 1.425 |
| Diff | -0.005 | -0.007 | -0.006 | -0.005 | -0.006 | -0.001 |
| | -1.355 | -1.527 | -1.47 | -1.196 | -1.365 | -0.219 |
+----------+--------------------+--------------------+--------------------+--------------------+--------------------+--------+
==============================================================================================================================
# RIsk Adjustment
bi_1_de.factor_adjustment(risk_model)
bi_1_de.print_summary()
==============================================================================================================================
+----------+--------------------+--------------------+--------------------+--------------------+--------------------+--------+
| Group | asset_growth_rate1 | asset_growth_rate2 | asset_growth_rate3 | asset_growth_rate4 | asset_growth_rate5 | Diff |
+----------+--------------------+--------------------+--------------------+--------------------+--------------------+--------+
| Msmvttl1 | 0.014 | 0.017 | 0.017 | 0.019 | 0.018 | 0.005 |
| | 1.727 | 2.106 | 2.18 | 2.503 | 2.352 | 2.072 |
| alpha | 0.013 | 0.016 | 0.017 | 0.018 | 0.017 | 0.004 |
| | 1.516 | 1.901 | 2.062 | 2.319 | 2.037 | 1.876 |
| Msmvttl2 | 0.012 | 0.014 | 0.016 | 0.015 | 0.019 | 0.007 |
| | 1.505 | 1.765 | 2.081 | 1.946 | 2.464 | 2.831 |
| alpha | 0.012 | 0.013 | 0.016 | 0.015 | 0.018 | 0.006 |
| | 1.306 | 1.596 | 1.969 | 1.871 | 2.09 | 2.959 |
| Msmvttl3 | 0.01 | 0.012 | 0.014 | 0.014 | 0.014 | 0.004 |
| | 1.371 | 1.637 | 1.974 | 1.92 | 1.918 | 1.7 |
| alpha | 0.01 | 0.011 | 0.014 | 0.013 | 0.013 | 0.004 |
| | 1.186 | 1.368 | 1.81 | 1.69 | 1.573 | 1.293 |
| Msmvttl4 | 0.009 | 0.011 | 0.011 | 0.013 | 0.015 | 0.007 |
| | 1.249 | 1.533 | 1.602 | 1.821 | 2.054 | 2.6 |
| alpha | 0.009 | 0.01 | 0.01 | 0.013 | 0.015 | 0.006 |
| | 1.124 | 1.392 | 1.274 | 1.544 | 1.721 | 3.201 |
| Msmvttl5 | 0.009 | 0.01 | 0.011 | 0.014 | 0.013 | 0.004 |
| | 1.29 | 1.625 | 1.715 | 2.176 | 1.794 | 1.425 |
| alpha | 0.008 | 0.01 | 0.01 | 0.014 | 0.013 | 0.005 |
| | 1.051 | 1.276 | 1.211 | 1.73 | 1.445 | 1.67 |
| Diff | -0.005 | -0.007 | -0.006 | -0.005 | -0.006 | -0.001 |
| | -1.355 | -1.527 | -1.47 | -1.196 | -1.365 | -0.219 |
| alpha | -0.005 | -0.006 | -0.007 | -0.004 | -0.005 | 0.0 |
| | -1.266 | -1.484 | -1.251 | -0.802 | -0.968 | 0.058 |
+----------+--------------------+--------------------+--------------------+--------------------+--------------------+--------+
The result from dataset #1 is consistent with literatures that in univariate analysis the differenced return is not significant since the t-value is below 2.3, while in bivariate analysis the differenced return in most part is insignificant since the t-value is less than 2.3, suggesting that investment factor provides no excess return. The factor adjustment tends to strengthen the portfolio excess return; while the dependent-sort bivariate tends to strengthen the portfolio excess return.
# %% construct test_data for bivariate analysis
# dataset 2 : tail stocks & ROE Bivariate
from portfolio_analysis import Bivariate, Univariate
import numpy as np
# select stocks whose size is among the up 30% stocks in each month and whose trading
# days are more than or equal to 10 days
test_data_2 = return_company[return_company['Ndaytrd']>=10]
test_data_2 = test_data_2[['emrwd', 'Msmvttl', 'asset_growth_rate', 'Date_merge']].dropna()
test_data_2 = test_data_2[(test_data_2['Date_merge'] >= '2004-01-01') & (test_data_2['Date_merge'] <= '2019-12-01')]
# Univariate analysis
uni_2 = Univariate(np.array(test_data_2[['emrwd', 'asset_growth_rate', 'Date_merge']]), number=9)
uni_2.summary_and_test()
uni_2.print_summary_by_time()
uni_2.print_summary()
====================================================================================================
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+
| Group | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Diff |
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+
| Average | 0.017 | 0.017 | 0.017 | 0.017 | 0.017 | 0.017 | 0.016 | 0.017 | 0.017 | 0.018 | 0.001 |
| T-Test | 2.052 | 2.204 | 2.301 | 2.303 | 2.323 | 2.33 | 2.249 | 2.392 | 2.283 | 2.411 | 0.313 |
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+
====================================================================================================
# Bivariate analysis
bi_2 = Bivariate(np.array(test_data_2), number=4)
bi_2.average_by_time()
bi_2.summary_and_test()
bi_2.print_summary_by_time()
bi_2.print_summary()
===============================================================
+-------+--------+--------+--------+--------+--------+-------+
| Group | 1 | 2 | 3 | 4 | 5 | Diff |
+-------+--------+--------+--------+--------+--------+-------+
| 1 | 0.027 | 0.026 | 0.027 | 0.027 | 0.027 | 0.0 |
| | 3.113 | 3.25 | 3.257 | 3.312 | 3.372 | 0.079 |
| 2 | 0.015 | 0.019 | 0.02 | 0.021 | 0.021 | 0.006 |
| | 1.885 | 2.331 | 2.482 | 2.706 | 2.674 | 2.551 |
| 3 | 0.012 | 0.014 | 0.017 | 0.015 | 0.017 | 0.005 |
| | 1.561 | 1.788 | 2.198 | 2.067 | 2.286 | 2.264 |
| 4 | 0.009 | 0.01 | 0.013 | 0.013 | 0.015 | 0.005 |
| | 1.271 | 1.475 | 1.745 | 1.888 | 1.999 | 2.397 |
| 5 | 0.007 | 0.011 | 0.01 | 0.012 | 0.013 | 0.006 |
| | 0.987 | 1.729 | 1.582 | 1.882 | 1.83 | 2.2 |
| Diff | -0.02 | -0.015 | -0.017 | -0.014 | -0.014 | 0.006 |
| | -4.431 | -3.522 | -3.695 | -3.205 | -3.197 | 1.813 |
+-------+--------+--------+--------+--------+--------+-------+
===============================================================
# Factor adjustment
# Fama French 3 factors model adjust
# risk factor model
bi_2.factor_adjustment(risk_model)
bi_2.print_summary()
===============================================================
+-------+--------+--------+--------+--------+--------+--------+
| Group | 1 | 2 | 3 | 4 | 5 | Diff |
+-------+--------+--------+--------+--------+--------+--------+
| 1 | 0.027 | 0.026 | 0.027 | 0.027 | 0.027 | 0.0 |
| | 3.113 | 3.25 | 3.257 | 3.312 | 3.372 | 0.079 |
| alpha | 0.025 | 0.024 | 0.025 | 0.026 | 0.025 | -0.0 |
| | 2.716 | 2.713 | 2.785 | 2.901 | 2.894 | -0.047 |
| 2 | 0.015 | 0.019 | 0.02 | 0.021 | 0.021 | 0.006 |
| | 1.885 | 2.331 | 2.482 | 2.706 | 2.674 | 2.551 |
| alpha | 0.014 | 0.018 | 0.019 | 0.02 | 0.02 | 0.006 |
| | 1.649 | 2.113 | 2.268 | 2.462 | 2.335 | 3.0 |
| 3 | 0.012 | 0.014 | 0.017 | 0.015 | 0.017 | 0.005 |
| | 1.561 | 1.788 | 2.198 | 2.067 | 2.286 | 2.264 |
| alpha | 0.012 | 0.013 | 0.017 | 0.015 | 0.016 | 0.004 |
| | 1.365 | 1.577 | 2.051 | 1.98 | 1.968 | 1.962 |
| 4 | 0.009 | 0.01 | 0.013 | 0.013 | 0.015 | 0.005 |
| | 1.271 | 1.475 | 1.745 | 1.888 | 1.999 | 2.397 |
| alpha | 0.009 | 0.01 | 0.012 | 0.013 | 0.014 | 0.005 |
| | 1.138 | 1.281 | 1.572 | 1.66 | 1.612 | 2.137 |
| 5 | 0.007 | 0.011 | 0.01 | 0.012 | 0.013 | 0.006 |
| | 0.987 | 1.729 | 1.582 | 1.882 | 1.83 | 2.2 |
| alpha | 0.007 | 0.011 | 0.01 | 0.012 | 0.012 | 0.005 |
| | 0.879 | 1.445 | 1.227 | 1.478 | 1.453 | 2.232 |
| Diff | -0.02 | -0.015 | -0.017 | -0.014 | -0.014 | 0.006 |
| | -4.431 | -3.522 | -3.695 | -3.205 | -3.197 | 1.813 |
| alpha | -0.018 | -0.013 | -0.015 | -0.014 | -0.013 | 0.005 |
| | -3.702 | -2.572 | -2.825 | -2.332 | -2.022 | 1.56 |
+-------+--------+--------+--------+--------+--------+--------+
===============================================================
# Dependent-sort Bivariate Analysis
bi_2_de = Bivariate(test_data_2, number=4)
bi_2_de.fit(conditional=True)
bi_2_de.print_summary()
=============================================================================================================================
+----------+--------------------+--------------------+--------------------+--------------------+--------------------+-------+
| Group | asset_growth_rate1 | asset_growth_rate2 | asset_growth_rate3 | asset_growth_rate4 | asset_growth_rate5 | Diff |
+----------+--------------------+--------------------+--------------------+--------------------+--------------------+-------+
| Msmvttl1 | 0.027 | 0.027 | 0.027 | 0.026 | 0.027 | 0.001 |
| | 3.004 | 3.188 | 3.354 | 3.199 | 3.411 | 0.223 |
| Msmvttl2 | 0.015 | 0.018 | 0.019 | 0.021 | 0.02 | 0.005 |
| | 1.89 | 2.234 | 2.348 | 2.754 | 2.579 | 2.327 |
| Msmvttl3 | 0.012 | 0.014 | 0.017 | 0.015 | 0.018 | 0.005 |
| | 1.591 | 1.815 | 2.19 | 1.966 | 2.326 | 2.319 |
| Msmvttl4 | 0.009 | 0.011 | 0.013 | 0.014 | 0.015 | 0.005 |
| | 1.279 | 1.562 | 1.808 | 1.948 | 1.965 | 2.383 |
| Msmvttl5 | 0.009 | 0.01 | 0.011 | 0.014 | 0.013 | 0.004 |
| | 1.398 | 1.569 | 1.678 | 2.028 | 1.817 | 1.353 |
| Diff | -0.017 | -0.017 | -0.017 | -0.013 | -0.014 | 0.003 |
| | -3.627 | -3.415 | -3.638 | -2.696 | -3.202 | 0.86 |
+----------+--------------------+--------------------+--------------------+--------------------+--------------------+-------+
=============================================================================================================================
# Risk Adjustment
bi_2_de.factor_adjustment(risk_model)
bi_2_de.print_summary()
=============================================================================================================================
+----------+--------------------+--------------------+--------------------+--------------------+--------------------+-------+
| Group | asset_growth_rate1 | asset_growth_rate2 | asset_growth_rate3 | asset_growth_rate4 | asset_growth_rate5 | Diff |
+----------+--------------------+--------------------+--------------------+--------------------+--------------------+-------+
| Msmvttl1 | 0.027 | 0.027 | 0.027 | 0.026 | 0.027 | 0.001 |
| | 3.004 | 3.188 | 3.354 | 3.199 | 3.411 | 0.223 |
| alpha | 0.025 | 0.025 | 0.025 | 0.025 | 0.025 | 0.001 |
| | 2.644 | 2.72 | 2.858 | 2.768 | 2.914 | 0.261 |
| Msmvttl2 | 0.015 | 0.018 | 0.019 | 0.021 | 0.02 | 0.005 |
| | 1.89 | 2.234 | 2.348 | 2.754 | 2.579 | 2.327 |
| alpha | 0.014 | 0.017 | 0.018 | 0.02 | 0.019 | 0.005 |
| | 1.653 | 2.034 | 2.147 | 2.484 | 2.269 | 2.56 |
| Msmvttl3 | 0.012 | 0.014 | 0.017 | 0.015 | 0.018 | 0.005 |
| | 1.591 | 1.815 | 2.19 | 1.966 | 2.326 | 2.319 |
| alpha | 0.012 | 0.013 | 0.017 | 0.014 | 0.017 | 0.004 |
| | 1.398 | 1.611 | 2.054 | 1.895 | 2.006 | 1.941 |
| Msmvttl4 | 0.009 | 0.011 | 0.013 | 0.014 | 0.015 | 0.005 |
| | 1.279 | 1.562 | 1.808 | 1.948 | 1.965 | 2.383 |
| alpha | 0.009 | 0.01 | 0.012 | 0.013 | 0.014 | 0.005 |
| | 1.116 | 1.379 | 1.602 | 1.718 | 1.577 | 2.234 |
| Msmvttl5 | 0.009 | 0.01 | 0.011 | 0.014 | 0.013 | 0.004 |
| | 1.398 | 1.569 | 1.678 | 2.028 | 1.817 | 1.353 |
| alpha | 0.009 | 0.009 | 0.01 | 0.013 | 0.013 | 0.004 |
| | 1.169 | 1.217 | 1.222 | 1.636 | 1.488 | 1.545 |
| Diff | -0.017 | -0.017 | -0.017 | -0.013 | -0.014 | 0.003 |
| | -3.627 | -3.415 | -3.638 | -2.696 | -3.202 | 0.86 |
| alpha | -0.015 | -0.016 | -0.015 | -0.012 | -0.012 | 0.003 |
| | -3.292 | -2.822 | -2.637 | -1.908 | -2.144 | 0.985 |
+----------+--------------------+--------------------+--------------------+--------------------+--------------------+-------+
The result from dataset #2 is consistent with literatures that in univariate analysis the differenced return is not significant since the t-value is below 2.3, while in bivariate analysis the differenced return in most part is insignificant since the t-value is less than 2.3, suggesting that investment factor provides no excess return. The factor adjustment tends to strengthen the portfolio excess return; while the dependent-sort bivariate tends to strengthen the portfolio excess return.
Momentum Effect
The momentum factor starts from Jegadeesh and Titman (1993) and exists widely in global stock markets (Jegadeesh and Titman, 2001; Rouwenhorst, 1998, 1999; De Groot et al., 2012; Asness et al., 2013) as well as in other markets, like commodity market (Narayan et al., 2015) and bond market (Isreal et al., 2018). However, in China stock market, it is suggested that there exist no such effect (Liu and Lee, 2001; Li et al., 2010).
The momentum effect is quite simple that stocks perform well in past would continue good performance in the future and vice versa. The conventional proxy variable for momentum effect is total yield from past 12 month to past 1 month. Since there may exist short term reversal effect, the last month yield is excluded.
In this demo, the conventional proxy variable in preceding text is chosen. The dataset starts from Jan, 2000 and is collected from CSMAR dataset. WARNING: Do Not use dataset in this demo for any commercial purpose.
# %% import package
import pandas as pd
import sys, os
sys.path.append(os.path.abspath(".."))
# %% import data
# Monthly return of stocks in China security market
month_return = pd.read_hdf('.\data\month_return.h5', key='month_return')
#month_return = month_return.set_index(['Stkcd', 'Trdmnt'], drop=False)
Data need some preprocessing.
# %% preprocessing data
# forward the monthly return for each stock
# emrwd is the return including dividend
month_return['emrwd'] = month_return.groupby(['Stkcd'])['Mretwd'].shift(-1)
# emrnd is the return including no dividend
month_return['emrnd'] = month_return.groupby(['Stkcd'])['Mretnd'].shift(-1)
# select the A share stock
month_return = month_return[month_return['Markettype'].isin([1, 4, 16])]
# % distinguish the stocks whose size is among the up 30% stocks in each month
def percentile(stocks) :
return stocks >= stocks.quantile(q=.3)
month_return['cap'] = month_return.groupby(['Trdmnt'])['Msmvttl'].apply(percentile)
Construct momentum proxy variable.
# %% construct momentum variable
import numpy as np
month_return['rolling_12'] = np.array(month_return.groupby(['Stkcd'])['Mretwd'].rolling(12).sum())
month_return['momentum'] = month_return['rolling_12'] - month_return['Mretwd']
Attach some further data preprocessing.
# %% construct label
month_return['Stkcd_merge'] = month_return['Stkcd'].astype(dtype='string')
month_return['Date_merge'] = pd.to_datetime(month_return['Trdmnt'])
# data starts from 2000-01
return_company = month_return[month_return['Date_merge']>='2000-01']
Two datasets are constituted. One includes tail 30% stock, while one includes not. Univariate analysis and Bivariate analysis are attached.
# %% construct test_data for bivariate analysis
# dataset 1
from portfolio_analysis import Bivariate, Univariate
import numpy as np
# select stocks whose size is among the up 30% stocks in each month and whose trading
# days are more than or equal to 10 days
test_data_1 = return_company[(return_company['cap']==True) & (return_company['Ndaytrd']>=10)]
test_data_1 = test_data_1[['emrwd', 'Msmvttl', 'momentum', 'Date_merge']].dropna()
test_data_1 = test_data_1[(test_data_1['Date_merge'] >= '2000-01-01') & (test_data_1['Date_merge'] <= '2019-12-01')]
# Univariate analysis
uni_1 = Univariate(np.array(test_data_1[['emrwd', 'momentum', 'Date_merge']]), number=9)
uni_1.summary_and_test()
uni_1.print_summary_by_time()
uni_1.print_summary()
===================================================================================================
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+------+-------+
| Group | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Diff |
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+------+-------+
| Average | 0.008 | 0.01 | 0.01 | 0.012 | 0.011 | 0.011 | 0.011 | 0.012 | 0.011 | 0.01 | 0.002 |
| T-Test | 1.304 | 1.542 | 1.625 | 1.935 | 1.86 | 1.874 | 1.849 | 1.944 | 1.779 | 1.63 | 0.517 |
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+------+-------+
===================================================================================================
# Bivariate analysis
bi_1 = Bivariate(np.array(test_data_1), number=4)
bi_1.average_by_time()
bi_1.summary_and_test()
bi_1.print_summary_by_time()
bi_1.print_summary()
==============================================================
+-------+--------+--------+--------+--------+--------+-------+
| Group | 1 | 2 | 3 | 4 | 5 | Diff |
+-------+--------+--------+--------+--------+--------+-------+
| 1 | 0.012 | 0.015 | 0.014 | 0.015 | 0.013 | 0.001 |
| | 1.781 | 2.256 | 2.24 | 2.234 | 1.916 | 0.467 |
| 2 | 0.01 | 0.013 | 0.012 | 0.012 | 0.011 | 0.0 |
| | 1.599 | 2.074 | 1.873 | 1.836 | 1.613 | 0.14 |
| 3 | 0.009 | 0.009 | 0.009 | 0.011 | 0.01 | 0.001 |
| | 1.42 | 1.514 | 1.447 | 1.711 | 1.58 | 0.329 |
| 4 | 0.007 | 0.008 | 0.01 | 0.011 | 0.008 | 0.002 |
| | 1.064 | 1.401 | 1.735 | 1.831 | 1.378 | 0.492 |
| 5 | 0.006 | 0.008 | 0.009 | 0.008 | 0.009 | 0.003 |
| | 1.002 | 1.395 | 1.58 | 1.403 | 1.67 | 0.99 |
| Diff | -0.006 | -0.007 | -0.006 | -0.007 | -0.004 | 0.002 |
| | -1.875 | -2.071 | -1.829 | -1.895 | -1.016 | 0.584 |
+-------+--------+--------+--------+--------+--------+-------+
# Risk Adjustment
risk_model = risk_premium[['MKT', 'SMB', 'HML']]
risk_model = risk_model['2000':'2019']
bi_1.factor_adjustment(risk_model)
bi_1.print_summary()
===============================================================
+-------+--------+--------+--------+--------+--------+--------+
| Group | 1 | 2 | 3 | 4 | 5 | Diff |
+-------+--------+--------+--------+--------+--------+--------+
| 1 | 0.012 | 0.015 | 0.014 | 0.015 | 0.013 | 0.001 |
| | 1.781 | 2.256 | 2.24 | 2.234 | 1.916 | 0.467 |
| alpha | 0.012 | 0.014 | 0.013 | 0.014 | 0.013 | 0.002 |
| | 1.645 | 1.907 | 2.051 | 1.991 | 1.656 | 0.512 |
| 2 | 0.01 | 0.013 | 0.012 | 0.012 | 0.011 | 0.0 |
| | 1.599 | 2.074 | 1.873 | 1.836 | 1.613 | 0.14 |
| alpha | 0.01 | 0.013 | 0.012 | 0.011 | 0.01 | -0.0 |
| | 1.478 | 1.773 | 1.736 | 1.543 | 1.372 | -0.108 |
| 3 | 0.009 | 0.009 | 0.009 | 0.011 | 0.01 | 0.001 |
| | 1.42 | 1.514 | 1.447 | 1.711 | 1.58 | 0.329 |
| alpha | 0.009 | 0.008 | 0.008 | 0.01 | 0.01 | 0.001 |
| | 1.302 | 1.236 | 1.192 | 1.47 | 1.511 | 0.44 |
| 4 | 0.007 | 0.008 | 0.01 | 0.011 | 0.008 | 0.002 |
| | 1.064 | 1.401 | 1.735 | 1.831 | 1.378 | 0.492 |
| alpha | 0.006 | 0.008 | 0.01 | 0.011 | 0.009 | 0.003 |
| | 0.942 | 1.168 | 1.419 | 1.536 | 1.395 | 1.01 |
| 5 | 0.006 | 0.008 | 0.009 | 0.008 | 0.009 | 0.003 |
| | 1.002 | 1.395 | 1.58 | 1.403 | 1.67 | 0.99 |
| alpha | 0.005 | 0.007 | 0.009 | 0.008 | 0.01 | 0.005 |
| | 0.659 | 1.022 | 1.388 | 1.152 | 1.573 | 1.39 |
| Diff | -0.006 | -0.007 | -0.006 | -0.007 | -0.004 | 0.002 |
| | -1.875 | -2.071 | -1.829 | -1.895 | -1.016 | 0.584 |
| alpha | -0.007 | -0.006 | -0.004 | -0.007 | -0.003 | 0.004 |
| | -2.139 | -1.876 | -1.244 | -1.586 | -0.629 | 0.993 |
+-------+--------+--------+--------+--------+--------+--------+
# Dependent-sort Bivariate Analysis
bi_1_de = Bivariate(test_data_1, number=4)
bi_1_de.fit(conditional=True)
bi_1_de.print_summary()
================================================================================
+----------+-----------+-----------+-----------+-----------+-----------+-------+
| Group | momentum1 | momentum2 | momentum3 | momentum4 | momentum5 | Diff |
+----------+-----------+-----------+-----------+-----------+-----------+-------+
| Msmvttl1 | 0.012 | 0.014 | 0.013 | 0.015 | 0.014 | 0.002 |
| | 1.823 | 2.097 | 1.997 | 2.245 | 2.048 | 0.581 |
| Msmvttl2 | 0.01 | 0.014 | 0.012 | 0.011 | 0.011 | 0.001 |
| | 1.563 | 2.096 | 1.876 | 1.769 | 1.616 | 0.208 |
| Msmvttl3 | 0.009 | 0.009 | 0.009 | 0.01 | 0.01 | 0.002 |
| | 1.343 | 1.44 | 1.526 | 1.665 | 1.599 | 0.572 |
| Msmvttl4 | 0.007 | 0.009 | 0.009 | 0.011 | 0.008 | 0.001 |
| | 1.131 | 1.546 | 1.615 | 1.778 | 1.378 | 0.395 |
| Msmvttl5 | 0.007 | 0.009 | 0.009 | 0.009 | 0.011 | 0.004 |
| | 1.24 | 1.644 | 1.641 | 1.585 | 1.908 | 1.14 |
| Diff | -0.005 | -0.005 | -0.004 | -0.006 | -0.003 | 0.003 |
| | -1.621 | -1.379 | -1.197 | -1.606 | -0.675 | 0.769 |
+----------+-----------+-----------+-----------+-----------+-----------+-------+
# Risk Adjustment
bi_1_de.factor_adjustment(risk_model)
bi_1_de.print_summary()
================================================================================
+----------+-----------+-----------+-----------+-----------+-----------+-------+
| Group | momentum1 | momentum2 | momentum3 | momentum4 | momentum5 | Diff |
+----------+-----------+-----------+-----------+-----------+-----------+-------+
| Msmvttl1 | 0.012 | 0.014 | 0.013 | 0.015 | 0.014 | 0.002 |
| | 1.823 | 2.097 | 1.997 | 2.245 | 2.048 | 0.581 |
| alpha | 0.012 | 0.013 | 0.013 | 0.014 | 0.014 | 0.002 |
| | 1.686 | 1.796 | 1.819 | 1.969 | 1.841 | 0.591 |
| Msmvttl2 | 0.01 | 0.014 | 0.012 | 0.011 | 0.011 | 0.001 |
| | 1.563 | 2.096 | 1.876 | 1.769 | 1.616 | 0.208 |
| alpha | 0.01 | 0.013 | 0.012 | 0.011 | 0.01 | 0.0 |
| | 1.466 | 1.807 | 1.723 | 1.59 | 1.394 | 0.088 |
| Msmvttl3 | 0.009 | 0.009 | 0.009 | 0.01 | 0.01 | 0.002 |
| | 1.343 | 1.44 | 1.526 | 1.665 | 1.599 | 0.572 |
| alpha | 0.008 | 0.008 | 0.008 | 0.01 | 0.01 | 0.002 |
| | 1.223 | 1.205 | 1.232 | 1.415 | 1.532 | 0.708 |
| Msmvttl4 | 0.007 | 0.009 | 0.009 | 0.011 | 0.008 | 0.001 |
| | 1.131 | 1.546 | 1.615 | 1.778 | 1.378 | 0.395 |
| alpha | 0.007 | 0.008 | 0.009 | 0.01 | 0.009 | 0.003 |
| | 0.989 | 1.299 | 1.301 | 1.517 | 1.433 | 0.992 |
| Msmvttl5 | 0.007 | 0.009 | 0.009 | 0.009 | 0.011 | 0.004 |
| | 1.24 | 1.644 | 1.641 | 1.585 | 1.908 | 1.14 |
| alpha | 0.007 | 0.008 | 0.009 | 0.009 | 0.012 | 0.006 |
| | 0.937 | 1.202 | 1.33 | 1.36 | 1.771 | 1.589 |
| Diff | -0.005 | -0.005 | -0.004 | -0.006 | -0.003 | 0.003 |
| | -1.621 | -1.379 | -1.197 | -1.606 | -0.675 | 0.769 |
| alpha | -0.005 | -0.005 | -0.004 | -0.005 | -0.001 | 0.004 |
| | -1.522 | -1.298 | -1.013 | -1.034 | -0.286 | 1.468 |
+----------+-----------+-----------+-----------+-----------+-----------+-------+
The result from dataset #1 is consistent with literatures that in univariate analysis the differenced return is insignificant since the t-value is below 2.3, while in bivariate analysis the differenced return in most part is insignificant since the t-value is less than 2.3, suggesting that momentum factor provides no excess return. The factor adjustment tends to strengthen the portfolio excess return; while the dependent-sort bivariate tends to strengthen the portfolio excess return.
# %% construct test_data for bivariate analysis
# dataset 2
from portfolio_analysis import Bivariate
import numpy as np
# select stocks whose size is among the up 30% stocks in each month and whose trading
# days are more than or equal to 10 days
test_data_2 = return_company[return_company['Ndaytrd']>=10]
test_data_2 = test_data_2[['emrwd', 'Msmvttl', 'momentum', 'Date_merge']].dropna()
test_data_2 = test_data_2[(test_data_2['Date_merge'] >= '2005-01-01') & (test_data_2['Date_merge'] <= '2019-12-01')]
# Univariate analysis
uni_2 = Univariate(np.array(test_data_1[['emrwd', 'momentum', 'Date_merge']]), number=9)
uni_2.summary_and_test()
uni_2.print_summary_by_time()
uni_2.print_summary()
===================================================================================================
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+------+-------+
| Group | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Diff |
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+------+-------+
| Average | 0.008 | 0.01 | 0.01 | 0.012 | 0.011 | 0.011 | 0.011 | 0.012 | 0.011 | 0.01 | 0.002 |
| T-Test | 1.304 | 1.542 | 1.625 | 1.935 | 1.86 | 1.874 | 1.849 | 1.944 | 1.779 | 1.63 | 0.517 |
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+------+-------+
===================================================================================================
# Independent-sort Bivariate analysis
bi_2 = Bivariate(np.array(test_data_2), number=4)
bi_2.average_by_time()
bi_2.summary_and_test()
bi_2.print_summary_by_time()
bi_2.print_summary()
===============================================================
+-------+--------+--------+--------+--------+--------+--------+
| Group | 1 | 2 | 3 | 4 | 5 | Diff |
+-------+--------+--------+--------+--------+--------+--------+
| 1 | 0.037 | 0.033 | 0.033 | 0.032 | 0.034 | -0.003 |
| | 3.631 | 3.617 | 3.778 | 3.489 | 3.164 | -0.953 |
| 2 | 0.02 | 0.023 | 0.023 | 0.023 | 0.02 | 0.0 |
| | 2.359 | 2.748 | 2.837 | 2.712 | 2.307 | 0.057 |
| 3 | 0.017 | 0.02 | 0.018 | 0.017 | 0.018 | 0.001 |
| | 2.077 | 2.441 | 2.355 | 2.136 | 2.107 | 0.281 |
| 4 | 0.014 | 0.013 | 0.015 | 0.016 | 0.016 | 0.002 |
| | 1.702 | 1.798 | 1.975 | 2.047 | 2.029 | 0.687 |
| 5 | 0.01 | 0.013 | 0.014 | 0.012 | 0.013 | 0.003 |
| | 1.424 | 1.859 | 2.104 | 1.751 | 1.824 | 0.654 |
| Diff | -0.026 | -0.02 | -0.018 | -0.02 | -0.021 | 0.006 |
| | -4.106 | -3.852 | -4.186 | -3.809 | -2.916 | 1.186 |
+-------+--------+--------+--------+--------+--------+--------+
===============================================================
# Risk Adjustment
risk_model = risk_premium[['MKT', 'SMB', 'HML']]
risk_model = risk_model['2005':'2019']
bi_2.factor_adjustment(risk_model)
bi_2.print_summary()
===============================================================
+-------+--------+--------+--------+--------+--------+--------+
| Group | 1 | 2 | 3 | 4 | 5 | Diff |
+-------+--------+--------+--------+--------+--------+--------+
| 1 | 0.037 | 0.033 | 0.033 | 0.032 | 0.034 | -0.003 |
| | 3.631 | 3.617 | 3.778 | 3.489 | 3.164 | -0.953 |
| alpha | 0.037 | 0.032 | 0.03 | 0.03 | 0.033 | -0.004 |
| | 3.164 | 3.236 | 3.291 | 3.016 | 2.745 | -1.181 |
| 2 | 0.02 | 0.023 | 0.023 | 0.023 | 0.02 | 0.0 |
| | 2.359 | 2.748 | 2.837 | 2.712 | 2.307 | 0.057 |
| alpha | 0.019 | 0.021 | 0.022 | 0.022 | 0.019 | 0.0 |
| | 2.329 | 2.584 | 2.603 | 2.475 | 2.096 | 0.019 |
| 3 | 0.017 | 0.02 | 0.018 | 0.017 | 0.018 | 0.001 |
| | 2.077 | 2.441 | 2.355 | 2.136 | 2.107 | 0.281 |
| alpha | 0.017 | 0.019 | 0.018 | 0.016 | 0.017 | 0.0 |
| | 2.079 | 2.237 | 2.26 | 2.01 | 1.925 | 0.154 |
| 4 | 0.014 | 0.013 | 0.015 | 0.016 | 0.016 | 0.002 |
| | 1.702 | 1.798 | 1.975 | 2.047 | 2.029 | 0.687 |
| alpha | 0.013 | 0.012 | 0.014 | 0.015 | 0.016 | 0.003 |
| | 1.626 | 1.629 | 1.725 | 1.824 | 1.85 | 0.751 |
| 5 | 0.01 | 0.013 | 0.014 | 0.012 | 0.013 | 0.003 |
| | 1.424 | 1.859 | 2.104 | 1.751 | 1.824 | 0.654 |
| alpha | 0.01 | 0.013 | 0.014 | 0.012 | 0.014 | 0.004 |
| | 1.173 | 1.484 | 1.773 | 1.386 | 1.676 | 0.837 |
| Diff | -0.026 | -0.02 | -0.018 | -0.02 | -0.021 | 0.006 |
| | -4.106 | -3.852 | -4.186 | -3.809 | -2.916 | 1.186 |
| alpha | -0.027 | -0.019 | -0.016 | -0.019 | -0.019 | 0.008 |
| | -3.941 | -3.516 | -2.868 | -3.331 | -2.567 | 1.645 |
+-------+--------+--------+--------+--------+--------+--------+
===============================================================
# Dependent-sort Bivariate Analysis
bi_2_de = Bivariate(test_data_2, number=4)
bi_2_de.fit(conditional=True)
bi_2_de.print_summary()
=================================================================================
+----------+-----------+-----------+-----------+-----------+-----------+--------+
| Group | momentum1 | momentum2 | momentum3 | momentum4 | momentum5 | Diff |
+----------+-----------+-----------+-----------+-----------+-----------+--------+
| Msmvttl1 | 0.036 | 0.034 | 0.035 | 0.031 | 0.031 | -0.004 |
| | 3.527 | 3.661 | 3.746 | 3.581 | 3.302 | -1.194 |
| Msmvttl2 | 0.02 | 0.023 | 0.023 | 0.022 | 0.021 | 0.001 |
| | 2.377 | 2.763 | 2.746 | 2.653 | 2.407 | 0.224 |
| Msmvttl3 | 0.017 | 0.02 | 0.018 | 0.017 | 0.018 | 0.001 |
| | 2.072 | 2.451 | 2.333 | 2.142 | 2.091 | 0.269 |
| Msmvttl4 | 0.014 | 0.014 | 0.016 | 0.017 | 0.015 | 0.001 |
| | 1.737 | 1.895 | 2.045 | 2.224 | 1.862 | 0.257 |
| Msmvttl5 | 0.012 | 0.013 | 0.014 | 0.014 | 0.014 | 0.002 |
| | 1.679 | 1.923 | 2.102 | 1.993 | 1.863 | 0.394 |
| Diff | -0.023 | -0.02 | -0.021 | -0.018 | -0.017 | 0.006 |
| | -3.716 | -3.788 | -3.638 | -3.408 | -2.896 | 1.205 |
+----------+-----------+-----------+-----------+-----------+-----------+--------+
=================================================================================
# Risk Adjustment
bi_2_de.factor_adjustment(risk_model)
bi_2_de.print_summary()
=================================================================================
+----------+-----------+-----------+-----------+-----------+-----------+--------+
| Group | momentum1 | momentum2 | momentum3 | momentum4 | momentum5 | Diff |
+----------+-----------+-----------+-----------+-----------+-----------+--------+
| Msmvttl1 | 0.036 | 0.034 | 0.035 | 0.031 | 0.031 | -0.004 |
| | 3.527 | 3.661 | 3.746 | 3.581 | 3.302 | -1.194 |
| alpha | 0.035 | 0.033 | 0.034 | 0.028 | 0.029 | -0.006 |
| | 3.246 | 3.24 | 3.292 | 3.187 | 2.961 | -1.488 |
| Msmvttl2 | 0.02 | 0.023 | 0.023 | 0.022 | 0.021 | 0.001 |
| | 2.377 | 2.763 | 2.746 | 2.653 | 2.407 | 0.224 |
| alpha | 0.019 | 0.021 | 0.022 | 0.021 | 0.02 | 0.001 |
| | 2.323 | 2.592 | 2.615 | 2.407 | 2.176 | 0.207 |
| Msmvttl3 | 0.017 | 0.02 | 0.018 | 0.017 | 0.018 | 0.001 |
| | 2.072 | 2.451 | 2.333 | 2.142 | 2.091 | 0.269 |
| alpha | 0.017 | 0.019 | 0.018 | 0.016 | 0.017 | 0.001 |
| | 2.094 | 2.198 | 2.255 | 2.067 | 1.927 | 0.182 |
| Msmvttl4 | 0.014 | 0.014 | 0.016 | 0.017 | 0.015 | 0.001 |
| | 1.737 | 1.895 | 2.045 | 2.224 | 1.862 | 0.257 |
| alpha | 0.013 | 0.013 | 0.014 | 0.017 | 0.015 | 0.002 |
| | 1.644 | 1.659 | 1.755 | 1.946 | 1.762 | 0.445 |
| Msmvttl5 | 0.012 | 0.013 | 0.014 | 0.014 | 0.014 | 0.002 |
| | 1.679 | 1.923 | 2.102 | 1.993 | 1.863 | 0.394 |
| alpha | 0.012 | 0.013 | 0.013 | 0.014 | 0.015 | 0.003 |
| | 1.415 | 1.468 | 1.636 | 1.659 | 1.726 | 0.698 |
| Diff | -0.023 | -0.02 | -0.021 | -0.018 | -0.017 | 0.006 |
| | -3.716 | -3.788 | -3.638 | -3.408 | -2.896 | 1.205 |
| alpha | -0.023 | -0.021 | -0.021 | -0.015 | -0.015 | 0.008 |
| | -3.75 | -3.493 | -3.386 | -2.322 | -2.355 | 1.691 |
+----------+-----------+-----------+-----------+-----------+-----------+--------+
The result from dataset #2 is consistent with literatures that in univariate analysis the differenced return is insignificant since the t-value is below 2.3, while in bivariate analysis the differenced return in most part is insignificant since the t-value is less than 2.3, suggesting that momentum factor provides no excess return. The factor adjustment tends to strengthen the portfolio excess return; while the dependent-sort bivariate tends to strengthen the portfolio excess return.
Turnover Factor
Trading volume would effect the stock performance, which has a long history in industry while in academic research is burgeoning. Instead of trading volume, turnover is a standard substitution. The common sense is that turnover is generally negative correlated with the future return (Chordia et al., 2001). While Subrahmanyam (2005) found the asymmetric structure that for poor performance stock, the correlation is negative; for good performance stock, the correlation is positive. In other global market, Hu (1997) and Chang et al. (2010) find negative correlation in Japan market; Dey (2005) find positive correlation in emerging market. In China market, Liu et al. (2019) find negative correlation, which can explain the short term reversal effect.
In this demo, the proxy variable for turnover factor is abnormal turnover, which is the ratio of average turnover in past 1 month to average turnover in past 12 month. he dataset starts from Jan, 2000 and is collected from CSMAR dataset. WARNING: Do Not use dataset in this demo for any commercial purpose.
# %% import package
import pandas as pd
import sys, os
sys.path.append(os.path.abspath(".."))
# %% import data
# Monthly return of stocks in China security market
month_return = pd.read_hdf('.\data\month_return.h5', key='month_return')
trade_data = pd.read_hdf('.\data\mean_filter_trade.h5', key='data')
Conduct some data preprocessing.
# %% preprocessing data
# forward the monthly return for each stock
# emrwd is the return including dividend
month_return['emrwd'] = month_return.groupby(['Stkcd'])['Mretwd'].shift(-1)
# emrnd is the return including no dividend
month_return['emrnd'] = month_return.groupby(['Stkcd'])['Mretnd'].shift(-1)
# select the A share stock
month_return = month_return[month_return['Markettype'].isin([1, 4, 16])]
# % distinguish the stocks whose size is among the up 30% stocks in each month
def percentile(stocks) :
return stocks >= stocks.quantile(q=.3)
month_return['cap'] = month_return.groupby(['Trdmnt'])['Msmvttl'].apply(percentile)
Construct the proxy variable.
# %% constrcut variable
import numpy as np
trade_data['rolling_Turnover'] = np.array(trade_data['Turnover'].groupby('Symbol').rolling(12).mean())
trade_data['specific_Turnover'] = trade_data['Turnover'] / trade_data['rolling_Turnover']
Some further data processing.
# %% prepare merge data
from pandas.tseries.offsets import *
month_return['Stkcd_merge'] = month_return['Stkcd'].astype(dtype='string')
month_return['Date_merge'] = pd.to_datetime(month_return['Trdmnt'])
#month_return['Yearmonth'] = month_return['Date_merge'].map(lambda x : 1000*x.year + x.month)
#month_return['Date_merge'] += MonthEnd()
trade_data['Stkcd_merge'] = trade_data['Symbol'].dropna().astype(dtype='int').astype(dtype='string')
trade_data['TradingDate'] = trade_data.index.map(lambda x : x[1])
trade_data['Date_merge'] = pd.to_datetime(trade_data['TradingDate'])
#company_data['Yearmonth'] = company_data['Date_merge'].map(lambda x : 1000*x.year + x.month)
trade_data['Date_merge'] += MonthBegin()
# %% dataset starts from '2000-01'
trade_data = trade_data[trade_data['Date_merge'] >= '2000-01']
month_return = month_return[month_return['Date_merge'] >= '2000-01']
return_company = pd.merge(trade_data, month_return, on=['Stkcd_merge', 'Date_merge'])
Two datasets are constituted. One includes tail 30% stock, while one includes not. Univariate analysis and Bivariate analysis are attached.
# %% construct test_data for bivariate analysis
# dataset 1 :
from portfolio_analysis import Bivariate, Univariate
import numpy as np
# select stocks whose size is among the up 30% stocks in each month and whose trading
# days are more than or equal to 10 days
test_data_1 = return_company[(return_company['cap']==True) & (return_company['Ndaytrd']>=10)]
test_data_1 = test_data_1[['emrwd', 'Msmvttl', 'specific_Turnover', 'Date_merge']].dropna()
test_data_1 = test_data_1[(test_data_1['Date_merge'] >= '2000-01-01') & (test_data_1['Date_merge'] <= '2019-12-01')]
# Univariate analysis
uni_1 = Univariate(np.array(test_data_1[['emrwd', 'specific_Turnover', 'Date_merge']]), number=9)
uni_1.summary_and_test()
uni_1.print_summary_by_time()
uni_1.print_summary()
=====================================================================================================
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+--------+
| Group | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Diff |
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+--------+
| Average | 0.009 | 0.011 | 0.012 | 0.013 | 0.012 | 0.012 | 0.011 | 0.011 | 0.009 | 0.005 | -0.004 |
| T-Test | 1.644 | 1.945 | 2.088 | 2.132 | 2.02 | 1.997 | 1.87 | 1.74 | 1.545 | 0.841 | -1.426 |
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+--------+
=====================================================================================================
# Bivariate analysis
bi_1 = Bivariate(np.array(test_data_1), number=4)
bi_1.average_by_time()
bi_1.summary_and_test()
bi_1.print_summary_by_time()
bi_1.print_summary()
================================================================
+-------+--------+--------+--------+--------+--------+--------+
| Group | 1 | 2 | 3 | 4 | 5 | Diff |
+-------+--------+--------+--------+--------+--------+--------+
| 1 | 0.014 | 0.016 | 0.015 | 0.014 | 0.009 | -0.004 |
| | 2.153 | 2.447 | 2.307 | 2.139 | 1.412 | -1.827 |
| 2 | 0.011 | 0.013 | 0.013 | 0.011 | 0.009 | -0.002 |
| | 1.878 | 2.081 | 2.029 | 1.661 | 1.364 | -0.882 |
| 3 | 0.01 | 0.01 | 0.011 | 0.01 | 0.005 | -0.005 |
| | 1.732 | 1.628 | 1.768 | 1.665 | 0.842 | -1.928 |
| 4 | 0.009 | 0.011 | 0.01 | 0.009 | 0.007 | -0.002 |
| | 1.656 | 1.857 | 1.679 | 1.587 | 1.13 | -0.723 |
| 5 | 0.008 | 0.011 | 0.01 | 0.009 | 0.005 | -0.003 |
| | 1.515 | 2.045 | 1.935 | 1.63 | 0.854 | -1.275 |
| Diff | -0.005 | -0.005 | -0.004 | -0.005 | -0.005 | 0.001 |
| | -1.561 | -1.536 | -1.264 | -1.361 | -1.333 | 0.367 |
+-------+--------+--------+--------+--------+--------+--------+
================================================================
# Risk Adjustment
risk_model = risk_premium[['MKT', 'SMB', 'HML']]
risk_model = risk_model['2000':'2019']
bi_1.factor_adjustment(risk_model)
bi_1.print_summary()
===============================================================
+-------+--------+--------+--------+--------+--------+--------+
| Group | 1 | 2 | 3 | 4 | 5 | Diff |
+-------+--------+--------+--------+--------+--------+--------+
| 1 | 0.014 | 0.016 | 0.015 | 0.014 | 0.009 | -0.004 |
| | 2.153 | 2.447 | 2.307 | 2.139 | 1.412 | -1.827 |
| alpha | 0.013 | 0.016 | 0.014 | 0.014 | 0.008 | -0.005 |
| | 1.947 | 2.153 | 1.983 | 2.019 | 1.183 | -2.608 |
| 2 | 0.011 | 0.013 | 0.013 | 0.011 | 0.009 | -0.002 |
| | 1.878 | 2.081 | 2.029 | 1.661 | 1.364 | -0.882 |
| alpha | 0.012 | 0.013 | 0.012 | 0.01 | 0.009 | -0.003 |
| | 1.597 | 1.925 | 1.849 | 1.531 | 1.173 | -1.764 |
| 3 | 0.01 | 0.01 | 0.011 | 0.01 | 0.005 | -0.005 |
| | 1.732 | 1.628 | 1.768 | 1.665 | 0.842 | -1.928 |
| alpha | 0.011 | 0.009 | 0.01 | 0.009 | 0.004 | -0.006 |
| | 1.56 | 1.429 | 1.591 | 1.475 | 0.634 | -3.213 |
| 4 | 0.009 | 0.011 | 0.01 | 0.009 | 0.007 | -0.002 |
| | 1.656 | 1.857 | 1.679 | 1.587 | 1.13 | -0.723 |
| alpha | 0.01 | 0.011 | 0.009 | 0.008 | 0.007 | -0.003 |
| | 1.404 | 1.606 | 1.458 | 1.334 | 0.964 | -1.437 |
| 5 | 0.008 | 0.011 | 0.01 | 0.009 | 0.005 | -0.003 |
| | 1.515 | 2.045 | 1.935 | 1.63 | 0.854 | -1.275 |
| alpha | 0.009 | 0.011 | 0.011 | 0.009 | 0.005 | -0.004 |
| | 1.23 | 1.704 | 1.651 | 1.361 | 0.713 | -1.914 |
| Diff | -0.005 | -0.005 | -0.004 | -0.005 | -0.005 | 0.001 |
| | -1.561 | -1.536 | -1.264 | -1.361 | -1.333 | 0.367 |
| alpha | -0.004 | -0.005 | -0.004 | -0.005 | -0.003 | 0.001 |
| | -1.057 | -1.349 | -0.986 | -1.143 | -0.832 | 0.537 |
+-------+--------+--------+--------+--------+--------+--------+
===============================================================
# Dependent-sort Bivariate Analysis
bi_1_de = Bivariate(test_data_1, number=4)
bi_1_de.fit(conditional=True)
bi_1_de.print_summary()
==============================================================================================================================
+----------+--------------------+--------------------+--------------------+--------------------+--------------------+--------+
| Group | specific_Turnover1 | specific_Turnover2 | specific_Turnover3 | specific_Turnover4 | specific_Turnover5 | Diff |
+----------+--------------------+--------------------+--------------------+--------------------+--------------------+--------+
| Msmvttl1 | 0.014 | 0.015 | 0.015 | 0.014 | 0.01 | -0.004 |
| | 2.121 | 2.361 | 2.227 | 2.185 | 1.483 | -1.678 |
| Msmvttl2 | 0.012 | 0.013 | 0.013 | 0.011 | 0.009 | -0.002 |
| | 1.91 | 2.1 | 1.948 | 1.754 | 1.354 | -1.002 |
| Msmvttl3 | 0.01 | 0.01 | 0.01 | 0.011 | 0.006 | -0.004 |
| | 1.666 | 1.699 | 1.715 | 1.681 | 0.883 | -1.684 |
| Msmvttl4 | 0.009 | 0.011 | 0.011 | 0.01 | 0.006 | -0.003 |
| | 1.656 | 1.849 | 1.874 | 1.659 | 0.949 | -1.139 |
| Msmvttl5 | 0.007 | 0.011 | 0.011 | 0.011 | 0.005 | -0.003 |
| | 1.402 | 2.085 | 2.093 | 1.891 | 0.793 | -1.051 |
| Diff | -0.006 | -0.004 | -0.004 | -0.004 | -0.005 | 0.001 |
| | -1.788 | -1.188 | -0.984 | -1.064 | -1.512 | 0.31 |
+----------+--------------------+--------------------+--------------------+--------------------+--------------------+--------+
==============================================================================================================================
# Risk Adjustment
bi_1_de.factor_adjustment(risk_model)
bi_1_de.print_summary()
==============================================================================================================================
+----------+--------------------+--------------------+--------------------+--------------------+--------------------+--------+
| Group | specific_Turnover1 | specific_Turnover2 | specific_Turnover3 | specific_Turnover4 | specific_Turnover5 | Diff |
+----------+--------------------+--------------------+--------------------+--------------------+--------------------+--------+
| Msmvttl1 | 0.014 | 0.015 | 0.015 | 0.014 | 0.01 | -0.004 |
| | 2.121 | 2.361 | 2.227 | 2.185 | 1.483 | -1.678 |
| alpha | 0.013 | 0.015 | 0.014 | 0.014 | 0.009 | -0.004 |
| | 1.915 | 2.08 | 1.928 | 2.103 | 1.26 | -2.325 |
| Msmvttl2 | 0.012 | 0.013 | 0.013 | 0.011 | 0.009 | -0.002 |
| | 1.91 | 2.1 | 1.948 | 1.754 | 1.354 | -1.002 |
| alpha | 0.012 | 0.013 | 0.012 | 0.011 | 0.009 | -0.003 |
| | 1.659 | 1.934 | 1.76 | 1.606 | 1.185 | -2.273 |
| Msmvttl3 | 0.01 | 0.01 | 0.01 | 0.011 | 0.006 | -0.004 |
| | 1.666 | 1.699 | 1.715 | 1.681 | 0.883 | -1.684 |
| alpha | 0.01 | 0.01 | 0.01 | 0.01 | 0.005 | -0.006 |
| | 1.508 | 1.498 | 1.534 | 1.473 | 0.678 | -2.96 |
| Msmvttl4 | 0.009 | 0.011 | 0.011 | 0.01 | 0.006 | -0.003 |
| | 1.656 | 1.849 | 1.874 | 1.659 | 0.949 | -1.139 |
| alpha | 0.009 | 0.011 | 0.011 | 0.009 | 0.005 | -0.004 |
| | 1.413 | 1.616 | 1.56 | 1.494 | 0.766 | -2.048 |
| Msmvttl5 | 0.007 | 0.011 | 0.011 | 0.011 | 0.005 | -0.003 |
| | 1.402 | 2.085 | 2.093 | 1.891 | 0.793 | -1.051 |
| alpha | 0.008 | 0.012 | 0.011 | 0.01 | 0.004 | -0.004 |
| | 1.134 | 1.71 | 1.768 | 1.469 | 0.601 | -1.843 |
| Diff | -0.006 | -0.004 | -0.004 | -0.004 | -0.005 | 0.001 |
| | -1.788 | -1.188 | -0.984 | -1.064 | -1.512 | 0.31 |
| alpha | -0.005 | -0.003 | -0.003 | -0.004 | -0.005 | 0.0 |
| | -1.437 | -0.868 | -0.671 | -1.043 | -1.232 | 0.183 |
+----------+--------------------+--------------------+--------------------+--------------------+--------------------+--------+
The result from dataset #1 is not completely consistent with literatures that in univariate analysis the differenced return is insignificant since the absolute t-value is below 2.3, while in bivariate analysis the differenced return in most part is insignificant since the absolute t-value is less than 2.3, suggesting that turnover factor provides no excess return. The factor adjustment tends to strengthen the portfolio excess return; while the dependent-sort bivariate tends to weaken the portfolio excess return.
# %% construct test_data for bivariate analysis
# dataset 2 :
from portfolio_analysis import Bivariate
import numpy as np
# select stocks whose size is among the up 30% stocks in each month and whose trading
# days are more than or equal to 10 days
test_data_2 = return_company[return_company['Ndaytrd']>=10]
test_data_2 = test_data_2[['emrwd', 'Msmvttl', 'specific_Turnover', 'Date_merge']].dropna()
test_data_2 = test_data_2[(test_data_2['Date_merge'] >= '2004-01-01') & (test_data_2['Date_merge'] <= '2019-12-01')]
# Univariate analysis
uni_2 = Univariate(np.array(test_data_2[['emrwd', 'specific_Turnover', 'Date_merge']]), number=9)
uni_2.summary_and_test()
uni_2.print_summary_by_time()
uni_2.print_summary()
=====================================================================================================
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+--------+
| Group | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Diff |
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+--------+
| Average | 0.016 | 0.018 | 0.019 | 0.02 | 0.019 | 0.019 | 0.018 | 0.016 | 0.016 | 0.012 | -0.004 |
| T-Test | 2.218 | 2.511 | 2.59 | 2.648 | 2.566 | 2.555 | 2.422 | 2.217 | 2.077 | 1.454 | -1.353 |
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+--------+
=====================================================================================================
# Independent-sort Bivariate analysis
bi_2 = Bivariate(np.array(test_data_2), number=4)
bi_2.average_by_time()
bi_2.summary_and_test()
bi_2.print_summary_by_time()
bi_2.print_summary()
===============================================================
+-------+--------+--------+--------+--------+--------+--------+
| Group | 1 | 2 | 3 | 4 | 5 | Diff |
+-------+--------+--------+--------+--------+--------+--------+
| 1 | 0.029 | 0.03 | 0.033 | 0.026 | 0.025 | -0.004 |
| | 3.507 | 3.455 | 3.075 | 3.203 | 2.579 | -1.289 |
| 2 | 0.018 | 0.021 | 0.022 | 0.018 | 0.013 | -0.004 |
| | 2.334 | 2.697 | 2.715 | 2.257 | 1.631 | -1.955 |
| 3 | 0.015 | 0.016 | 0.017 | 0.015 | 0.012 | -0.003 |
| | 2.115 | 2.237 | 2.255 | 1.969 | 1.529 | -1.119 |
| 4 | 0.012 | 0.013 | 0.013 | 0.014 | 0.009 | -0.003 |
| | 1.86 | 1.759 | 1.822 | 1.858 | 1.177 | -1.216 |
| 5 | 0.011 | 0.015 | 0.012 | 0.012 | 0.009 | -0.002 |
| | 1.729 | 2.289 | 1.812 | 1.752 | 1.254 | -0.724 |
| Diff | -0.018 | -0.015 | -0.021 | -0.015 | -0.016 | 0.002 |
| | -3.758 | -3.114 | -2.752 | -3.186 | -2.481 | 0.48 |
+-------+--------+--------+--------+--------+--------+--------+
===============================================================
# Risk Adjustment
risk_model = risk_premium[['MKT', 'SMB', 'HML']]
risk_model = risk_model['2004':'2019']
bi_2.factor_adjustment(risk_model)
bi_2.print_summary()
===============================================================
+-------+--------+--------+--------+--------+--------+--------+
| Group | 1 | 2 | 3 | 4 | 5 | Diff |
+-------+--------+--------+--------+--------+--------+--------+
| 1 | 0.029 | 0.03 | 0.033 | 0.026 | 0.025 | -0.004 |
| | 3.507 | 3.455 | 3.075 | 3.203 | 2.579 | -1.289 |
| alpha | 0.028 | 0.029 | 0.032 | 0.024 | 0.024 | -0.004 |
| | 3.031 | 2.749 | 2.737 | 2.676 | 2.213 | -1.18 |
| 2 | 0.018 | 0.021 | 0.022 | 0.018 | 0.013 | -0.004 |
| | 2.334 | 2.697 | 2.715 | 2.257 | 1.631 | -1.955 |
| alpha | 0.017 | 0.02 | 0.021 | 0.017 | 0.011 | -0.006 |
| | 2.158 | 2.405 | 2.38 | 2.001 | 1.353 | -2.672 |
| 3 | 0.015 | 0.016 | 0.017 | 0.015 | 0.012 | -0.003 |
| | 2.115 | 2.237 | 2.255 | 1.969 | 1.529 | -1.119 |
| alpha | 0.016 | 0.016 | 0.016 | 0.014 | 0.011 | -0.005 |
| | 1.909 | 2.136 | 1.973 | 1.896 | 1.282 | -2.623 |
| 4 | 0.012 | 0.013 | 0.013 | 0.014 | 0.009 | -0.003 |
| | 1.86 | 1.759 | 1.822 | 1.858 | 1.177 | -1.216 |
| alpha | 0.013 | 0.012 | 0.012 | 0.012 | 0.008 | -0.005 |
| | 1.626 | 1.495 | 1.586 | 1.632 | 0.924 | -3.123 |
| 5 | 0.011 | 0.015 | 0.012 | 0.012 | 0.009 | -0.002 |
| | 1.729 | 2.289 | 1.812 | 1.752 | 1.254 | -0.724 |
| alpha | 0.012 | 0.015 | 0.012 | 0.011 | 0.008 | -0.004 |
| | 1.336 | 1.876 | 1.561 | 1.388 | 0.916 | -1.945 |
| Diff | -0.018 | -0.015 | -0.021 | -0.015 | -0.016 | 0.002 |
| | -3.758 | -3.114 | -2.752 | -3.186 | -2.481 | 0.48 |
| alpha | -0.016 | -0.014 | -0.02 | -0.013 | -0.016 | 0.0 |
| | -2.902 | -2.732 | -2.876 | -2.258 | -2.465 | 0.062 |
+-------+--------+--------+--------+--------+--------+--------+
===============================================================
# Dependent-sort Bivariate Analysis
bi_2_de = Bivariate(test_data_2, number=4)
bi_2_de.fit(conditional=True)
bi_2_de.print_summary()
==============================================================================================================================
+----------+--------------------+--------------------+--------------------+--------------------+--------------------+--------+
| Group | specific_Turnover1 | specific_Turnover2 | specific_Turnover3 | specific_Turnover4 | specific_Turnover5 | Diff |
+----------+--------------------+--------------------+--------------------+--------------------+--------------------+--------+
| Msmvttl1 | 0.028 | 0.029 | 0.031 | 0.034 | 0.023 | -0.005 |
| | 3.371 | 3.396 | 3.523 | 3.108 | 2.607 | -1.892 |
| Msmvttl2 | 0.018 | 0.02 | 0.022 | 0.018 | 0.013 | -0.004 |
| | 2.328 | 2.613 | 2.81 | 2.265 | 1.621 | -2.07 |
| Msmvttl3 | 0.015 | 0.017 | 0.017 | 0.015 | 0.012 | -0.004 |
| | 2.118 | 2.265 | 2.219 | 2.006 | 1.468 | -1.401 |
| Msmvttl4 | 0.013 | 0.013 | 0.013 | 0.014 | 0.009 | -0.004 |
| | 1.879 | 1.844 | 1.875 | 1.854 | 1.132 | -1.385 |
| Msmvttl5 | 0.011 | 0.013 | 0.014 | 0.011 | 0.009 | -0.001 |
| | 1.671 | 2.006 | 2.208 | 1.671 | 1.31 | -0.474 |
| Diff | -0.017 | -0.016 | -0.017 | -0.022 | -0.014 | 0.003 |
| | -3.706 | -3.182 | -3.386 | -2.867 | -2.528 | 0.928 |
+----------+--------------------+--------------------+--------------------+--------------------+--------------------+--------+
==============================================================================================================================
# Risk Adjustment
bi_2_de.factor_adjustment(risk_model)
bi_2_de.print_summary()
===============================================================================================================================
+----------+--------------------+--------------------+--------------------+--------------------+--------------------+--------+
| Group | specific_Turnover1 | specific_Turnover2 | specific_Turnover3 | specific_Turnover4 | specific_Turnover5 | Diff |
+----------+--------------------+--------------------+--------------------+--------------------+--------------------+--------+
| Msmvttl1 | 0.028 | 0.029 | 0.031 | 0.034 | 0.023 | -0.005 |
| | 3.371 | 3.396 | 3.523 | 3.108 | 2.607 | -1.892 |
| alpha | 0.026 | 0.027 | 0.03 | 0.033 | 0.021 | -0.004 |
| | 2.941 | 2.925 | 2.821 | 2.735 | 2.226 | -1.8 |
| Msmvttl2 | 0.018 | 0.02 | 0.022 | 0.018 | 0.013 | -0.004 |
| | 2.328 | 2.613 | 2.81 | 2.265 | 1.621 | -2.07 |
| alpha | 0.017 | 0.02 | 0.022 | 0.017 | 0.011 | -0.006 |
| | 2.153 | 2.33 | 2.463 | 2.081 | 1.326 | -2.996 |
| Msmvttl3 | 0.015 | 0.017 | 0.017 | 0.015 | 0.012 | -0.004 |
| | 2.118 | 2.265 | 2.219 | 2.006 | 1.468 | -1.401 |
| alpha | 0.016 | 0.017 | 0.016 | 0.014 | 0.011 | -0.005 |
| | 1.907 | 2.149 | 1.95 | 1.886 | 1.284 | -2.633 |
| Msmvttl4 | 0.013 | 0.013 | 0.013 | 0.014 | 0.009 | -0.004 |
| | 1.879 | 1.844 | 1.875 | 1.854 | 1.132 | -1.385 |
| alpha | 0.013 | 0.013 | 0.012 | 0.013 | 0.007 | -0.006 |
| | 1.614 | 1.562 | 1.624 | 1.636 | 0.882 | -3.374 |
| Msmvttl5 | 0.011 | 0.013 | 0.014 | 0.011 | 0.009 | -0.001 |
| | 1.671 | 2.006 | 2.208 | 1.671 | 1.31 | -0.474 |
| alpha | 0.011 | 0.013 | 0.014 | 0.01 | 0.008 | -0.003 |
| | 1.318 | 1.642 | 1.8 | 1.202 | 0.954 | -1.509 |
| Diff | -0.017 | -0.016 | -0.017 | -0.022 | -0.014 | 0.003 |
| | -3.706 | -3.182 | -3.386 | -2.867 | -2.528 | 0.928 |
| alpha | -0.015 | -0.014 | -0.016 | -0.023 | -0.013 | 0.001 |
| | -2.835 | -2.632 | -2.713 | -2.967 | -2.339 | 0.379 |
+----------+--------------------+--------------------+--------------------+--------------------+--------------------+--------+
The result from dataset #2 is not completely consistent with literatures that in univariate analysis the differenced return is insignificant since the absolute t-value is below 2.3, while in bivariate analysis the differenced return in most part is insignificant since the absolute t-value is less than 2.3, suggesting that turnover factor provides no excess return. The factor adjustment tends to strengthen the portfolio excess return; while the dependent-sort bivariate tends to weaken the portfolio excess return.
Liquidity Factor
Liquidity is found an supplementary factor that drive stock return especially small stocks. A security's liquidity refers to the ease with which the security can be bought and/or sold. CAPM and APT assume that all security are perfectly liquid, meaning that transaction cost are zero. The classic measure of liquidity is from Amihud (2002), which is defined as $$ Illiq_i=\frac 1D\sum_{d=1}^D{\frac {|R_{i,d}|}{VOLD_{i,d}}}, $$ where R is the return of stock i on day d, VOLD is the money volume of stock i traded on day d, and D is the number of days in the estimation period. If a stock is more liquid, then the indicator tend to be small and vice versa.
It is widely observed that illiquidity is positive correlated with future stock return. In another word, liquidity is negative correlated with future stock return.
In this demo, the proxy variable for liquidity factor is Amihud's indicator. The dataset starts from Jan, 2000 and is collected from CSMAR dataset. WARNING: Do Not use dataset in this demo for any commercial purpose.
# %% set path
import sys, os
sys.path.append(os.path.abspath(".."))
# %% import data
# Monthly return of stocks in China security market
import pandas as pd
month_return = pd.read_hdf('.\data\month_return.h5', key='month_return')
company_data = pd.read_hdf('.\data\last_filter_pe.h5', key='data')
Data preprocessing
# %% preprocessing data
# forward the monthly return for each stock
# emrwd is the return including dividend
month_return['emrwd'] = month_return.groupby(['Stkcd'])['Mretwd'].shift(-1)
# emrnd is the return including no dividend
month_return['emrnd'] = month_return.groupby(['Stkcd'])['Mretnd'].shift(-1)
# select the A share stock
month_return = month_return[month_return['Markettype'].isin([1, 4, 16])]
# % distinguish the stocks whose size is among the up 30% stocks in each month
def percentile(stocks) :
return stocks >= stocks.quantile(q=.3)
month_return['cap'] = month_return.groupby(['Trdmnt'])['Msmvttl'].apply(percentile)
Construct proxy variable
# %% construct proxy variable
import numpy as np
month_return['liquidity_monthly'] = month_return['Mretwd'].apply(np.abs) / month_return['Mnvaltrd']
Further data preprocessing
# %% construct dataset
month_return['Stkcd_merge'] = month_return['Stkcd'].astype(dtype='string')
month_return['Date_merge'] = pd.to_datetime(month_return['Trdmnt'])
return_company = month_return
Dataset #1. The result from dataset #1 is consistent with literatures that in univariate analysis the differenced return is significant since the absolute t-value is greater than 2.3, and in bivariate analysis the differenced return in most part is significant since the absolute t-value is greater than 2.3, suggesting that liquidity factor provides excess return. The factor adjustment tends to strengthen the portfolio excess return; while the dependent-sort bivariate tends to strengthen the portfolio excess return.
# %% construct test_data for bivariate analysis
# dataset 1 :
from portfolio_analysis import Bivariate, Univariate
import numpy as np
# select stocks whose size is among the up 30% stocks in each month and whose trading
# days are more than or equal to 10 days
test_data_1 = return_company[(return_company['cap']==True) & (return_company['Ndaytrd']>=10)]
test_data_1 = test_data_1[['emrwd', 'Msmvttl', 'liquidity_monthly', 'Date_merge']].dropna()
test_data_1 = test_data_1[(test_data_1['Date_merge'] >= '2000-01-01') & (test_data_1['Date_merge'] <= '2019-12-01')]
# Univariate analysis
uni_1 = Univariate(np.array(test_data_1[['emrwd', 'liquidity_monthly', 'Date_merge']]), number=9)
uni_1.summary_and_test()
uni_1.print_summary_by_time()
uni_1.print_summary()
===================================================================================================
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+
| Group | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Diff |
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+
| Average | 0.005 | 0.006 | 0.008 | 0.008 | 0.009 | 0.01 | 0.011 | 0.012 | 0.014 | 0.017 | 0.012 |
| T-Test | 0.9 | 1.08 | 1.329 | 1.276 | 1.515 | 1.608 | 1.878 | 2.002 | 2.299 | 2.797 | 4.404 |
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+
# Independent-sort Bivariate analysis
bi_1 = Bivariate(np.array(test_data_1), number=3)
bi_1.average_by_time()
bi_1.summary_and_test()
bi_1.print_summary_by_time()
bi_1.print_summary()
====================================================
+-------+-------+-------+--------+--------+--------+
| Group | 1 | 2 | 3 | 4 | Diff |
+-------+-------+-------+--------+--------+--------+
| 1 | 0.004 | 0.007 | 0.011 | 0.018 | 0.013 |
| | 0.675 | 1.12 | 1.609 | 2.66 | 5.671 |
| 2 | 0.006 | 0.008 | 0.01 | 0.014 | 0.008 |
| | 0.926 | 1.188 | 1.627 | 2.386 | 3.765 |
| 3 | 0.004 | 0.008 | 0.011 | 0.012 | 0.007 |
| | 0.711 | 1.318 | 1.805 | 2.079 | 3.194 |
| 4 | 0.008 | 0.01 | 0.01 | 0.01 | 0.002 |
| | 1.459 | 1.711 | 1.83 | 1.644 | 0.484 |
| Diff | 0.003 | 0.002 | -0.001 | -0.008 | -0.012 |
| | 1.026 | 0.715 | -0.26 | -2.397 | -3.497 |
+-------+-------+-------+--------+--------+--------+
====================================================
# Risk Adjustment
risk_model = risk_premium[['MKT', 'SMB', 'HML']]
risk_model = risk_model['2000':'2019']
bi_1.factor_adjustment(risk_model)
bi_1.print_summary()
====================================================
+-------+-------+-------+--------+--------+--------+
| Group | 1 | 2 | 3 | 4 | Diff |
+-------+-------+-------+--------+--------+--------+
| 1 | 0.004 | 0.007 | 0.011 | 0.018 | 0.013 |
| | 0.675 | 1.12 | 1.609 | 2.66 | 5.671 |
| alpha | 0.003 | 0.006 | 0.01 | 0.018 | 0.015 |
| | 0.385 | 0.852 | 1.387 | 2.499 | 7.72 |
| 2 | 0.006 | 0.008 | 0.01 | 0.014 | 0.008 |
| | 0.926 | 1.188 | 1.627 | 2.386 | 3.765 |
| alpha | 0.004 | 0.007 | 0.01 | 0.015 | 0.011 |
| | 0.608 | 0.947 | 1.482 | 2.198 | 6.722 |
| 3 | 0.004 | 0.008 | 0.011 | 0.012 | 0.007 |
| | 0.711 | 1.318 | 1.805 | 2.079 | 3.194 |
| alpha | 0.004 | 0.007 | 0.01 | 0.013 | 0.009 |
| | 0.572 | 1.119 | 1.53 | 1.959 | 4.325 |
| 4 | 0.008 | 0.01 | 0.01 | 0.01 | 0.002 |
| | 1.459 | 1.711 | 1.83 | 1.644 | 0.484 |
| alpha | 0.008 | 0.009 | 0.01 | 0.011 | 0.003 |
| | 1.179 | 1.393 | 1.622 | 1.569 | 0.865 |
| Diff | 0.003 | 0.002 | -0.001 | -0.008 | -0.012 |
| | 1.026 | 0.715 | -0.26 | -2.397 | -3.497 |
| alpha | 0.005 | 0.003 | 0.001 | -0.006 | -0.011 |
| | 1.404 | 1.009 | 0.164 | -1.97 | -3.135 |
+-------+-------+-------+--------+--------+--------+
====================================================
# Dependent-sort Bivariate Analysis
bi_1_de = Bivariate(test_data_1, number=3)
bi_1_de.fit(conditional=True)
bi_1_de.print_summary()
=========================================================================================================
+----------+--------------------+--------------------+--------------------+--------------------+--------+
| Group | liquidity_monthly1 | liquidity_monthly2 | liquidity_monthly3 | liquidity_monthly4 | Diff |
+----------+--------------------+--------------------+--------------------+--------------------+--------+
| Msmvttl1 | 0.007 | 0.01 | 0.015 | 0.019 | 0.013 |
| | 1.023 | 1.538 | 2.219 | 2.909 | 6.07 |
| Msmvttl2 | 0.007 | 0.01 | 0.011 | 0.015 | 0.008 |
| | 1.025 | 1.482 | 1.734 | 2.434 | 3.936 |
| Msmvttl3 | 0.004 | 0.008 | 0.01 | 0.012 | 0.007 |
| | 0.71 | 1.31 | 1.684 | 2.064 | 3.571 |
| Msmvttl4 | 0.007 | 0.009 | 0.01 | 0.009 | 0.002 |
| | 1.295 | 1.531 | 1.751 | 1.718 | 1.047 |
| Diff | 0.0 | -0.002 | -0.005 | -0.01 | -0.01 |
| | 0.055 | -0.506 | -1.594 | -3.182 | -4.244 |
+----------+--------------------+--------------------+--------------------+--------------------+--------+
=========================================================================================================
# Risk Adjustment
bi_1_de.factor_adjustment(risk_model)
bi_1_de.print_summary()
=========================================================================================================
+----------+--------------------+--------------------+--------------------+--------------------+--------+
| Group | liquidity_monthly1 | liquidity_monthly2 | liquidity_monthly3 | liquidity_monthly4 | Diff |
+----------+--------------------+--------------------+--------------------+--------------------+--------+
| Msmvttl1 | 0.007 | 0.01 | 0.015 | 0.019 | 0.013 |
| | 1.023 | 1.538 | 2.219 | 2.909 | 6.07 |
| alpha | 0.005 | 0.009 | 0.015 | 0.019 | 0.014 |
| | 0.711 | 1.316 | 2.083 | 2.714 | 7.476 |
| Msmvttl2 | 0.007 | 0.01 | 0.011 | 0.015 | 0.008 |
| | 1.025 | 1.482 | 1.734 | 2.434 | 3.936 |
| alpha | 0.005 | 0.009 | 0.011 | 0.015 | 0.01 |
| | 0.732 | 1.254 | 1.617 | 2.264 | 6.989 |
| Msmvttl3 | 0.004 | 0.008 | 0.01 | 0.012 | 0.007 |
| | 0.71 | 1.31 | 1.684 | 2.064 | 3.571 |
| alpha | 0.004 | 0.007 | 0.009 | 0.013 | 0.009 |
| | 0.569 | 1.1 | 1.367 | 1.945 | 4.717 |
| Msmvttl4 | 0.007 | 0.009 | 0.01 | 0.009 | 0.002 |
| | 1.295 | 1.531 | 1.751 | 1.718 | 1.047 |
| alpha | 0.007 | 0.008 | 0.009 | 0.01 | 0.003 |
| | 1.102 | 1.209 | 1.385 | 1.512 | 1.2 |
| Diff | 0.0 | -0.002 | -0.005 | -0.01 | -0.01 |
| | 0.055 | -0.506 | -1.594 | -3.182 | -4.244 |
| alpha | 0.002 | -0.001 | -0.005 | -0.01 | -0.012 |
| | 0.578 | -0.231 | -1.347 | -2.983 | -5.334 |
+----------+--------------------+--------------------+--------------------+--------------------+--------+
Dataset #2. The result from dataset #2 is consistent with literatures that in univariate analysis the differenced return is significant since the absolute t-value is greater than 2.3, and in bivariate analysis the differenced return in most part is significant since the absolute t-value is greater than 2.3, suggesting that liquidity factor provides excess return. The factor adjustment tends to strengthen the portfolio excess return; while the dependent-sort bivariate tends to strengthen the portfolio excess return.
# %% construct test_data for bivariate analysis
# dataset 2 : tail stocks & ROE Bivariate
from portfolio_analysis import Bivariate, Univariate
import numpy as np
# select stocks whose size is among the up 30% stocks in each month and whose trading
# days are more than or equal to 10 days
test_data_2 = return_company[return_company['Ndaytrd']>=10]
test_data_2 = test_data_2[['emrwd', 'Msmvttl', 'liquidity_monthly', 'Date_merge']].dropna()
test_data_2 = test_data_2[(test_data_2['Date_merge'] >= '2000-01-01') & (test_data_2['Date_merge'] <= '2019-12-01')]
# Univariate analysis
uni_2 = Univariate(np.array(test_data_2[['emrwd', 'liquidity_monthly', 'Date_merge']]), number=9)
uni_2.summary_and_test()
uni_2.print_summary_by_time()
uni_2.print_summary()
=====================================================================
+---------+-------+-------+-------+------+-------+-------+-------+-------+------+-------+-------+
| Group | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Diff |
+---------+-------+-------+-------+------+-------+-------+-------+-------+------+-------+-------+
| Average | 0.006 | 0.007 | 0.008 | 0.01 | 0.012 | 0.014 | 0.014 | 0.016 | 0.02 | 0.028 | 0.023 |
| T-Test | 0.997 | 1.197 | 1.399 | 1.65 | 1.858 | 2.192 | 2.254 | 2.61 | 3.06 | 3.636 | 5.148 |
+---------+-------+-------+-------+------+-------+-------+-------+-------+------+-------+-------+
# Bivariate analysis
bi_2 = Bivariate(np.array(test_data_2), number=3)
bi_2.average_by_time()
bi_2.summary_and_test()
bi_2.print_summary_by_time()
bi_2.print_summary()
======================================================
+-------+--------+--------+--------+--------+--------+
| Group | 1 | 2 | 3 | 4 | Diff |
+-------+--------+--------+--------+--------+--------+
| 1 | 0.011 | 0.017 | 0.02 | 0.028 | 0.017 |
| | 1.591 | 2.43 | 2.761 | 3.556 | 5.125 |
| 2 | 0.006 | 0.009 | 0.014 | 0.019 | 0.013 |
| | 0.898 | 1.295 | 2.098 | 2.88 | 6.09 |
| 3 | 0.006 | 0.009 | 0.011 | 0.016 | 0.01 |
| | 0.876 | 1.491 | 1.839 | 2.643 | 4.418 |
| 4 | 0.008 | 0.009 | 0.01 | 0.012 | 0.004 |
| | 1.389 | 1.637 | 1.916 | 2.019 | 1.351 |
| Diff | -0.003 | -0.008 | -0.009 | -0.016 | -0.012 |
| | -0.871 | -2.214 | -2.66 | -3.303 | -3.088 |
+-------+--------+--------+--------+--------+--------+
======================================================
# Risk Adjustment
risk_model = risk_premium[['MKT', 'SMB', 'HML']]
risk_model = risk_model['2000':'2019']
bi_2.factor_adjustment(risk_model)
bi_2.print_summary()
======================================================
+-------+--------+--------+--------+--------+--------+
| Group | 1 | 2 | 3 | 4 | Diff |
+-------+--------+--------+--------+--------+--------+
| 1 | 0.011 | 0.017 | 0.02 | 0.028 | 0.017 |
| | 1.591 | 2.43 | 2.761 | 3.556 | 5.125 |
| alpha | 0.008 | 0.014 | 0.018 | 0.028 | 0.019 |
| | 1.058 | 1.833 | 2.325 | 3.006 | 5.448 |
| 2 | 0.006 | 0.009 | 0.014 | 0.019 | 0.013 |
| | 0.898 | 1.295 | 2.098 | 2.88 | 6.09 |
| alpha | 0.004 | 0.008 | 0.014 | 0.019 | 0.015 |
| | 0.581 | 1.046 | 1.901 | 2.678 | 8.767 |
| 3 | 0.006 | 0.009 | 0.011 | 0.016 | 0.01 |
| | 0.876 | 1.491 | 1.839 | 2.643 | 4.418 |
| alpha | 0.004 | 0.008 | 0.011 | 0.017 | 0.013 |
| | 0.638 | 1.257 | 1.72 | 2.397 | 5.888 |
| 4 | 0.008 | 0.009 | 0.01 | 0.012 | 0.004 |
| | 1.389 | 1.637 | 1.916 | 2.019 | 1.351 |
| alpha | 0.007 | 0.009 | 0.011 | 0.013 | 0.005 |
| | 1.127 | 1.37 | 1.783 | 1.836 | 1.338 |
| Diff | -0.003 | -0.008 | -0.009 | -0.016 | -0.012 |
| | -0.871 | -2.214 | -2.66 | -3.303 | -3.088 |
| alpha | -0.001 | -0.005 | -0.007 | -0.015 | -0.014 |
| | -0.221 | -1.295 | -2.076 | -3.332 | -3.3 |
+-------+--------+--------+--------+--------+--------+
======================================================
# Dependent-sort Bivariate Analysis
bi_2_de = Bivariate(test_data_2, number=3)
bi_2_de.fit(conditional=True)
bi_2_de.print_summary()
=========================================================================================================
+----------+--------------------+--------------------+--------------------+--------------------+--------+
| Group | liquidity_monthly1 | liquidity_monthly2 | liquidity_monthly3 | liquidity_monthly4 | Diff |
+----------+--------------------+--------------------+--------------------+--------------------+--------+
| Msmvttl1 | 0.016 | 0.02 | 0.023 | 0.033 | 0.017 |
| | 2.34 | 2.849 | 3.245 | 3.669 | 3.395 |
| Msmvttl2 | 0.007 | 0.011 | 0.015 | 0.02 | 0.012 |
| | 1.08 | 1.657 | 2.211 | 2.972 | 6.519 |
| Msmvttl3 | 0.006 | 0.009 | 0.011 | 0.015 | 0.009 |
| | 0.891 | 1.359 | 1.74 | 2.438 | 4.372 |
| Msmvttl4 | 0.006 | 0.009 | 0.009 | 0.01 | 0.004 |
| | 1.123 | 1.528 | 1.545 | 1.867 | 1.954 |
| Diff | -0.01 | -0.012 | -0.014 | -0.023 | -0.013 |
| | -2.632 | -3.118 | -3.94 | -3.842 | -2.543 |
+----------+--------------------+--------------------+--------------------+--------------------+--------+
=========================================================================================================
# Risk Adjustment
bi_2_de.factor_adjustment(risk_model)
bi_2_de.print_summary()
=========================================================================================================
+----------+--------------------+--------------------+--------------------+--------------------+--------+
| Group | liquidity_monthly1 | liquidity_monthly2 | liquidity_monthly3 | liquidity_monthly4 | Diff |
+----------+--------------------+--------------------+--------------------+--------------------+--------+
| Msmvttl1 | 0.016 | 0.02 | 0.023 | 0.033 | 0.017 |
| | 2.34 | 2.849 | 3.245 | 3.669 | 3.395 |
| alpha | 0.014 | 0.019 | 0.022 | 0.033 | 0.02 |
| | 1.78 | 2.364 | 2.831 | 2.978 | 3.475 |
| Msmvttl2 | 0.007 | 0.011 | 0.015 | 0.02 | 0.012 |
| | 1.08 | 1.657 | 2.211 | 2.972 | 6.519 |
| alpha | 0.006 | 0.01 | 0.015 | 0.02 | 0.014 |
| | 0.774 | 1.422 | 2.062 | 2.766 | 8.405 |
| Msmvttl3 | 0.006 | 0.009 | 0.011 | 0.015 | 0.009 |
| | 0.891 | 1.359 | 1.74 | 2.438 | 4.372 |
| alpha | 0.004 | 0.008 | 0.011 | 0.015 | 0.011 |
| | 0.649 | 1.104 | 1.604 | 2.25 | 6.684 |
| Msmvttl4 | 0.006 | 0.009 | 0.009 | 0.01 | 0.004 |
| | 1.123 | 1.528 | 1.545 | 1.867 | 1.954 |
| alpha | 0.006 | 0.008 | 0.008 | 0.011 | 0.005 |
| | 0.944 | 1.226 | 1.255 | 1.676 | 2.097 |
| Diff | -0.01 | -0.012 | -0.014 | -0.023 | -0.013 |
| | -2.632 | -3.118 | -3.94 | -3.842 | -2.543 |
| alpha | -0.007 | -0.011 | -0.013 | -0.023 | -0.015 |
| | -1.668 | -2.359 | -2.76 | -3.655 | -2.894 |
+----------+--------------------+--------------------+--------------------+--------------------+--------+
Skewness Factor
In Markowitz's (1952) mean-variance paradigm, only mean and variance are considered by investor for form a portfolio, and from the paradigm CAPM is developed. Skewness, the third moment, of return is introduced by Arditti (1967, 1971), who shows that investors demand a higher rate of return on investments whose return distributions are negatively skewed. Scott and Horvath (1980) extend the analysis to include other higher moments of return.
Harvey and Siddique (2000) introduce systematic skewness into the pricing of securities and therefore divide the total skewness into systematic skewness (aka co-skewness) and idiosyncratic skewness. It is often found that co-skewness is negatively correlated with stocks' future return and idiosyncratic skewness is diversified which is challenged by some literatures (Kane, 1982; Barberis and Huang, 2008).
Total Skewness is defined as $$ Skew_i=\frac{\frac 1n\sum_{t=1}^n(R_{i,t}-\bar R_i)^3}{(\frac 1n\sum_{t=1}^n(R_{i,t}-\bar R_i)^2)^{\frac 32}}. $$ Coskewness (Systematic skewness) is defined as (Harvey and Siddique, 2000) $$ r_{i,t}=\alpha_i+\beta_{MKT, i}MKT_t+Coskew_iMKT_t^2+\epsilon_{i,t}. $$ Idiosyncratic skewness is defined as $$ IdioSkew_i=\frac{\frac 1n\sum_{t=1}^n(\epsilon_{i,t}-\bar \epsilon_i)^3}{(\frac 1n\sum_{t=1}^n(\epsilon_{i,t}-\bar \epsilon_i)^2)^{\frac 32}}, $$ where the residuals are from the regression model $$ r_{i,t}=\alpha_i+\beta_{MKT, i}MKT_t+\beta_{SMB,i}SMB_t+\beta_{HML,i}HML_t+\epsilon_{i,t}. $$ The calculation period is 12 months. In this demo, the dataset starts from Jan, 2000 and is collected from CSMAR dataset. WARNING: Do Not use dataset in this demo for any commercial purpose.
# %% set system path
import sys,os
sys.path.append(os.path.abspath(".."))
# %% import data
import pandas as pd
month_return = pd.read_hdf('.\\data\\month_return.h5', key='month_return')
company_data = pd.read_hdf('.\\data\\last_filter_pe.h5', key='data')
trade_data = pd.read_hdf('.\\data\\mean_filter_trade.h5', key='data')
beta = pd.read_hdf('.\\data\\beta.h5', key='data')
risk_premium = pd.read_hdf('.\\data\\risk_premium.h5', key='data')
Data preprocessing
# %% data preprocessing
# forward the monthly return for each stock
# emrwd is the return including dividend
month_return['emrwd'] = month_return.groupby(['Stkcd'])['Mretwd'].shift(-1)
# emrnd is the return including no dividend
month_return['emrnd'] = month_return.groupby(['Stkcd'])['Mretnd'].shift(-1)
# select the A share stock
month_return = month_return[month_return['Markettype'].isin([1, 4, 16])]
# % distinguish the stocks whose size is among the up 30% stocks in each month
def percentile(stocks) :
return stocks >= stocks.quantile(q=.3)
month_return['cap'] = month_return.groupby(['Trdmnt'])['Msmvttl'].apply(percentile)
# merge data
data = month_return[['Stkcd', 'Trdmnt', 'Mretwd']]
data['Date_merge'] = pd.to_datetime(data['Trdmnt'])
risk_premium['Date_merge'] = risk_premium.index
data = pd.merge(data, risk_premium[['MKT', 'SMB', 'HML', 'Date_merge']], on=['Date_merge']).dropna()
Construct proxy variable
# %% construct proxy variable
import numpy as np
import statsmodels.api as sm
from scipy.stats import skew
skewness = pd.Series(index=data.index, dtype=float, name='skewness')
coskewness = pd.Series(index=data.index, dtype=float, name='coskewness')
idioskewness = pd.Series(index=data.index, dtype=float, name='idioskewness')
for i in data.groupby('Stkcd'):
row, col = np.shape(i[1])
for j in range(row-12):
skewness.loc[i[1].index[j+11]] = skew(i[1].iloc[j:j+12, 2])
endog = np.array([i[1].iloc[j:j+12, 4], i[1].iloc[j:j+12, 4]**2]).T
model_coskew = sm.OLS(i[1].iloc[j:j+12, 2], sm.add_constant(endog)).fit()
coskewness.loc[i[1].index[j+11]] = model_coskew.params[2]
model_idioskew = sm.OLS(i[1].iloc[j:j+12, 2], sm.add_constant(i[1].iloc[j:j+12, 4:7])).fit()
idioskewness.loc[i[1].index[j+11]] = skew(model_idioskew.resid)
return_company = pd.concat([data, skewness, coskewness, idioskewness, month_return[['cap', 'Msmvttl', 'Ndaytrd', 'emrwd']]], axis=1)
Total Skewness. The result from dataset #1 is inconsistent with literatures that in univariate analysis though the differenced return is significant since the absolute t-value is greater than 2.3, but the order of return sequence show no consistency.
In bivariate analysis the differenced return is insignificant since the absolute t-value is less than 2.3, suggesting that total skewness factor provides no excess return. The factor adjustment tends to weaken the portfolio excess return; while the dependent-sort bivariate tends to strengthen the portfolio excess return.
# %% construct test_data for bivariate analysis
# dataset 1
from portfolio_analysis import Bivariate, Univariate
import numpy as np
# select stocks whose size is among the up 30% stocks in each month and whose trading
# days are more than or equal to 10 days
test_data_1 = return_company[(return_company['cap']==True) & (return_company['Ndaytrd']>=10)]
test_data_1 = test_data_1[['emrwd', 'Msmvttl', 'skewness', 'Date_merge']].dropna()
test_data_1 = test_data_1[(test_data_1['Date_merge'] >= '2000-01-01') & (test_data_1['Date_merge'] <= '2019-12-01')]
# Univariate analysis
uni_1 = Univariate(np.array(test_data_1[['emrwd', 'skewness', 'Date_merge']]), number=9)
uni_1.summary_and_test()
uni_1.print_summary_by_time()
uni_1.print_summary()
=====================================================================
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+
| Group | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Diff |
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+
| Average | 0.008 | 0.008 | 0.007 | 0.009 | 0.007 | 0.009 | 0.009 | 0.009 | 0.008 | 0.011 | 0.003 |
| T-Test | 8.576 | 8.419 | 7.786 | 9.093 | 7.652 | 9.199 | 9.362 | 8.877 | 8.584 | 10.6 | 2.362 |
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+
# Bivariate analysis
bi_1 = Bivariate(np.array(test_data_1), number=4)
bi_1.average_by_time()
bi_1.summary_and_test()
bi_1.print_summary_by_time()
bi_1.print_summary()
====================================================================
+-------+---------+---------+---------+---------+---------+--------+
| Group | 1 | 2 | 3 | 4 | 5 | Diff |
+-------+---------+---------+---------+---------+---------+--------+
| 1 | 0.024 | 0.022 | 0.021 | 0.023 | 0.025 | 0.001 |
| | 14.565 | 13.84 | 13.484 | 14.584 | 14.149 | 0.323 |
| 2 | 0.008 | 0.013 | 0.01 | 0.012 | 0.012 | 0.004 |
| | 5.627 | 9.234 | 6.737 | 8.375 | 7.731 | 1.911 |
| 3 | 0.007 | 0.006 | 0.007 | 0.009 | 0.008 | 0.0 |
| | 4.488 | 4.209 | 4.475 | 6.156 | 5.395 | 0.111 |
| 4 | 0.004 | 0.006 | 0.006 | 0.004 | 0.006 | 0.001 |
| | 2.697 | 3.714 | 3.905 | 2.497 | 3.58 | 0.535 |
| 5 | -0.003 | -0.004 | -0.003 | -0.003 | -0.002 | 0.0 |
| | -1.843 | -2.713 | -1.823 | -2.029 | -1.567 | 0.228 |
| Diff | -0.027 | -0.026 | -0.024 | -0.026 | -0.027 | -0.0 |
| | -11.849 | -11.725 | -10.724 | -11.715 | -12.268 | -0.094 |
+-------+---------+---------+---------+---------+---------+--------+
====================================================================
# Risk Adjustment
risk_model = risk_premium[['MKT', 'SMB', 'HML']]
risk_model = risk_model['2000':'2019']
bi_1.factor_adjustment(risk_model)
bi_1.print_summary()
===================================================================
+-------+---------+---------+--------+---------+---------+--------+
| Group | 1 | 2 | 3 | 4 | 5 | Diff |
+-------+---------+---------+--------+---------+---------+--------+
| 1 | 0.026 | 0.023 | 0.022 | 0.026 | 0.026 | 0.0 |
| | 12.803 | 14.141 | 13.638 | 16.104 | 15.155 | 0.183 |
| alpha | 0.026 | 0.023 | 0.022 | 0.025 | 0.026 | 0.0 |
| | 10.87 | 10.593 | 10.481 | 11.664 | 11.215 | 0.099 |
| 2 | 0.01 | 0.013 | 0.011 | 0.012 | 0.013 | 0.003 |
| | 6.505 | 9.595 | 6.935 | 8.557 | 8.474 | 1.51 |
| alpha | 0.01 | 0.013 | 0.011 | 0.012 | 0.013 | 0.003 |
| | 5.658 | 8.328 | 6.28 | 8.797 | 7.819 | 1.078 |
| 3 | 0.008 | 0.007 | 0.007 | 0.01 | 0.008 | 0.0 |
| | 4.625 | 4.855 | 4.591 | 6.799 | 5.666 | 0.123 |
| alpha | 0.007 | 0.007 | 0.007 | 0.009 | 0.008 | 0.001 |
| | 4.946 | 4.67 | 6.211 | 5.793 | 6.825 | 0.448 |
| 4 | 0.004 | 0.006 | 0.007 | 0.003 | 0.005 | 0.001 |
| | 2.596 | 4.007 | 4.413 | 2.268 | 3.239 | 0.413 |
| alpha | 0.004 | 0.007 | 0.007 | 0.004 | 0.006 | 0.002 |
| | 2.351 | 4.104 | 3.081 | 2.18 | 3.105 | 0.781 |
| 5 | -0.003 | -0.005 | -0.003 | -0.003 | -0.003 | 0.0 |
| | -1.882 | -3.172 | -1.897 | -2.287 | -2.015 | 0.007 |
| alpha | -0.003 | -0.005 | -0.003 | -0.004 | -0.003 | -0.0 |
| | -1.799 | -2.836 | -1.467 | -3.032 | -1.838 | -0.008 |
| Diff | -0.029 | -0.028 | -0.025 | -0.029 | -0.029 | -0.0 |
| | -11.138 | -12.246 | -10.82 | -13.018 | -13.407 | -0.142 |
| alpha | -0.029 | -0.028 | -0.025 | -0.029 | -0.029 | -0.0 |
| | -10.215 | -10.218 | -7.54 | -12.935 | -9.892 | -0.111 |
+-------+---------+---------+--------+---------+---------+--------+
===================================================================
# Dependent-sort Bivariate Analysis
bi_1_de = Bivariate(test_data_1, number=4)
bi_1_de.fit(conditional=True)
bi_1_de.print_summary()
=================================================================================
+----------+-----------+-----------+-----------+-----------+-----------+--------+
| Group | skewness1 | skewness2 | skewness3 | skewness4 | skewness5 | Diff |
+----------+-----------+-----------+-----------+-----------+-----------+--------+
| Msmvttl1 | 0.025 | 0.022 | 0.025 | 0.024 | 0.027 | 0.002 |
| | 13.883 | 14.068 | 14.984 | 15.097 | 15.046 | 0.781 |
| Msmvttl2 | 0.01 | 0.014 | 0.01 | 0.01 | 0.014 | 0.004 |
| | 6.404 | 10.045 | 6.751 | 7.626 | 9.445 | 2.245 |
| Msmvttl3 | 0.007 | 0.007 | 0.007 | 0.01 | 0.008 | 0.001 |
| | 4.608 | 5.092 | 4.79 | 6.592 | 5.893 | 0.282 |
| Msmvttl4 | 0.004 | 0.005 | 0.008 | 0.005 | 0.006 | 0.001 |
| | 2.63 | 3.031 | 4.702 | 2.846 | 3.566 | 0.488 |
| Msmvttl5 | -0.003 | -0.004 | -0.004 | -0.003 | -0.004 | -0.001 |
| | -1.963 | -2.304 | -2.524 | -1.95 | -2.531 | -0.338 |
| Diff | -0.028 | -0.026 | -0.029 | -0.027 | -0.031 | -0.003 |
| | -11.528 | -11.245 | -13.18 | -12.68 | -13.898 | -0.829 |
+----------+-----------+-----------+-----------+-----------+-----------+--------+
=================================================================================
# Risk Adjustment
bi_1_de.factor_adjustment(risk_model)
bi_1_de.print_summary()
=================================================================================
+----------+-----------+-----------+-----------+-----------+-----------+--------+
| Group | skewness1 | skewness2 | skewness3 | skewness4 | skewness5 | Diff |
+----------+-----------+-----------+-----------+-----------+-----------+--------+
| Msmvttl1 | 0.025 | 0.022 | 0.025 | 0.024 | 0.027 | 0.002 |
| | 13.883 | 14.068 | 14.984 | 15.097 | 15.046 | 0.781 |
| alpha | 0.025 | 0.022 | 0.026 | 0.024 | 0.027 | 0.001 |
| | 11.528 | 11.107 | 11.127 | 10.555 | 11.258 | 0.502 |
| Msmvttl2 | 0.01 | 0.014 | 0.01 | 0.01 | 0.014 | 0.004 |
| | 6.404 | 10.045 | 6.751 | 7.626 | 9.445 | 2.245 |
| alpha | 0.01 | 0.013 | 0.01 | 0.01 | 0.014 | 0.004 |
| | 5.098 | 9.066 | 5.474 | 6.922 | 8.522 | 1.442 |
| Msmvttl3 | 0.007 | 0.007 | 0.007 | 0.01 | 0.008 | 0.001 |
| | 4.608 | 5.092 | 4.79 | 6.592 | 5.893 | 0.282 |
| alpha | 0.007 | 0.007 | 0.008 | 0.009 | 0.008 | 0.001 |
| | 5.135 | 4.941 | 8.396 | 6.303 | 6.523 | 0.485 |
| Msmvttl4 | 0.004 | 0.005 | 0.008 | 0.005 | 0.006 | 0.001 |
| | 2.63 | 3.031 | 4.702 | 2.846 | 3.566 | 0.488 |
| alpha | 0.004 | 0.005 | 0.008 | 0.005 | 0.006 | 0.002 |
| | 2.421 | 3.472 | 3.252 | 2.208 | 3.591 | 0.862 |
| Msmvttl5 | -0.003 | -0.004 | -0.004 | -0.003 | -0.004 | -0.001 |
| | -1.963 | -2.304 | -2.524 | -1.95 | -2.531 | -0.338 |
| alpha | -0.003 | -0.004 | -0.003 | -0.004 | -0.003 | -0.0 |
| | -2.13 | -2.176 | -2.126 | -2.867 | -2.394 | -0.216 |
| Diff | -0.028 | -0.026 | -0.029 | -0.027 | -0.031 | -0.003 |
| | -11.528 | -11.245 | -13.18 | -12.68 | -13.898 | -0.829 |
| alpha | -0.028 | -0.025 | -0.029 | -0.028 | -0.03 | -0.002 |
| | -10.231 | -9.896 | -9.87 | -11.904 | -10.194 | -0.604 |
+----------+-----------+-----------+-----------+-----------+-----------+--------+
Co-skewness. The result from dataset #2 is inconsistent with literatures that in univariate analysis though the differenced return is significant since the absolute t-value is greater than 2.3, but the order of return sequence show no consistency.
In bivariate analysis the differenced return is insignificant since the absolute t-value is less than 2.3, suggesting that co-skewness factor provides no excess return. The factor adjustment tends to weaken the portfolio excess return; while the dependent-sort bivariate tends to strengthen the portfolio excess return.
# %% construct test_data for bivariate analysis
# dataset 2
from portfolio_analysis import Bivariate, Univariate
import numpy as np
# select stocks whose size is among the up 30% stocks in each month and whose trading
# days are more than or equal to 10 days
test_data_2 = return_company[(return_company['cap']==True) & (return_company['Ndaytrd']>=10)]
test_data_2 = test_data_2[['emrwd', 'Msmvttl', 'coskewness', 'Date_merge']].dropna()
test_data_2 = test_data_2[(test_data_2['Date_merge'] >= '2000-01-01') & (test_data_2['Date_merge'] <= '2019-12-01')]
# Univariate analysis
uni_2 = Univariate(np.array(test_data_2[['emrwd', 'coskewness', 'Date_merge']]), number=9)
uni_2.summary_and_test()
uni_2.print_summary_by_time()
uni_2.print_summary()
=====================================================================
+---------+-------+-------+-------+-------+-------+-------+-------+-------+--------+-------+-------+
| Group | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Diff |
+---------+-------+-------+-------+-------+-------+-------+-------+-------+--------+-------+-------+
| Average | 0.008 | 0.009 | 0.007 | 0.01 | 0.007 | 0.009 | 0.009 | 0.008 | 0.009 | 0.011 | 0.003 |
| T-Test | 8.241 | 9.001 | 7.365 | 9.666 | 7.632 | 9.234 | 9.014 | 8.691 | 10.114 | 11.73 | 2.595 |
+---------+-------+-------+-------+-------+-------+-------+-------+-------+--------+-------+-------+
# Bivariate analysis
bi_2 = Bivariate(np.array(test_data_2), number=4)
bi_2.average_by_time()
bi_2.summary_and_test()
bi_2.print_summary_by_time()
bi_2.print_summary()
==================================================================
+-------+---------+---------+--------+--------+---------+--------+
| Group | 1 | 2 | 3 | 4 | 5 | Diff |
+-------+---------+---------+--------+--------+---------+--------+
| 1 | 0.022 | 0.022 | 0.023 | 0.022 | 0.025 | 0.003 |
| | 14.748 | 13.599 | 15.127 | 13.191 | 13.98 | 1.465 |
| 2 | 0.009 | 0.012 | 0.009 | 0.011 | 0.013 | 0.004 |
| | 6.551 | 8.696 | 5.983 | 7.881 | 9.526 | 1.958 |
| 3 | 0.007 | 0.008 | 0.007 | 0.008 | 0.006 | -0.001 |
| | 4.559 | 4.966 | 4.612 | 5.373 | 4.528 | -0.26 |
| 4 | 0.006 | 0.005 | 0.004 | 0.005 | 0.006 | 0.0 |
| | 3.778 | 2.985 | 2.629 | 3.513 | 3.853 | 0.02 |
| 5 | -0.002 | -0.004 | -0.002 | -0.004 | -0.002 | 0.0 |
| | -1.129 | -2.603 | -1.222 | -2.493 | -1.143 | 0.011 |
| Diff | -0.024 | -0.026 | -0.025 | -0.026 | -0.027 | -0.003 |
| | -11.291 | -11.861 | -11.57 | -11.34 | -11.015 | -1.08 |
+-------+---------+---------+--------+--------+---------+--------+
==================================================================
# Risk Adjustment
risk_model = risk_premium[['MKT', 'SMB', 'HML']]
risk_model = risk_model['2000':'2019']
bi_2.factor_adjustment(risk_model)
bi_2.print_summary()
==================================================================
+-------+---------+---------+--------+--------+---------+--------+
| Group | 1 | 2 | 3 | 4 | 5 | Diff |
+-------+---------+---------+--------+--------+---------+--------+
| 1 | 0.022 | 0.022 | 0.023 | 0.022 | 0.025 | 0.003 |
| | 14.748 | 13.599 | 15.127 | 13.191 | 13.98 | 1.465 |
| alpha | 0.022 | 0.022 | 0.023 | 0.022 | 0.026 | 0.003 |
| | 11.225 | 11.137 | 10.08 | 9.801 | 9.568 | 1.311 |
| 2 | 0.009 | 0.012 | 0.009 | 0.011 | 0.013 | 0.004 |
| | 6.551 | 8.696 | 5.983 | 7.881 | 9.526 | 1.958 |
| alpha | 0.01 | 0.012 | 0.009 | 0.01 | 0.013 | 0.003 |
| | 7.241 | 8.351 | 5.363 | 8.371 | 8.967 | 1.73 |
| 3 | 0.007 | 0.008 | 0.007 | 0.008 | 0.006 | -0.001 |
| | 4.559 | 4.966 | 4.612 | 5.373 | 4.528 | -0.26 |
| alpha | 0.008 | 0.007 | 0.006 | 0.007 | 0.007 | -0.001 |
| | 4.378 | 5.254 | 4.569 | 4.778 | 3.691 | -0.335 |
| 4 | 0.006 | 0.005 | 0.004 | 0.005 | 0.006 | 0.0 |
| | 3.778 | 2.985 | 2.629 | 3.513 | 3.853 | 0.02 |
| alpha | 0.007 | 0.005 | 0.004 | 0.004 | 0.007 | 0.001 |
| | 3.74 | 2.782 | 2.635 | 3.258 | 3.772 | 0.382 |
| 5 | -0.002 | -0.004 | -0.002 | -0.004 | -0.002 | 0.0 |
| | -1.129 | -2.603 | -1.222 | -2.493 | -1.143 | 0.011 |
| alpha | -0.001 | -0.004 | -0.002 | -0.005 | -0.001 | 0.0 |
| | -0.81 | -2.895 | -1.374 | -2.329 | -0.753 | 0.099 |
| Diff | -0.024 | -0.026 | -0.025 | -0.026 | -0.027 | -0.003 |
| | -11.291 | -11.861 | -11.57 | -11.34 | -11.015 | -1.08 |
| alpha | -0.023 | -0.026 | -0.025 | -0.027 | -0.027 | -0.003 |
| | -8.296 | -11.797 | -8.175 | -9.631 | -8.631 | -1.096 |
+-------+---------+---------+--------+--------+---------+--------+
==================================================================
# Dependent-sort Bivariate Analysis
bi_2_de = Bivariate(test_data_2, number=4)
bi_2_de.fit(conditional=True)
bi_2_de.print_summary()
===========================================================================================
+----------+-------------+-------------+-------------+-------------+-------------+--------+
| Group | coskewness1 | coskewness2 | coskewness3 | coskewness4 | coskewness5 | Diff |
+----------+-------------+-------------+-------------+-------------+-------------+--------+
| Msmvttl1 | 0.022 | 0.023 | 0.023 | 0.021 | 0.026 | 0.004 |
| | 15.027 | 14.737 | 13.893 | 12.808 | 13.624 | 1.668 |
| Msmvttl2 | 0.01 | 0.012 | 0.009 | 0.011 | 0.013 | 0.003 |
| | 6.71 | 8.817 | 5.996 | 7.893 | 9.698 | 1.662 |
| Msmvttl3 | 0.008 | 0.007 | 0.006 | 0.008 | 0.007 | -0.001 |
| | 5.212 | 4.467 | 4.333 | 5.813 | 4.943 | -0.455 |
| Msmvttl4 | 0.007 | 0.004 | 0.003 | 0.006 | 0.007 | -0.0 |
| | 3.996 | 2.765 | 1.95 | 3.507 | 4.153 | -0.066 |
| Msmvttl5 | -0.003 | -0.004 | -0.002 | -0.004 | -0.002 | 0.001 |
| | -1.756 | -2.163 | -1.366 | -3.015 | -1.135 | 0.516 |
| Diff | -0.024 | -0.027 | -0.025 | -0.026 | -0.027 | -0.003 |
| | -11.754 | -12.865 | -11.688 | -11.242 | -11.09 | -0.938 |
+----------+-------------+-------------+-------------+-------------+-------------+--------+
===========================================================================================
# Risk Adjustment
bi_2_de.factor_adjustment(risk_model)
bi_2_de.print_summary()
===========================================================================================
+----------+-------------+-------------+-------------+-------------+-------------+--------+
| Group | coskewness1 | coskewness2 | coskewness3 | coskewness4 | coskewness5 | Diff |
+----------+-------------+-------------+-------------+-------------+-------------+--------+
| Msmvttl1 | 0.022 | 0.023 | 0.023 | 0.021 | 0.026 | 0.004 |
| | 15.027 | 14.737 | 13.893 | 12.808 | 13.624 | 1.668 |
| alpha | 0.022 | 0.023 | 0.023 | 0.021 | 0.026 | 0.004 |
| | 11.154 | 11.054 | 11.059 | 9.445 | 9.471 | 1.442 |
| Msmvttl2 | 0.01 | 0.012 | 0.009 | 0.011 | 0.013 | 0.003 |
| | 6.71 | 8.817 | 5.996 | 7.893 | 9.698 | 1.662 |
| alpha | 0.01 | 0.011 | 0.009 | 0.01 | 0.013 | 0.003 |
| | 6.977 | 9.706 | 5.931 | 6.934 | 9.711 | 1.632 |
| Msmvttl3 | 0.008 | 0.007 | 0.006 | 0.008 | 0.007 | -0.001 |
| | 5.212 | 4.467 | 4.333 | 5.813 | 4.943 | -0.455 |
| alpha | 0.008 | 0.006 | 0.006 | 0.008 | 0.007 | -0.001 |
| | 5.329 | 4.418 | 3.825 | 5.402 | 4.479 | -0.545 |
| Msmvttl4 | 0.007 | 0.004 | 0.003 | 0.006 | 0.007 | -0.0 |
| | 3.996 | 2.765 | 1.95 | 3.507 | 4.153 | -0.066 |
| alpha | 0.007 | 0.004 | 0.003 | 0.005 | 0.008 | 0.001 |
| | 4.072 | 2.478 | 2.034 | 2.543 | 4.116 | 0.344 |
| Msmvttl5 | -0.003 | -0.004 | -0.002 | -0.004 | -0.002 | 0.001 |
| | -1.756 | -2.163 | -1.366 | -3.015 | -1.135 | 0.516 |
| alpha | -0.002 | -0.004 | -0.003 | -0.005 | -0.001 | 0.001 |
| | -1.32 | -2.634 | -1.364 | -2.641 | -0.87 | 0.343 |
| Diff | -0.024 | -0.027 | -0.025 | -0.026 | -0.027 | -0.003 |
| | -11.754 | -12.865 | -11.688 | -11.242 | -11.09 | -0.938 |
| alpha | -0.024 | -0.027 | -0.026 | -0.026 | -0.027 | -0.003 |
| | -8.363 | -11.398 | -8.568 | -9.063 | -9.138 | -1.054 |
+----------+-------------+-------------+-------------+-------------+-------------+--------+
Idiosyncratic skewness. The result from dataset #3 is consistent with literatures that in univariate analysis the differenced return is insignificant since the absolute t-value is less than 2.3.
In bivariate analysis the differenced return is insignificant since the absolute t-value is less than 2.3, suggesting that idiosyncratic skewness factor provides no excess return. The factor adjustment tends to weaken the portfolio excess return; while the dependent-sort bivariate tends to strengthen the portfolio excess return.
# %% construct test_data for bivariate analysis
# dataset 3
from portfolio_analysis import Bivariate, Univariate
import numpy as np
# select stocks whose size is among the up 30% stocks in each month and whose trading
# days are more than or equal to 10 days
test_data_3 = return_company[(return_company['cap']==True) & (return_company['Ndaytrd']>=10)]
test_data_3 = test_data_3[['emrwd', 'Msmvttl', 'idioskewness', 'Date_merge']].dropna()
test_data_3 = test_data_3[(test_data_3['Date_merge'] >= '2000-01-01') & (test_data_3['Date_merge'] <= '2019-12-01')]
# Univariate analysis
uni_3 = Univariate(np.array(test_data_3[['emrwd', 'idioskewness', 'Date_merge']]), number=9)
uni_3.summary_and_test()
uni_3.print_summary_by_time()
uni_3.print_summary()
=====================================================================
+---------+--------+-------+-------+-------+-------+--------+-------+-------+-------+-------+-------+
| Group | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Diff |
+---------+--------+-------+-------+-------+-------+--------+-------+-------+-------+-------+-------+
| Average | 0.01 | 0.008 | 0.008 | 0.009 | 0.009 | 0.011 | 0.006 | 0.009 | 0.008 | 0.01 | 0.001 |
| T-Test | 10.385 | 7.249 | 8.548 | 9.025 | 8.954 | 11.601 | 6.609 | 9.145 | 7.674 | 9.964 | 0.43 |
+---------+--------+-------+-------+-------+-------+--------+-------+-------+-------+-------+-------+
# Bivariate analysis
bi_3 = Bivariate(np.array(test_data_3), number=4)
bi_3.average_by_time()
bi_3.summary_and_test()
bi_3.print_summary_by_time()
bi_3.print_summary()
=====================================================================
+-------+---------+---------+---------+---------+---------+--------+
| Group | 1 | 2 | 3 | 4 | 5 | Diff |
+-------+---------+---------+---------+---------+---------+--------+
| 1 | 0.023 | 0.021 | 0.026 | 0.02 | 0.026 | 0.003 |
| | 12.798 | 13.936 | 15.498 | 13.077 | 13.947 | 1.32 |
| 2 | 0.012 | 0.011 | 0.012 | 0.01 | 0.01 | -0.002 |
| | 7.916 | 7.402 | 8.251 | 7.194 | 6.609 | -1.04 |
| 3 | 0.008 | 0.009 | 0.008 | 0.004 | 0.008 | -0.0 |
| | 5.345 | 6.356 | 4.972 | 2.965 | 5.339 | -0.032 |
| 4 | 0.005 | 0.003 | 0.006 | 0.007 | 0.005 | 0.0 |
| | 3.067 | 2.279 | 3.414 | 4.156 | 3.488 | 0.205 |
| 5 | -0.003 | -0.002 | -0.002 | -0.003 | -0.003 | -0.0 |
| | -2.029 | -1.535 | -1.256 | -1.865 | -2.183 | -0.138 |
| Diff | -0.026 | -0.023 | -0.028 | -0.023 | -0.029 | -0.003 |
| | -10.992 | -10.301 | -12.114 | -10.841 | -12.072 | -1.123 |
+-------+---------+---------+---------+---------+---------+--------+
# Risk Adjustment
risk_model = risk_premium[['MKT', 'SMB', 'HML']]
risk_model = risk_model['2000':'2019']
bi_3.factor_adjustment(risk_model)
bi_3.print_summary()
====================================================================
+-------+---------+---------+---------+---------+---------+--------+
| Group | 1 | 2 | 3 | 4 | 5 | Diff |
+-------+---------+---------+---------+---------+---------+--------+
| 1 | 0.023 | 0.021 | 0.026 | 0.02 | 0.026 | 0.003 |
| | 12.798 | 13.936 | 15.498 | 13.077 | 13.947 | 1.32 |
| alpha | 0.023 | 0.02 | 0.026 | 0.02 | 0.026 | 0.003 |
| | 9.487 | 13.54 | 12.17 | 10.378 | 8.92 | 1.256 |
| 2 | 0.012 | 0.011 | 0.012 | 0.01 | 0.01 | -0.002 |
| | 7.916 | 7.402 | 8.251 | 7.194 | 6.609 | -1.04 |
| alpha | 0.012 | 0.011 | 0.012 | 0.011 | 0.009 | -0.002 |
| | 7.981 | 6.271 | 7.674 | 5.908 | 6.248 | -1.234 |
| 3 | 0.008 | 0.009 | 0.008 | 0.004 | 0.008 | -0.0 |
| | 5.345 | 6.356 | 4.972 | 2.965 | 5.339 | -0.032 |
| alpha | 0.008 | 0.009 | 0.007 | 0.005 | 0.007 | -0.001 |
| | 4.75 | 6.149 | 4.293 | 3.236 | 5.673 | -0.338 |
| 4 | 0.005 | 0.003 | 0.006 | 0.007 | 0.005 | 0.0 |
| | 3.067 | 2.279 | 3.414 | 4.156 | 3.488 | 0.205 |
| alpha | 0.005 | 0.004 | 0.006 | 0.006 | 0.006 | 0.001 |
| | 2.598 | 2.4 | 3.689 | 2.833 | 4.091 | 0.538 |
| 5 | -0.003 | -0.002 | -0.002 | -0.003 | -0.003 | -0.0 |
| | -2.029 | -1.535 | -1.256 | -1.865 | -2.183 | -0.138 |
| alpha | -0.004 | -0.002 | -0.002 | -0.003 | -0.003 | 0.0 |
| | -2.699 | -1.615 | -1.436 | -1.45 | -2.196 | 0.156 |
| Diff | -0.026 | -0.023 | -0.028 | -0.023 | -0.029 | -0.003 |
| | -10.992 | -10.301 | -12.114 | -10.841 | -12.072 | -1.123 |
| alpha | -0.027 | -0.023 | -0.028 | -0.023 | -0.029 | -0.002 |
| | -9.37 | -9.835 | -11.551 | -8.126 | -7.987 | -0.823 |
+-------+---------+---------+---------+---------+---------+--------+
====================================================================
# Dependent-sort Bivariate Analysis
bi_3_de = Bivariate(test_data_3, number=4)
bi_3_de.fit(conditional=True)
bi_3_de.print_summary()
=====================================================================================================
+----------+---------------+---------------+---------------+---------------+---------------+--------+
| Group | idioskewness1 | idioskewness2 | idioskewness3 | idioskewness4 | idioskewness5 | Diff |
+----------+---------------+---------------+---------------+---------------+---------------+--------+
| Msmvttl1 | 0.023 | 0.021 | 0.026 | 0.019 | 0.026 | 0.004 |
| | 13.228 | 14.232 | 14.596 | 12.032 | 14.168 | 1.486 |
| Msmvttl2 | 0.012 | 0.011 | 0.012 | 0.01 | 0.01 | -0.002 |
| | 7.92 | 7.591 | 7.947 | 7.268 | 6.951 | -0.896 |
| Msmvttl3 | 0.008 | 0.009 | 0.006 | 0.005 | 0.008 | 0.0 |
| | 5.183 | 6.701 | 4.315 | 3.307 | 5.637 | 0.055 |
| Msmvttl4 | 0.005 | 0.004 | 0.005 | 0.007 | 0.005 | 0.0 |
| | 3.264 | 2.821 | 2.84 | 4.52 | 3.486 | 0.092 |
| Msmvttl5 | -0.004 | -0.002 | -0.002 | -0.002 | -0.003 | 0.0 |
| | -2.556 | -1.531 | -1.645 | -1.667 | -2.262 | 0.075 |
| Diff | -0.026 | -0.024 | -0.028 | -0.022 | -0.03 | -0.003 |
| | -11.797 | -10.66 | -11.94 | -10.141 | -12.317 | -1.116 |
+----------+---------------+---------------+---------------+---------------+---------------+--------+
=====================================================================================================
# Risk Adjustment
bi_3_de.factor_adjustment(risk_model)
bi_3_de.print_summary()
=====================================================================================================
+----------+---------------+---------------+---------------+---------------+---------------+--------+
| Group | idioskewness1 | idioskewness2 | idioskewness3 | idioskewness4 | idioskewness5 | Diff |
+----------+---------------+---------------+---------------+---------------+---------------+--------+
| Msmvttl1 | 0.023 | 0.021 | 0.026 | 0.019 | 0.026 | 0.004 |
| | 13.228 | 14.232 | 14.596 | 12.032 | 14.168 | 1.486 |
| alpha | 0.023 | 0.021 | 0.026 | 0.019 | 0.026 | 0.003 |
| | 9.05 | 13.313 | 13.045 | 8.722 | 9.87 | 1.563 |
| Msmvttl2 | 0.012 | 0.011 | 0.012 | 0.01 | 0.01 | -0.002 |
| | 7.92 | 7.591 | 7.947 | 7.268 | 6.951 | -0.896 |
| alpha | 0.011 | 0.011 | 0.011 | 0.011 | 0.01 | -0.002 |
| | 8.045 | 6.556 | 8.285 | 6.954 | 6.793 | -0.934 |
| Msmvttl3 | 0.008 | 0.009 | 0.006 | 0.005 | 0.008 | 0.0 |
| | 5.183 | 6.701 | 4.315 | 3.307 | 5.637 | 0.055 |
| alpha | 0.008 | 0.009 | 0.006 | 0.005 | 0.007 | -0.001 |
| | 4.697 | 6.736 | 3.358 | 3.378 | 6.268 | -0.348 |
| Msmvttl4 | 0.005 | 0.004 | 0.005 | 0.007 | 0.005 | 0.0 |
| | 3.264 | 2.821 | 2.84 | 4.52 | 3.486 | 0.092 |
| alpha | 0.005 | 0.005 | 0.005 | 0.006 | 0.006 | 0.001 |
| | 2.929 | 3.137 | 3.249 | 3.452 | 4.07 | 0.385 |
| Msmvttl5 | -0.004 | -0.002 | -0.002 | -0.002 | -0.003 | 0.0 |
| | -2.556 | -1.531 | -1.645 | -1.667 | -2.262 | 0.075 |
| alpha | -0.004 | -0.002 | -0.002 | -0.002 | -0.004 | 0.0 |
| | -2.976 | -1.67 | -1.772 | -1.361 | -2.424 | 0.225 |
| Diff | -0.026 | -0.024 | -0.028 | -0.022 | -0.03 | -0.003 |
| | -11.797 | -10.66 | -11.94 | -10.141 | -12.317 | -1.116 |
| alpha | -0.027 | -0.023 | -0.029 | -0.021 | -0.03 | -0.003 |
| | -9.394 | -9.507 | -11.812 | -7.469 | -8.528 | -0.972 |
+----------+---------------+---------------+---------------+---------------+---------------+--------+
Idiosyncratic Volatility
According to CAPM and APT, investors can create portfolios that have zero exposure to firm specific risk by holding a well-diversified portfolio with a large number of securities. Firm-specific risk, therefore, does not command a risk premium. The empirical implication of this is that measures of firm-specific risk, or risk that is not related to a systematic factor, should exhibit no relation with future stock returns. However, Merton (1987) develop models of market equilibrium that relax CAPM's assumptions, whose main implication is that, in equilibrium, firm-specific risk is priced. Specifically, there is a positive risk premium associated with firm-specific risk.
The most widely cited study of the cross-sectional relation between firm-specific risk and expected stock returns is Ang, Hodrick, Xing, and Zhang (2006), which finds a strong negative cross-sectional relation between idiosyncratic volatility and future stock returns.
Total volatility is defined as $$ Vol_i=100\sqrt {\frac {\sum_{t=1}^n(R_{i,t}-\bar R_i)^2}{n-1}}\sqrt m $$ Idiosyncratic volatility is defined as $$ IdioVol_i=100RSE_i\times \sqrt m $$ whose RSE is $$ RSE_i=\sqrt {\frac {\sum_{j=1}^n\epsilon_{i,j}^2}{n-k}} $$ where n is the number of data points and k is the number of parameters estimated by the regression, which is $$ r_{i,t}=\alpha_i+\beta_{MKT,i}MKT_t+\beta_{SMB,i}SMB_t+\beta_{HML,i}HML_t+\beta_{MOM,i}+\epsilon_{i,t}. $$ The calculation period is 12 months. In this demo, the dataset starts from Jan, 2000 and is collected from CSMAR dataset. WARNING: Do Not use dataset in this demo for any commercial purpose.
# %% set system path
import sys,os
sys.path.append(os.path.abspath(".."))
# %% import data
import pandas as pd
month_return = pd.read_hdf('.\\data\\month_return.h5', key='month_return')
company_data = pd.read_hdf('.\\data\\last_filter_pe.h5', key='data')
trade_data = pd.read_hdf('.\\data\\mean_filter_trade.h5', key='data')
beta = pd.read_hdf('.\\data\\beta.h5', key='data')
risk_premium = pd.read_hdf('.\\data\\risk_premium.h5', key='data')
Data preprocessing
# %% data preprocessing
# forward the monthly return for each stock
# emrwd is the return including dividend
month_return['emrwd'] = month_return.groupby(['Stkcd'])['Mretwd'].shift(-1)
# emrnd is the return including no dividend
month_return['emrnd'] = month_return.groupby(['Stkcd'])['Mretnd'].shift(-1)
# select the A share stock
month_return = month_return[month_return['Markettype'].isin([1, 4, 16])]
# % distinguish the stocks whose size is among the up 30% stocks in each month
def percentile(stocks) :
return stocks >= stocks.quantile(q=.3)
month_return['cap'] = month_return.groupby(['Trdmnt'])['Msmvttl'].apply(percentile)
# merge data
data = month_return[['Stkcd', 'Trdmnt', 'Mretwd']]
data['Date_merge'] = pd.to_datetime(data['Trdmnt'])
risk_premium['Date_merge'] = risk_premium.index
data = pd.merge(data, risk_premium[['MKT', 'SMB', 'HML', 'Date_merge']], on=['Date_merge']).dropna()
Construct proxy variable
# %% construct proxy variable
import numpy as np
import statsmodels.api as sm
volatility = pd.Series(index=data.index, dtype=float, name='volatility')
idiovolatility = pd.Series(index=data.index, dtype=float, name='idiovolatility')
for i in data.groupby('Stkcd'):
row, col = np.shape(i[1])
for j in range(row-12):
volatility.loc[i[1].index[j+11]] = np.std(i[1].iloc[j:j+12, 2])
model_idiovol = sm.OLS(i[1].iloc[j:j+12, 2], sm.add_constant(i[1].iloc[j:j+12, 4:7])).fit()
idiovolatility.loc[i[1].index[j+11]] = np.std(model_idiovol.resid)
return_company = pd.concat([data, volatility, idiovolatility, month_return[['cap', 'Msmvttl', 'Ndaytrd', 'emrwd']]], axis=1)
Dataset #1: Volatility. The result from dataset #1 is inconsistent with literatures that in univariate analysis the differenced return is insignificant since the absolute t-value is less than 2.3, and the order of return sequence show no consistency.
In bivariate analysis the differenced return is insignificant since the absolute t-value is less than 2.3, suggesting that total volatility factor provides no excess return. The factor adjustment tends to strengthen the portfolio excess return; while the dependent-sort bivariate tends to weaken the portfolio excess return.
# %% construct test_data for bivariate analysis
# dataset 1
from portfolio_analysis import Bivariate, Univariate
import numpy as np
# select stocks whose size is among the up 30% stocks in each month and whose trading
# days are more than or equal to 10 days
test_data_1 = return_company[(return_company['cap']==True) & (return_company['Ndaytrd']>=10)]
test_data_1 = test_data_1[['emrwd', 'Msmvttl', 'volatility', 'Date_merge']].dropna()
test_data_1 = test_data_1[(test_data_1['Date_merge'] >= '2000-01-01') & (test_data_1['Date_merge'] <= '2019-12-01')]
# Univariate analysis
uni_1 = Univariate(np.array(test_data_1[['emrwd', 'volatility', 'Date_merge']]), number=9)
uni_1.summary_and_test()
uni_1.print_summary_by_time()
uni_1.print_summary()
====================================================================================================
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+--------+-------+
| Group | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Diff |
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+--------+-------+
| Average | 0.009 | 0.009 | 0.008 | 0.009 | 0.008 | 0.009 | 0.01 | 0.008 | 0.009 | 0.011 | 0.002 |
| T-Test | 8.083 | 8.567 | 8.566 | 8.338 | 8.097 | 9.132 | 9.712 | 8.322 | 8.402 | 11.275 | 1.471 |
+---------+-------+-------+-------+-------+-------+-------+-------+-------+-------+--------+-------+
# Bivariate analysis
bi_1 = Bivariate(np.array(test_data_1), number=4)
bi_1.average_by_time()
bi_1.summary_and_test()
bi_1.print_summary_by_time()
bi_1.print_summary()
=================================================================
+-------+--------+--------+---------+--------+---------+--------+
| Group | 1 | 2 | 3 | 4 | 5 | Diff |
+-------+--------+--------+---------+--------+---------+--------+
| 1 | 0.024 | 0.026 | 0.021 | 0.022 | 0.024 | -0.0 |
| | 13.854 | 14.019 | 13.417 | 13.479 | 14.148 | -0.181 |
| 2 | 0.01 | 0.01 | 0.013 | 0.011 | 0.011 | 0.001 |
| | 7.093 | 6.576 | 9.397 | 7.681 | 7.068 | 0.416 |
| 3 | 0.006 | 0.009 | 0.008 | 0.005 | 0.007 | 0.001 |
| | 4.114 | 6.551 | 5.156 | 3.951 | 5.56 | 0.411 |
| 4 | 0.004 | 0.003 | 0.005 | 0.006 | 0.008 | 0.004 |
| | 2.283 | 2.044 | 3.007 | 3.804 | 4.639 | 1.377 |
| 5 | -0.001 | -0.006 | -0.005 | -0.0 | -0.003 | -0.002 |
| | -0.501 | -3.827 | -3.517 | -0.287 | -1.802 | -0.884 |
| Diff | -0.025 | -0.032 | -0.026 | -0.022 | -0.026 | -0.001 |
| | -10.79 | -13.72 | -12.341 | -9.892 | -12.785 | -0.487 |
+-------+--------+--------+---------+--------+---------+--------+
=================================================================
# Risk Adjustment
risk_model = risk_premium[['MKT', 'SMB', 'HML']]
risk_model = risk_model.loc[test_data_1['Date_merge'].unique()]
bi_1.factor_adjustment(risk_model)
bi_1.print_summary()
==================================================================
+-------+--------+---------+---------+--------+---------+--------+
| Group | 1 | 2 | 3 | 4 | 5 | Diff |
+-------+--------+---------+---------+--------+---------+--------+
| 1 | 0.024 | 0.026 | 0.021 | 0.022 | 0.024 | -0.0 |
| | 13.854 | 14.019 | 13.417 | 13.479 | 14.148 | -0.181 |
| alpha | 0.024 | 0.025 | 0.021 | 0.022 | 0.024 | -0.0 |
| | 10.259 | 8.958 | 9.653 | 11.34 | 12.171 | -0.189 |
| 2 | 0.01 | 0.01 | 0.013 | 0.011 | 0.011 | 0.001 |
| | 7.093 | 6.576 | 9.397 | 7.681 | 7.068 | 0.416 |
| alpha | 0.009 | 0.01 | 0.013 | 0.011 | 0.011 | 0.001 |
| | 6.632 | 5.461 | 7.061 | 6.417 | 6.671 | 0.537 |
| 3 | 0.006 | 0.009 | 0.008 | 0.005 | 0.007 | 0.001 |
| | 4.114 | 6.551 | 5.156 | 3.951 | 5.56 | 0.411 |
| alpha | 0.006 | 0.009 | 0.007 | 0.006 | 0.007 | 0.001 |
| | 3.57 | 7.651 | 4.941 | 4.278 | 4.117 | 0.355 |
| 4 | 0.004 | 0.003 | 0.005 | 0.006 | 0.008 | 0.004 |
| | 2.283 | 2.044 | 3.007 | 3.804 | 4.639 | 1.377 |
| alpha | 0.005 | 0.003 | 0.005 | 0.006 | 0.008 | 0.003 |
| | 2.02 | 2.316 | 2.984 | 3.791 | 3.951 | 1.399 |
| 5 | -0.001 | -0.006 | -0.005 | -0.0 | -0.003 | -0.002 |
| | -0.501 | -3.827 | -3.517 | -0.287 | -1.802 | -0.884 |
| alpha | -0.001 | -0.007 | -0.005 | 0.0 | -0.003 | -0.002 |
| | -0.542 | -3.953 | -3.285 | 0.046 | -2.47 | -1.071 |
| Diff | -0.025 | -0.032 | -0.026 | -0.022 | -0.026 | -0.001 |
| | -10.79 | -13.72 | -12.341 | -9.892 | -12.785 | -0.487 |
| alpha | -0.025 | -0.032 | -0.026 | -0.022 | -0.026 | -0.001 |
| | -8.186 | -10.372 | -8.567 | -8.355 | -12.049 | -0.471 |
+-------+--------+---------+---------+--------+---------+--------+
==================================================================
# Dependent-sort Bivariate Analysis
bi_1_de = Bivariate(test_data_1, number=4)
bi_1_de.fit(conditional=True)
bi_1_de.print_summary()
===========================================================================================
+----------+-------------+-------------+-------------+-------------+-------------+--------+
| Group | volatility1 | volatility2 | volatility3 | volatility4 | volatility5 | Diff |
+----------+-------------+-------------+-------------+-------------+-------------+--------+
| Msmvttl1 | 0.023 | 0.025 | 0.022 | 0.022 | 0.023 | -0.0 |
| | 14.192 | 14.0 | 13.191 | 13.433 | 14.479 | -0.066 |
| Msmvttl2 | 0.01 | 0.01 | 0.013 | 0.011 | 0.011 | 0.001 |
| | 7.379 | 6.496 | 9.582 | 7.81 | 7.025 | 0.344 |
| Msmvttl3 | 0.006 | 0.008 | 0.009 | 0.005 | 0.007 | 0.001 |
| | 4.011 | 6.061 | 6.207 | 3.312 | 5.689 | 0.683 |
| Msmvttl4 | 0.005 | 0.004 | 0.003 | 0.007 | 0.008 | 0.003 |
| | 2.523 | 2.452 | 1.817 | 4.53 | 4.813 | 1.194 |
| Msmvttl5 | -0.002 | -0.007 | -0.004 | -0.001 | -0.002 | -0.0 |
| | -1.212 | -4.468 | -2.611 | -0.366 | -1.324 | -0.075 |
| Diff | -0.025 | -0.031 | -0.026 | -0.022 | -0.025 | -0.0 |
| | -11.064 | -13.642 | -11.847 | -9.948 | -12.232 | -0.004 |
+----------+-------------+-------------+-------------+-------------+-------------+--------+
===========================================================================================
# Risk Adjustment
bi_1_de.factor_adjustment(risk_model)
bi_1_de.print_summary()
===========================================================================================
+----------+-------------+-------------+-------------+-------------+-------------+--------+
| Group | volatility1 | volatility2 | volatility3 | volatility4 | volatility5 | Diff |
+----------+-------------+-------------+-------------+-------------+-------------+--------+
| Msmvttl1 | 0.023 | 0.025 | 0.022 | 0.022 | 0.023 | -0.0 |
| | 14.192 | 14.0 | 13.191 | 13.433 | 14.479 | -0.066 |
| alpha | 0.024 | 0.024 | 0.022 | 0.022 | 0.023 | -0.0 |
| | 11.229 | 8.841 | 8.754 | 10.762 | 13.008 | -0.148 |
| Msmvttl2 | 0.01 | 0.01 | 0.013 | 0.011 | 0.011 | 0.001 |
| | 7.379 | 6.496 | 9.582 | 7.81 | 7.025 | 0.344 |
| alpha | 0.01 | 0.009 | 0.013 | 0.011 | 0.011 | 0.001 |
| | 7.029 | 5.064 | 7.467 | 7.879 | 7.523 | 0.668 |
| Msmvttl3 | 0.006 | 0.008 | 0.009 | 0.005 | 0.007 | 0.001 |
| | 4.011 | 6.061 | 6.207 | 3.312 | 5.689 | 0.683 |
| alpha | 0.006 | 0.008 | 0.009 | 0.005 | 0.007 | 0.002 |
| | 3.278 | 5.555 | 6.785 | 2.958 | 4.157 | 0.668 |
| Msmvttl4 | 0.005 | 0.004 | 0.003 | 0.007 | 0.008 | 0.003 |
| | 2.523 | 2.452 | 1.817 | 4.53 | 4.813 | 1.194 |
| alpha | 0.005 | 0.004 | 0.003 | 0.007 | 0.008 | 0.003 |
| | 2.193 | 2.43 | 2.034 | 4.316 | 3.979 | 0.977 |
| Msmvttl5 | -0.002 | -0.007 | -0.004 | -0.001 | -0.002 | -0.0 |
| | -1.212 | -4.468 | -2.611 | -0.366 | -1.324 | -0.075 |
| alpha | -0.002 | -0.007 | -0.004 | 0.0 | -0.002 | -0.0 |
| | -1.261 | -4.975 | -2.463 | 0.093 | -1.701 | -0.174 |
| Diff | -0.025 | -0.031 | -0.026 | -0.022 | -0.025 | -0.0 |
| | -11.064 | -13.642 | -11.847 | -9.948 | -12.232 | -0.004 |
| alpha | -0.025 | -0.032 | -0.025 | -0.022 | -0.025 | -0.0 |
| | -9.396 | -10.239 | -7.804 | -8.028 | -12.645 | -0.014 |
+----------+-------------+-------------+-------------+-------------+-------------+--------+
Dataset #2: Idiosyncratic Volatility. The result from dataset #2 is inconsistent with literatures that in univariate analysis the differenced return is insignificant since the absolute t-value is less than 2.3, and the order of return sequence show no consistency.
In bivariate analysis the differenced return is insignificant since the absolute t-value is less than 2.3, suggesting that idiosyncratic volatility factor provides no excess return. The factor adjustment tends to strengthen the portfolio excess return; while the dependent-sort bivariate tends to weaken the portfolio excess return.
# %% construct test_data for bivariate analysis
# dataset 2
from portfolio_analysis import Bivariate, Univariate
import numpy as np
# select stocks whose size is among the up 30% stocks in each month and whose trading
# days are more than or equal to 10 days
test_data_2 = return_company[(return_company['cap']==True) & (return_company['Ndaytrd']>=10)]
test_data_2 = test_data_2[['emrwd', 'Msmvttl', 'idiovolatility', 'Date_merge']].dropna()
test_data_2 = test_data_2[(test_data_2['Date_merge'] >= '2000-01-01') & (test_data_2['Date_merge'] <= '2019-12-01')]
# Univariate analysis
uni_2 = Univariate(np.array(test_data_2[['emrwd', 'idiovolatility', 'Date_merge']]), number=9)
uni_2.summary_and_test()
uni_2.print_summary_by_time()
uni_2.print_summary()
=====================================================================================================
+---------+-------+-------+-------+-------+-------+-------+--------+-------+-------+--------+-------+
| Group | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Diff |
+---------+-------+-------+-------+-------+-------+-------+--------+-------+-------+--------+-------+
| Average | 0.009 | 0.008 | 0.008 | 0.009 | 0.009 | 0.008 | 0.01 | 0.007 | 0.009 | 0.01 | 0.001 |
| T-Test | 9.291 | 9.162 | 7.904 | 8.555 | 9.006 | 9.615 | 10.437 | 7.742 | 9.179 | 10.445 | 0.941 |
+---------+-------+-------+-------+-------+-------+-------+--------+-------+-------+--------+-------+
# Bivariate analysis
bi_2 = Bivariate(np.array(test_data_2), number=4)
bi_2.average_by_time()
bi_2.summary_and_test()
bi_2.print_summary_by_time()
bi_2.print_summary()
==================================================================
+-------+---------+--------+---------+--------+---------+--------+
| Group | 1 | 2 | 3 | 4 | 5 | Diff |
+-------+---------+--------+---------+--------+---------+--------+
| 1 | 0.025 | 0.021 | 0.023 | 0.022 | 0.025 | -0.001 |
| | 13.38 | 12.289 | 12.749 | 12.311 | 15.666 | -0.34 |
| 2 | 0.01 | 0.009 | 0.012 | 0.011 | 0.011 | 0.001 |
| | 7.286 | 6.693 | 8.082 | 8.541 | 8.022 | 0.514 |
| 3 | 0.006 | 0.006 | 0.007 | 0.008 | 0.008 | 0.002 |
| | 4.009 | 4.115 | 5.047 | 5.496 | 5.562 | 0.928 |
| 4 | 0.005 | 0.008 | 0.005 | 0.003 | 0.006 | 0.002 |
| | 3.072 | 4.216 | 2.919 | 1.984 | 4.165 | 0.852 |
| 5 | -0.003 | -0.003 | -0.004 | -0.001 | -0.003 | -0.0 |
| | -2.12 | -1.627 | -2.343 | -0.898 | -2.162 | -0.012 |
| Diff | -0.028 | -0.024 | -0.027 | -0.023 | -0.028 | 0.001 |
| | -11.514 | -9.464 | -11.654 | -9.987 | -13.271 | 0.25 |
+-------+---------+--------+---------+--------+---------+--------+
==================================================================
# Risk Adjustment
risk_model = risk_premium[['MKT', 'SMB', 'HML']]
risk_model = risk_model.loc[test_data_2['Date_merge'].unique()]
bi_2.factor_adjustment(risk_model)
bi_2.print_summary()
==================================================================
+-------+---------+--------+---------+--------+---------+--------+
| Group | 1 | 2 | 3 | 4 | 5 | Diff |
+-------+---------+--------+---------+--------+---------+--------+
| 1 | 0.025 | 0.021 | 0.023 | 0.022 | 0.025 | -0.001 |
| | 13.38 | 12.289 | 12.749 | 12.311 | 15.666 | -0.34 |
| alpha | 0.025 | 0.022 | 0.023 | 0.021 | 0.025 | -0.0 |
| | 9.763 | 9.203 | 8.447 | 11.555 | 10.599 | -0.056 |
| 2 | 0.01 | 0.009 | 0.012 | 0.011 | 0.011 | 0.001 |
| | 7.286 | 6.693 | 8.082 | 8.541 | 8.022 | 0.514 |
| alpha | 0.009 | 0.009 | 0.013 | 0.011 | 0.011 | 0.002 |
| | 6.647 | 5.971 | 7.189 | 8.442 | 10.108 | 1.312 |
| 3 | 0.006 | 0.006 | 0.007 | 0.008 | 0.008 | 0.002 |
| | 4.009 | 4.115 | 5.047 | 5.496 | 5.562 | 0.928 |
| alpha | 0.006 | 0.005 | 0.007 | 0.009 | 0.008 | 0.002 |
| | 4.377 | 4.991 | 4.854 | 6.411 | 5.54 | 1.084 |
| 4 | 0.005 | 0.008 | 0.005 | 0.003 | 0.006 | 0.002 |
| | 3.072 | 4.216 | 2.919 | 1.984 | 4.165 | 0.852 |
| alpha | 0.005 | 0.008 | 0.004 | 0.003 | 0.007 | 0.002 |
| | 2.796 | 3.946 | 2.612 | 1.684 | 3.852 | 1.027 |
| 5 | -0.003 | -0.003 | -0.004 | -0.001 | -0.003 | -0.0 |
| | -2.12 | -1.627 | -2.343 | -0.898 | -2.162 | -0.012 |
| alpha | -0.003 | -0.003 | -0.003 | -0.001 | -0.004 | -0.0 |
| | -2.782 | -1.515 | -1.966 | -0.759 | -2.726 | -0.234 |
| Diff | -0.028 | -0.024 | -0.027 | -0.023 | -0.028 | 0.001 |
| | -11.514 | -9.464 | -11.654 | -9.987 | -13.271 | 0.25 |
| alpha | -0.028 | -0.025 | -0.026 | -0.023 | -0.029 | -0.0 |
| | -9.507 | -6.88 | -8.776 | -11.24 | -10.372 | -0.069 |
+-------+---------+--------+---------+--------+---------+--------+
==================================================================
# Dependent-sort Bivariate Analysis
bi_2_de = Bivariate(test_data_2, number=4)
bi_2_de.fit(conditional=True)
bi_2_de.print_summary()
===============================================================================================================
+----------+-----------------+-----------------+-----------------+-----------------+-----------------+--------+
| Group | idiovolatility1 | idiovolatility2 | idiovolatility3 | idiovolatility4 | idiovolatility5 | Diff |
+----------+-----------------+-----------------+-----------------+-----------------+-----------------+--------+
| Msmvttl1 | 0.024 | 0.022 | 0.023 | 0.022 | 0.024 | -0.001 |
| | 13.717 | 12.779 | 13.288 | 12.328 | 15.606 | -0.363 |
| Msmvttl2 | 0.01 | 0.01 | 0.011 | 0.012 | 0.011 | 0.001 |
| | 6.995 | 7.112 | 7.672 | 8.864 | 7.98 | 0.656 |
| Msmvttl3 | 0.008 | 0.006 | 0.007 | 0.008 | 0.008 | 0.0 |
| | 4.748 | 3.848 | 5.149 | 5.3 | 5.517 | 0.191 |
| Msmvttl4 | 0.005 | 0.006 | 0.006 | 0.003 | 0.006 | 0.001 |
| | 3.722 | 3.581 | 3.629 | 1.877 | 4.056 | 0.25 |
| Msmvttl5 | -0.004 | -0.002 | -0.004 | -0.002 | -0.002 | 0.001 |
| | -2.667 | -1.29 | -2.649 | -1.438 | -1.628 | 0.707 |
| Diff | -0.028 | -0.024 | -0.027 | -0.024 | -0.026 | 0.002 |
| | -12.214 | -9.747 | -12.373 | -10.345 | -12.341 | 0.739 |
+----------+-----------------+-----------------+-----------------+-----------------+-----------------+--------+
===============================================================================================================
# Risk Adjustment
bi_2_de.factor_adjustment(risk_model)
bi_2_de.print_summary()
===============================================================================================================
+----------+-----------------+-----------------+-----------------+-----------------+-----------------+--------+
| Group | idiovolatility1 | idiovolatility2 | idiovolatility3 | idiovolatility4 | idiovolatility5 | Diff |
+----------+-----------------+-----------------+-----------------+-----------------+-----------------+--------+
| Msmvttl1 | 0.024 | 0.022 | 0.023 | 0.022 | 0.024 | -0.001 |
| | 13.717 | 12.779 | 13.288 | 12.328 | 15.606 | -0.363 |
| alpha | 0.024 | 0.023 | 0.023 | 0.022 | 0.024 | -0.0 |
| | 11.315 | 9.529 | 9.373 | 10.536 | 10.124 | -0.13 |
| Msmvttl2 | 0.01 | 0.01 | 0.011 | 0.012 | 0.011 | 0.001 |
| | 6.995 | 7.112 | 7.672 | 8.864 | 7.98 | 0.656 |
| alpha | 0.009 | 0.01 | 0.012 | 0.012 | 0.011 | 0.002 |
| | 6.258 | 7.269 | 7.512 | 7.83 | 9.558 | 1.477 |
| Msmvttl3 | 0.008 | 0.006 | 0.007 | 0.008 | 0.008 | 0.0 |
| | 4.748 | 3.848 | 5.149 | 5.3 | 5.517 | 0.191 |
| alpha | 0.007 | 0.005 | 0.007 | 0.008 | 0.008 | 0.001 |
| | 4.809 | 4.279 | 5.357 | 6.315 | 5.289 | 0.334 |
| Msmvttl4 | 0.005 | 0.006 | 0.006 | 0.003 | 0.006 | 0.001 |
| | 3.722 | 3.581 | 3.629 | 1.877 | 4.056 | 0.25 |
| alpha | 0.006 | 0.007 | 0.006 | 0.003 | 0.007 | 0.001 |
| | 3.256 | 3.581 | 3.166 | 1.434 | 3.788 | 0.428 |
| Msmvttl5 | -0.004 | -0.002 | -0.004 | -0.002 | -0.002 | 0.001 |
| | -2.667 | -1.29 | -2.649 | -1.438 | -1.628 | 0.707 |
| alpha | -0.004 | -0.002 | -0.004 | -0.002 | -0.003 | 0.001 |
| | -3.967 | -1.184 | -2.796 | -1.462 | -2.161 | 1.052 |
| Diff | -0.028 | -0.024 | -0.027 | -0.024 | -0.026 | 0.002 |
| | -12.214 | -9.747 | -12.373 | -10.345 | -12.341 | 0.739 |
| alpha | -0.028 | -0.025 | -0.026 | -0.024 | -0.027 | 0.002 |
| | -10.475 | -6.945 | -9.554 | -10.82 | -10.266 | 0.581 |
+----------+-----------------+-----------------+-----------------+-----------------+-----------------+--------+
fama_macbeth
Factor mimicking portfolio
factor: Size (SMB) and Value (HML)
Following Fama and French (1993), the SMB and HML portfolio and corresponding risk premium are calculated through the class Factor_mimicking_portfolio. The detail are introduced in EAP.fama_macbeth.Factor_mimicking_portfolio.
The data are collected from CSMAR dataset, by which SMB and HML in China stock market is constituted. WARNING: Do Not use dataset in this demo for any commercial purpose.
import sys,os
sys.path.append(os.path.abspath(".."))
# %% import data
# Monthly return of stocks in China security market
import pandas as pd
month_return = pd.read_hdf('.\data\month_return.h5', key='month_return')
company_data = pd.read_hdf('.\data\last_filter_pe.h5', key='data')
trade_data = pd.read_hdf('.\data\mean_filter_trade.h5', key='data')
Data need some preprocessing.
# %% data preprocessing
# select the A share stock
month_return = month_return[month_return['Markettype'].isin([1, 4, 16])]
# % distinguish the stocks whose size is among the up 30% stocks in each month
def percentile(stocks) :
return stocks >= stocks.quantile(q=.3)
month_return['cap'] = month_return.groupby(['Trdmnt'])['Msmvttl'].apply(percentile)
Construct proxy variable
# %% Construct proxy variable
import numpy as np
# RMW
# in this demo, the ROE(TTM) are used
# ROE(TTM) = PBV1B/PE(TTM)
company_data['ROE(TTM)'] = company_data['PBV1B']/company_data['PE1TTM']
# CMA
# % calculate the total asset
# asset = debt + equity
# debt = company_value - market_value
# equity = market_value / PB
company_data['debt'] = company_data['EV1'] - company_data['MarketValue']
company_data['equity'] = company_data['MarketValue']/company_data['PBV1A']
company_data['asset'] = company_data['debt'] + company_data['equity']
# asset growth rate
company_data['asset_growth_rate'] = company_data['asset'].groupby(['Symbol']).diff(12)/company_data['asset']
# Momentum
month_return['rolling_12'] = np.array(month_return.groupby(['Stkcd'])['Mretwd'].rolling(12).sum())
month_return['momentum'] = month_return['rolling_12'] - month_return['Mretwd']
# Turnover
trade_data['rolling_Turnover'] = np.array(trade_data['Turnover'].groupby('Symbol').rolling(12).mean())
trade_data['specific_Turnover'] = trade_data['Turnover'] / trade_data['rolling_Turnover']
Some further data preprocessing.
# %% merge data
from pandas.tseries.offsets import *
month_return['Stkcd_merge'] = month_return['Stkcd'].astype(dtype='string')
month_return['Date_merge'] = pd.to_datetime(month_return['Trdmnt'])
#month_return['Date_merge'] += MonthEnd()
company_data['Stkcd_merge'] = company_data['Symbol'].dropna().astype(dtype='int').astype(dtype='string')
company_data['Date_merge'] = pd.to_datetime(company_data['TradingDate'])
company_data['Date_merge'] += MonthBegin()
trade_data['Stkcd_merge'] = trade_data['Symbol'].dropna().astype(dtype='int').astype(dtype='string')
trade_data['TradingDate'] = trade_data.index.map(lambda x : x[1])
trade_data['Date_merge'] = pd.to_datetime(trade_data['TradingDate'])
#company_data['Yearmonth'] = company_data['Date_merge'].map(lambda x : 1000*x.year + x.month)
trade_data['Date_merge'] += MonthBegin()
# %% dataset starts from '2000-01'
company_data = company_data[company_data['Date_merge'] >= '2000-01']
month_return = month_return[month_return['Date_merge'] >= '2000-01']
return_company = pd.merge(company_data, month_return, on=['Stkcd_merge', 'Date_merge'])
return_company = pd.merge(return_company, trade_data, on=['Stkcd_merge', 'Date_merge'])
Construct factor mimicking portfolio and calculate factor risk premium.
# %% SMB and HML
from fama_macbeth import Factor_mimicking_portfolio as fmp
import numpy as np
# select stocks whose size is among the up 30% stocks in each month and whose trading
# days are more than or equal to 10 days
test_data_1 = return_company[(return_company['cap']==True) & (return_company['Ndaytrd']>=10)]
# construct data for univariate analysis
test_data_1 = test_data_1[['Mretwd', 'Msmvttl', 'PE1A', 'Date_merge', 'Msmvttl']].dropna()
test_data_1 = test_data_1[(test_data_1['Date_merge'] >= '2000-01-01') & (test_data_1['Date_merge'] <= '2019-12-01')]
# factor mimicking portfolio
fmp_1 = fmp(np.array(test_data_1))
SMB, HML = fmp_1.portfolio_return()
SMB = -SMB
plt.figure('SMB')
plt.plot(SMB, label='SMB')
plt.ylabel('risk premium')
plt.xlabel('time')
plt.legend()
plt.figure('HML')
plt.plot(HML, label='HML')
plt.ylabel('risk premium')
plt.xlabel('time')
plt.legend()
===========================================================
factor: Profitability
The profitability factor (RMW) is constituted by the same procedure with HML, using proxy variable ROE(TTM).
# Continue the previous code
# %% RMW
from fama_macbeth import Factor_mimicking_portfolio as fmp
import numpy as np
# select stocks whose size is among the up 30% stocks in each month and whose trading
# days are more than or equal to 10 days
test_data_2 = return_company[(return_company['cap']==True) & (return_company['Ndaytrd']>=10)]
# construct data for univariate analysis
test_data_2 = test_data_2[['Mretwd', 'Msmvttl', 'ROE(TTM)', 'Date_merge', 'Msmvttl']].dropna()
test_data_2 = test_data_2[(test_data_2['Date_merge'] >= '2004-01-01') & (test_data_2['Date_merge'] <= '2019-12-01')]
# factor mimicking portfolio
fmp_2 = fmp(np.array(test_data_2))
Row_fac, RMW = fmp_2.portfolio_return()
plt.figure('RMW')
plt.plot(RMW, label='RMW')
plt.ylabel('risk premium')
plt.xlabel('time')
plt.legend()
===============================================================
factor: Investment
The investment factor (CMA) is constituted by the same procedure with HML, using proxy variable, asset_growth_rate.
# %% CMA
from fama_macbeth import Factor_mimicking_portfolio as fmp
import numpy as np
# select stocks whose size is among the up 30% stocks in each month and whose trading
# days are more than or equal to 10 days
test_data_3 = return_company[(return_company['cap']==True) & (return_company['Ndaytrd']>=10)]
# construct data for univariate analysis
test_data_3 = test_data_3[['Mretwd', 'Msmvttl', 'asset_growth_rate', 'Date_merge', 'Msmvttl']].dropna()
test_data_3 = test_data_3[(test_data_3['Date_merge'] >= '2000-01-01') & (test_data_3['Date_merge'] <= '2019-12-01')]
# factor mimicking portfolio
fmp_3 = fmp(np.array(test_data_3))
Row_fac, CMA = fmp_3.portfolio_return()
plt.figure('CMA')
plt.plot(CMA, label='CMA')
plt.ylabel('risk premium')
plt.xlabel('time')
plt.legend()
==============================================================
factor: Momentum
The momentum factor (MOM) is constituted by the same procedure with HML, using proxy variable, sum of past 12 month return.
# %% Momentum
from fama_macbeth import Factor_mimicking_portfolio as fmp
import numpy as np
# select stocks whose size is among the up 30% stocks in each month and whose trading
# days are more than or equal to 10 days
test_data_4 = return_company[(return_company['cap']==True) & (return_company['Ndaytrd']>=10)]
# construct data for univariate analysis
test_data_4 = test_data_4[['Mretwd', 'Msmvttl', 'momentum', 'Date_merge', 'Msmvttl']].dropna()
test_data_4 = test_data_4[(test_data_4['Date_merge'] >= '2000-01-01') & (test_data_4['Date_merge'] <= '2019-12-01')]
# factor mimicking portfolio
fmp_4 = fmp(np.array(test_data_4))
Row_fac, MOM = fmp_4.portfolio_return()
plt.figure('MOM')
plt.plot(MOM, label='MOM')
plt.ylabel('risk premium')
plt.xlabel('time')
plt.legend()
===================================================
factor: Turnover
The turnover factor (Turn) is constituted by the same procedure with HML, using proxy variable, abnormal turnover rate.
# %% Turnover
from fama_macbeth import Factor_mimicking_portfolio as fmp
import numpy as np
# select stocks whose size is among the up 30% stocks in each month and whose trading
# days are more than or equal to 10 days
test_data_5 = return_company[(return_company['cap']==True) & (return_company['Ndaytrd']>=10)]
# construct data for univariate analysis
test_data_5 = test_data_5[['Mretwd', 'Msmvttl', 'specific_Turnover', 'Date_merge', 'Msmvttl']].dropna()
test_data_5 = test_data_5[(test_data_5['Date_merge'] >= '2000-01-01') & (test_data_5['Date_merge'] <= '2019-12-01')]
# factor mimicking portfolio
fmp_5 = fmp(np.array(test_data_5))
Row_fac, Turn = fmp_5.portfolio_return()
plt.figure('Turnover')
plt.plot(Turn, label='Turnover')
plt.ylabel('risk premium')
plt.xlabel('time')
plt.legend()
=======================================================================
Fama_macbeth_regress
Fama Macbeth regression tests existence of factor risk premium. Fama-Macbeth Regression follows two steps:
- Specify the model and take cross-sectional regression.
- Take the time-series average of regression coefficient
For more details, please read Empirical Asset Pricing: The Cross Section of Stock Returns. Bali, Engle, Murray, 2016.
Testing whether characteristics have systematic dynamics to asset return needs adding characteristics of stocks into FM regression model. In this demo, characteristics or factors include size, value, profitability, investment, momentum, and turnover, whose proxy variables are introduced in demo, Factor mimicking portfolio. WARNING: Do Not use dataset in this demo for any commercial purpose.
# %% set system path
import sys,os
sys.path.append(os.path.abspath(".."))
Data need some preprocessing.
# %% import data
# Monthly return of stocks in China security market
import pandas as pd
month_return = pd.read_hdf('.\data\month_return.h5', key='month_return')
company_data = pd.read_hdf('.\data\last_filter_pe.h5', key='data')
trade_data = pd.read_hdf('.\data\mean_filter_trade.h5', key='data')
beta = pd.read_hdf('.\\data\\beta.h5', key='data')
# %% data preprocessing
# forward the monthly return for each stock
# emrwd is the return including dividend
month_return['emrwd'] = month_return.groupby(['Stkcd'])['Mretwd'].shift(-1)
# emrnd is the return including no dividend
month_return['emrnd'] = month_return.groupby(['Stkcd'])['Mretnd'].shift(-1)
# select the A share stock
month_return = month_return[month_return['Markettype'].isin([1, 4, 16])]
# % distinguish the stocks whose size is among the up 30% stocks in each month
def percentile(stocks) :
return stocks >= stocks.quantile(q=.3)
month_return['cap'] = month_return.groupby(['Trdmnt'])['Msmvttl'].apply(percentile)
Construct proxy variables for factors.
# %% Construct proxy variable
import numpy as np
# SMB
# log(Size)
month_return['Size'] = np.log(month_return['Msmvttl'])
# HML
company_data['BM'] = 1 / company_data['PBV1A']
# RMW
# in this demo, the ROE(TTM) are used
# ROE(TTM) = PBV1B/PE(TTM)
company_data['ROE(TTM)'] = company_data['PBV1B']/company_data['PE1TTM']
# CMA
# % calculate the total asset
# asset = debt + equity
# debt = company_value - market_value
# equity = market_value / PB
company_data['debt'] = company_data['EV1'] - company_data['MarketValue']
company_data['equity'] = company_data['MarketValue']/company_data['PBV1A']
company_data['asset'] = company_data['debt'] + company_data['equity']
# asset growth rate
company_data['asset_growth_rate'] = company_data['asset'].groupby(['Symbol']).diff(12)/company_data['asset']
# Momentum
month_return['rolling_12'] = np.array(month_return.groupby(['Stkcd'])['Mretwd'].rolling(12).sum())
month_return['momentum'] = month_return['rolling_12'] - month_return['Mretwd']
# Turnover
trade_data['rolling_Turnover'] = np.array(trade_data['Turnover'].groupby('Symbol').rolling(12).mean())
trade_data['specific_Turnover'] = trade_data['Turnover'] / trade_data['rolling_Turnover']
Some further data preprocessing.
# %% merge data
from pandas.tseries.offsets import *
month_return['Stkcd_merge'] = month_return['Stkcd'].astype(dtype='string')
month_return['Date_merge'] = pd.to_datetime(month_return['Trdmnt'])
#month_return['Date_merge'] += MonthEnd()
company_data['Stkcd_merge'] = company_data['Symbol'].dropna().astype(dtype='int').astype(dtype='string')
company_data['Date_merge'] = pd.to_datetime(company_data['TradingDate'])
company_data['Date_merge'] += MonthBegin()
trade_data['Stkcd_merge'] = trade_data['Symbol'].dropna().astype(dtype='int').astype(dtype='string')
trade_data['TradingDate'] = trade_data.index.map(lambda x : x[1])
trade_data['Date_merge'] = pd.to_datetime(trade_data['TradingDate'])
#company_data['Yearmonth'] = company_data['Date_merge'].map(lambda x : 1000*x.year + x.month)
trade_data['Date_merge'] += MonthBegin()
# %% dataset starts from '2000-01'
company_data = company_data[company_data['Date_merge'] >= '2000-01']
month_return = month_return[month_return['Date_merge'] >= '2000-01']
return_company = pd.merge(company_data, month_return, on=['Stkcd_merge', 'Date_merge'])
return_company = pd.merge(return_company, trade_data, on=['Stkcd_merge', 'Date_merge'])
# beta
return_company = return_company.set_index(['Stkcd', 'Trdmnt'])
return_company = pd.merge(return_company, beta, left_index=True, right_index=True)
Conduct Fama-Macbeth regression.
# %% Fama-Macbeth regression
# dataset : #1
# exclude tail stocks
# range from 2000-01-01 ~ 2019-12-01
from fama_macbeth import Fama_macbeth_regress
test_data_1 = return_company[(return_company['cap']==True) & (return_company['Ndaytrd']>=10)]
test_data_1 = test_data_1[['emrwd', 'beta', 'Size', 'BM', 'ROE(TTM)', 'asset_growth_rate', 'momentum', 'specific_Turnover', 'Date_merge']].dropna()
test_data_1 = test_data_1[(test_data_1['Date_merge'] >= '2000-01-01') & (test_data_1['Date_merge'] <= '2019-12-01')]
model = Fama_macbeth_regress(test_data_1)
result = model.fit(add_constant=True)
model.summary_by_time()
model.summary()
=============================================================================================================================
para_average: [ 2.11712697e-16 7.76046176e-03 -2.11404539e-02 2.23096650e-02
2.59978312e-02 4.93686033e-03 1.13644979e-02 -2.65276499e-02]
tvalue: [ 1.49510717 0.92445793 -2.36234542 2.69894942 4.34532686 1.31038888
1.3544952 -4.77712106]
R: 0.09379246136154293
ADJ_R: 0.08697059984414297
sample number N: 1071.5882352941176
+---------------------+-----------------------------------------------------------+----------+--------------+---------------+
| Year | Param | R Square | Adj R Square | Sample Number |
+---------------------+-----------------------------------------------------------+----------+--------------+---------------+
| 2000-02-01 00:00:00 | [0.000 -0.065 -0.212 0.119 0.022 -0.054 0.024 -0.099] | 0.1 | 0.09 | 549 |
| 2000-03-01 00:00:00 | [-0.000 -0.093 0.067 0.081 0.062 0.055 -0.083 -0.025] | 0.04 | 0.03 | 535 |
| 2000-04-01 00:00:00 | [0.000 -0.028 -0.084 0.199 -0.026 -0.007 0.044 -0.058] | 0.04 | 0.03 | 542 |
| 2000-08-01 00:00:00 | [0.000 -0.179 -0.118 -0.089 0.153 -0.071 0.164 -0.084] | 0.1 | 0.09 | 508 |
| 2000-09-01 00:00:00 | [0.000 -0.153 -0.129 0.057 -0.088 -0.105 -0.122 0.112] | 0.15 | 0.14 | 506 |
| 2000-10-01 00:00:00 | [0.000 0.051 -0.061 0.086 -0.013 -0.051 -0.058 0.003] | 0.02 | 0.01 | 498 |
| 2001-02-01 00:00:00 | [-0.000 0.117 -0.122 0.021 0.014 -0.021 -0.058 0.008] | 0.03 | 0.01 | 598 |
| 2001-03-01 00:00:00 | [-0.000 0.003 -0.063 -0.256 -0.095 0.054 0.053 -0.048] | 0.08 | 0.07 | 598 |
| 2001-04-01 00:00:00 | [-0.000 0.059 -0.174 -0.184 -0.151 -0.005 0.137 -0.016] | 0.12 | 0.11 | 593 |
| 2001-08-01 00:00:00 | [0.000 0.044 0.101 0.045 0.063 -0.018 -0.118 -0.141] | 0.06 | 0.05 | 564 |
| 2001-09-01 00:00:00 | [-0.000 -0.045 0.098 0.156 -0.076 -0.082 0.013 0.087] | 0.06 | 0.05 | 565 |
| 2001-10-01 00:00:00 | [0.000 0.194 -0.068 -0.006 -0.074 0.099 -0.244 -0.219] | 0.16 | 0.15 | 565 |
| 2002-02-01 00:00:00 | [0.000 0.115 -0.158 -0.028 -0.122 0.074 -0.108 -0.153] | 0.13 | 0.12 | 622 |
| 2002-03-01 00:00:00 | [0.000 0.149 -0.066 0.095 -0.060 -0.186 0.004 -0.069] | 0.11 | 0.1 | 656 |
| 2002-04-01 00:00:00 | [-0.000 -0.093 0.072 -0.054 -0.170 0.005 0.112 -0.059] | 0.05 | 0.04 | 658 |
| 2002-08-01 00:00:00 | [0.000 -0.191 0.017 -0.095 -0.062 0.070 0.128 -0.073] | 0.08 | 0.07 | 611 |
| 2002-09-01 00:00:00 | [0.000 -0.115 0.043 0.044 0.041 -0.002 0.097 -0.031] | 0.03 | 0.02 | 616 |
| 2002-10-01 00:00:00 | [-0.000 -0.163 0.192 0.001 0.038 0.073 0.149 -0.043] | 0.13 | 0.12 | 616 |
| 2003-02-01 00:00:00 | [-0.000 -0.086 0.174 0.169 0.231 0.033 0.210 0.039] | 0.19 | 0.19 | 711 |
| 2003-03-01 00:00:00 | [0.000 -0.027 0.124 0.215 0.214 0.013 0.183 -0.033] | 0.16 | 0.15 | 718 |
| 2003-04-01 00:00:00 | [-0.000 0.222 0.092 0.043 0.001 0.049 0.014 0.023] | 0.06 | 0.06 | 726 |
| 2003-05-01 00:00:00 | [-0.000 -0.146 0.126 0.058 0.075 -0.009 -0.050 -0.161] | 0.05 | 0.04 | 676 |
| 2003-06-01 00:00:00 | [0.000 0.121 0.183 0.084 0.173 0.039 0.146 -0.008] | 0.14 | 0.13 | 677 |
| 2003-07-01 00:00:00 | [-0.000 -0.081 -0.034 -0.031 0.012 0.016 -0.203 0.004] | 0.04 | 0.03 | 677 |
| 2003-08-01 00:00:00 | [0.000 -0.088 -0.030 0.069 0.047 -0.008 0.021 0.001] | 0.01 | 0.0 | 710 |
| 2003-09-01 00:00:00 | [-0.000 -0.059 0.152 0.297 0.270 0.059 0.242 -0.038] | 0.28 | 0.27 | 716 |
| 2003-10-01 00:00:00 | [0.000 0.179 0.103 0.163 0.009 -0.003 -0.102 0.028] | 0.08 | 0.07 | 719 |
| 2003-11-01 00:00:00 | [-0.000 -0.082 0.189 0.066 0.080 0.081 0.241 -0.008] | 0.2 | 0.19 | 715 |
| 2003-12-01 00:00:00 | [-0.000 0.372 -0.095 0.004 0.108 0.079 -0.065 0.073] | 0.17 | 0.17 | 720 |
| 2004-01-01 00:00:00 | [-0.000 0.058 -0.065 0.081 0.011 -0.059 -0.116 0.060] | 0.06 | 0.05 | 720 |
| 2004-02-01 00:00:00 | [-0.000 0.009 -0.034 0.099 0.121 0.042 -0.105 0.137] | 0.05 | 0.04 | 770 |
| 2004-03-01 00:00:00 | [-0.000 -0.049 -0.180 0.111 0.087 0.049 0.077 -0.110] | 0.05 | 0.04 | 768 |
| 2004-04-01 00:00:00 | [-0.000 0.108 0.007 -0.015 -0.100 -0.113 0.041 0.061] | 0.05 | 0.05 | 775 |
| 2004-05-01 00:00:00 | [-0.000 -0.164 0.050 0.114 0.183 0.007 0.076 -0.124] | 0.12 | 0.11 | 747 |
| 2004-06-01 00:00:00 | [0.000 0.057 -0.009 0.021 0.065 -0.010 0.268 0.064] | 0.08 | 0.07 | 745 |
| 2004-07-01 00:00:00 | [0.000 -0.040 0.062 0.160 0.063 0.011 -0.052 -0.163] | 0.07 | 0.06 | 754 |
| 2004-08-01 00:00:00 | [-0.000 0.145 -0.036 0.062 0.072 0.106 0.259 0.151] | 0.14 | 0.13 | 767 |
| 2004-09-01 00:00:00 | [0.000 -0.008 -0.035 -0.083 0.068 0.088 0.155 -0.036] | 0.07 | 0.06 | 773 |
| 2004-10-01 00:00:00 | [-0.000 0.120 -0.143 -0.071 -0.095 0.022 -0.250 -0.053] | 0.13 | 0.13 | 774 |
| 2004-11-01 00:00:00 | [-0.000 -0.139 -0.002 0.083 0.183 -0.013 0.183 -0.168] | 0.1 | 0.09 | 778 |
| 2004-12-01 00:00:00 | [-0.000 -0.045 0.038 0.095 0.141 -0.000 0.071 0.036] | 0.03 | 0.02 | 784 |
| 2005-01-01 00:00:00 | [0.000 0.221 -0.071 0.051 0.159 0.083 -0.107 0.066] | 0.08 | 0.07 | 789 |
| 2005-02-01 00:00:00 | [0.000 -0.093 0.046 0.056 0.181 -0.012 0.272 -0.122] | 0.2 | 0.19 | 805 |
| 2005-03-01 00:00:00 | [-0.000 -0.105 0.088 0.085 0.139 0.042 0.179 -0.032] | 0.13 | 0.12 | 811 |
| 2005-04-01 00:00:00 | [0.000 0.057 -0.112 0.043 -0.130 -0.089 -0.328 -0.105] | 0.33 | 0.33 | 821 |
| 2005-05-01 00:00:00 | [-0.000 -0.012 0.102 0.053 0.089 0.064 0.100 -0.037] | 0.06 | 0.05 | 755 |
| 2005-06-01 00:00:00 | [0.000 -0.029 0.228 0.057 0.132 0.006 0.204 0.069] | 0.2 | 0.19 | 751 |
| 2005-07-01 00:00:00 | [0.000 0.178 -0.179 -0.114 -0.067 -0.048 -0.266 0.044] | 0.24 | 0.23 | 747 |
| 2005-08-01 00:00:00 | [0.000 -0.085 -0.193 -0.183 0.016 0.092 -0.025 0.108] | 0.08 | 0.08 | 790 |
| 2005-09-01 00:00:00 | [0.000 0.111 -0.019 -0.064 -0.047 0.075 0.203 -0.133] | 0.07 | 0.07 | 805 |
| 2005-10-01 00:00:00 | [0.000 0.108 -0.016 0.146 -0.057 0.058 -0.089 -0.002] | 0.08 | 0.07 | 708 |
| 2005-11-01 00:00:00 | [0.000 0.114 0.201 0.105 0.212 -0.005 0.177 -0.111] | 0.14 | 0.14 | 736 |
| 2005-12-01 00:00:00 | [0.000 0.151 0.059 0.032 0.071 -0.027 -0.014 -0.025] | 0.02 | 0.01 | 692 |
| 2006-01-01 00:00:00 | [-0.000 -0.174 0.085 0.190 0.052 -0.050 -0.096 -0.074] | 0.09 | 0.08 | 636 |
| 2006-02-01 00:00:00 | [-0.000 0.079 -0.033 0.008 0.155 -0.022 0.276 0.066] | 0.12 | 0.12 | 661 |
| 2006-03-01 00:00:00 | [-0.000 0.068 -0.013 -0.099 -0.011 -0.058 0.236 -0.002] | 0.08 | 0.07 | 654 |
| 2006-04-01 00:00:00 | [-0.000 0.010 -0.066 -0.052 -0.193 -0.030 -0.099 -0.098] | 0.09 | 0.08 | 615 |
| 2006-05-01 00:00:00 | [0.000 -0.154 -0.201 0.012 0.016 0.098 -0.018 -0.067] | 0.06 | 0.05 | 583 |
| 2006-06-01 00:00:00 | [0.000 -0.066 -0.149 0.016 0.020 -0.036 -0.015 0.002] | 0.03 | 0.01 | 598 |
| 2006-07-01 00:00:00 | [-0.000 -0.079 0.020 -0.022 -0.129 -0.022 0.180 -0.054] | 0.04 | 0.03 | 596 |
| 2006-08-01 00:00:00 | [-0.000 0.021 0.060 -0.224 -0.165 0.015 -0.106 -0.083] | 0.05 | 0.04 | 639 |
| 2006-09-01 00:00:00 | [0.000 -0.015 0.019 0.187 0.178 0.007 0.034 -0.089] | 0.05 | 0.04 | 632 |
| 2006-10-01 00:00:00 | [0.000 -0.168 0.384 0.081 0.120 0.030 0.208 0.089] | 0.28 | 0.27 | 620 |
| 2006-11-01 00:00:00 | [-0.000 -0.054 0.269 0.010 -0.008 -0.067 0.159 -0.001] | 0.12 | 0.11 | 628 |
| 2006-12-01 00:00:00 | [-0.000 0.112 -0.101 0.050 0.079 -0.024 -0.056 -0.033] | 0.03 | 0.02 | 607 |
| 2007-01-01 00:00:00 | [0.000 -0.019 -0.188 0.146 -0.037 -0.075 -0.005 0.029] | 0.1 | 0.09 | 609 |
| 2007-02-01 00:00:00 | [-0.000 -0.053 -0.214 0.140 -0.022 -0.003 -0.058 0.076] | 0.13 | 0.12 | 685 |
| 2007-03-01 00:00:00 | [-0.000 0.119 -0.022 0.192 0.000 -0.051 0.076 0.141] | 0.12 | 0.11 | 698 |
| 2007-04-01 00:00:00 | [0.000 -0.281 0.081 -0.036 -0.021 0.050 0.086 0.018] | 0.1 | 0.09 | 722 |
| 2007-05-01 00:00:00 | [-0.000 -0.070 0.081 -0.043 0.272 0.088 0.021 -0.213] | 0.27 | 0.26 | 678 |
| 2007-06-01 00:00:00 | [0.000 0.257 -0.156 0.048 0.031 0.116 0.061 -0.007] | 0.12 | 0.11 | 694 |
| 2007-07-01 00:00:00 | [-0.000 0.029 0.157 0.127 0.115 0.026 -0.040 -0.122] | 0.07 | 0.06 | 711 |
| 2007-08-01 00:00:00 | [-0.000 0.147 0.066 0.121 0.187 0.019 -0.040 -0.060] | 0.05 | 0.04 | 715 |
| 2007-09-01 00:00:00 | [0.000 -0.152 0.164 0.010 0.107 0.025 0.093 -0.015] | 0.13 | 0.12 | 736 |
| 2007-10-01 00:00:00 | [0.000 0.166 -0.131 -0.023 -0.136 -0.031 -0.437 0.006] | 0.33 | 0.32 | 732 |
| 2007-11-01 00:00:00 | [0.000 -0.006 -0.274 -0.083 0.069 0.002 0.030 0.096] | 0.07 | 0.06 | 738 |
| 2007-12-01 00:00:00 | [-0.000 -0.068 -0.223 0.038 0.045 0.110 -0.075 -0.093] | 0.07 | 0.06 | 741 |
| 2008-01-01 00:00:00 | [-0.000 0.055 -0.246 0.099 -0.033 -0.045 0.071 0.009] | 0.12 | 0.11 | 743 |
| 2008-02-01 00:00:00 | [0.000 -0.115 -0.022 0.119 -0.068 -0.042 0.010 -0.016] | 0.03 | 0.02 | 799 |
| 2008-03-01 00:00:00 | [-0.000 0.055 0.183 0.016 0.095 0.093 0.088 0.110] | 0.1 | 0.1 | 816 |
| 2008-04-01 00:00:00 | [0.000 0.005 -0.143 -0.098 -0.161 -0.056 0.066 -0.137] | 0.08 | 0.07 | 813 |
| 2008-05-01 00:00:00 | [-0.000 -0.184 0.110 -0.113 -0.012 -0.023 0.087 -0.060] | 0.08 | 0.07 | 801 |
| 2008-06-01 00:00:00 | [0.000 0.087 -0.324 -0.046 0.004 0.065 -0.160 -0.025] | 0.13 | 0.12 | 812 |
| 2008-07-01 00:00:00 | [-0.000 -0.142 0.160 0.097 0.049 -0.012 -0.172 -0.219] | 0.16 | 0.15 | 818 |
| 2008-08-01 00:00:00 | [0.000 0.074 0.205 0.057 -0.052 -0.004 -0.110 -0.011] | 0.05 | 0.04 | 819 |
| 2008-09-01 00:00:00 | [0.000 -0.183 -0.070 0.008 -0.078 -0.031 0.102 -0.198] | 0.08 | 0.07 | 829 |
| 2008-10-01 00:00:00 | [-0.000 0.153 -0.183 -0.043 -0.069 0.083 -0.141 -0.085] | 0.1 | 0.09 | 836 |
| 2008-11-01 00:00:00 | [0.000 -0.104 -0.286 -0.216 0.169 0.064 0.056 -0.156] | 0.15 | 0.15 | 836 |
| 2008-12-01 00:00:00 | [0.000 0.128 -0.112 0.054 0.043 0.046 -0.160 0.190] | 0.13 | 0.12 | 834 |
| 2009-01-01 00:00:00 | [0.000 -0.057 -0.125 0.052 0.004 -0.073 -0.235 -0.158] | 0.1 | 0.09 | 844 |
| 2009-02-01 00:00:00 | [0.000 0.209 -0.103 -0.005 -0.004 0.066 -0.117 0.043] | 0.09 | 0.08 | 857 |
| 2009-03-01 00:00:00 | [0.000 -0.045 -0.093 0.015 0.070 -0.023 -0.074 -0.012] | 0.01 | 0.01 | 868 |
| 2009-04-01 00:00:00 | [0.000 0.189 -0.008 0.003 -0.097 0.007 -0.144 0.063] | 0.07 | 0.06 | 871 |
| 2009-05-01 00:00:00 | [0.000 -0.025 0.253 0.124 0.099 -0.007 -0.010 -0.040] | 0.1 | 0.1 | 817 |
| 2009-06-01 00:00:00 | [-0.000 0.268 0.117 0.151 0.017 -0.016 -0.100 -0.077] | 0.11 | 0.1 | 818 |
| 2009-07-01 00:00:00 | [0.000 -0.309 -0.326 -0.104 0.079 0.045 -0.148 0.026] | 0.22 | 0.22 | 811 |
| 2009-08-01 00:00:00 | [0.000 0.011 0.027 -0.021 0.212 0.043 0.028 -0.014] | 0.06 | 0.05 | 810 |
| 2009-09-01 00:00:00 | [0.000 0.127 -0.125 -0.018 -0.006 -0.062 0.068 -0.044] | 0.06 | 0.05 | 810 |
| 2009-10-01 00:00:00 | [-0.000 -0.036 -0.283 0.044 0.006 0.037 -0.025 -0.102] | 0.08 | 0.08 | 812 |
| 2009-11-01 00:00:00 | [0.000 -0.065 -0.120 0.026 0.032 -0.001 -0.072 0.016] | 0.03 | 0.02 | 824 |
| 2009-12-01 00:00:00 | [0.000 -0.118 -0.318 -0.048 0.032 -0.108 -0.257 -0.002] | 0.21 | 0.2 | 824 |
| 2010-01-01 00:00:00 | [0.000 -0.018 -0.177 0.067 -0.087 -0.030 0.081 0.038] | 0.07 | 0.06 | 834 |
| 2010-02-01 00:00:00 | [0.000 0.203 -0.111 -0.043 0.005 0.039 0.052 -0.027] | 0.06 | 0.06 | 984 |
| 2010-03-01 00:00:00 | [-0.000 -0.214 -0.004 -0.120 0.028 -0.046 0.036 -0.205] | 0.11 | 0.11 | 982 |
| 2010-04-01 00:00:00 | [-0.000 -0.245 0.054 -0.106 0.035 0.019 0.111 0.022] | 0.1 | 0.1 | 976 |
| 2010-05-01 00:00:00 | [-0.000 0.033 0.018 0.006 0.076 0.100 -0.074 -0.066] | 0.03 | 0.03 | 955 |
| 2010-06-01 00:00:00 | [-0.000 0.252 -0.200 0.027 0.110 0.018 -0.157 0.115] | 0.13 | 0.12 | 952 |
| 2010-07-01 00:00:00 | [-0.000 -0.051 -0.183 -0.142 -0.027 -0.061 0.173 0.042] | 0.16 | 0.15 | 957 |
| 2010-08-01 00:00:00 | [-0.000 -0.115 0.012 -0.138 -0.018 -0.005 -0.024 -0.025] | 0.03 | 0.03 | 958 |
| 2010-09-01 00:00:00 | [-0.000 0.245 0.211 -0.074 0.028 0.040 -0.126 0.083] | 0.11 | 0.11 | 964 |
| 2010-10-01 00:00:00 | [-0.000 -0.208 -0.202 -0.097 0.030 0.001 0.176 -0.108] | 0.17 | 0.17 | 971 |
| 2010-11-01 00:00:00 | [-0.000 0.146 0.060 -0.001 0.013 0.151 0.001 0.137] | 0.08 | 0.08 | 978 |
| 2010-12-01 00:00:00 | [0.000 0.060 0.039 0.209 0.038 -0.037 -0.164 -0.019] | 0.12 | 0.12 | 984 |
| 2011-01-01 00:00:00 | [0.000 0.235 -0.171 -0.075 -0.110 -0.031 0.162 0.035] | 0.18 | 0.17 | 983 |
| 2011-02-01 00:00:00 | [0.000 0.159 -0.064 0.182 0.075 0.003 -0.099 0.049] | 0.08 | 0.07 | 1092 |
| 2011-03-01 00:00:00 | [-0.000 -0.069 0.034 0.222 0.033 -0.036 0.005 -0.025] | 0.06 | 0.05 | 1109 |
| 2011-04-01 00:00:00 | [-0.000 -0.080 0.027 -0.095 0.014 0.005 -0.095 0.060] | 0.02 | 0.01 | 1137 |
| 2011-05-01 00:00:00 | [0.000 0.090 -0.056 0.026 0.039 0.077 0.257 0.004] | 0.1 | 0.09 | 1128 |
| 2011-06-01 00:00:00 | [-0.000 -0.029 -0.126 -0.236 -0.002 0.015 -0.048 -0.111] | 0.09 | 0.08 | 1131 |
| 2011-07-01 00:00:00 | [0.000 -0.046 -0.104 -0.172 0.104 0.026 -0.108 -0.106] | 0.07 | 0.06 | 1141 |
| 2011-08-01 00:00:00 | [0.000 0.059 0.096 0.135 0.058 -0.137 -0.208 -0.107] | 0.13 | 0.12 | 1186 |
| 2011-09-01 00:00:00 | [0.000 -0.114 0.007 0.013 -0.070 0.054 0.053 0.073] | 0.02 | 0.02 | 1200 |
| 2011-10-01 00:00:00 | [-0.000 -0.044 -0.092 -0.190 -0.036 -0.006 -0.000 -0.098] | 0.05 | 0.04 | 1191 |
| 2011-11-01 00:00:00 | [0.000 -0.010 0.247 0.263 0.201 0.060 -0.017 0.022] | 0.19 | 0.18 | 1230 |
| 2011-12-01 00:00:00 | [0.000 0.307 0.198 0.279 0.131 -0.206 -0.059 -0.055] | 0.18 | 0.18 | 1243 |
| 2012-01-01 00:00:00 | [0.000 0.155 -0.238 -0.040 0.003 0.068 -0.028 0.063] | 0.12 | 0.12 | 1242 |
| 2012-02-01 00:00:00 | [0.000 -0.122 -0.116 -0.011 0.115 0.028 0.146 -0.155] | 0.08 | 0.08 | 1314 |
| 2012-03-01 00:00:00 | [-0.000 0.179 -0.019 0.191 0.087 -0.123 -0.118 -0.150] | 0.1 | 0.09 | 1349 |
| 2012-04-01 00:00:00 | [-0.000 0.026 -0.040 -0.092 0.034 0.058 0.087 0.021] | 0.04 | 0.03 | 1369 |
| 2012-05-01 00:00:00 | [-0.000 -0.153 -0.052 -0.053 0.011 0.078 0.159 -0.075] | 0.07 | 0.06 | 1321 |
| 2012-06-01 00:00:00 | [0.000 -0.022 0.121 0.109 0.059 0.042 0.202 -0.082] | 0.08 | 0.07 | 1327 |
| 2012-07-01 00:00:00 | [0.000 -0.013 -0.265 -0.130 -0.103 0.040 -0.033 -0.035] | 0.12 | 0.11 | 1334 |
| 2012-08-01 00:00:00 | [0.000 0.064 0.196 -0.064 0.030 -0.018 -0.075 -0.037] | 0.04 | 0.04 | 1334 |
| 2012-09-01 00:00:00 | [0.000 -0.047 -0.141 0.194 0.052 -0.055 0.151 0.051] | 0.05 | 0.05 | 1348 |
| 2012-10-01 00:00:00 | [-0.000 -0.074 0.195 0.319 0.091 -0.030 -0.009 -0.076] | 0.19 | 0.18 | 1338 |
| 2012-11-01 00:00:00 | [0.000 0.128 0.046 0.003 0.023 0.075 0.067 0.025] | 0.03 | 0.02 | 1331 |
| 2012-12-01 00:00:00 | [-0.000 -0.079 -0.071 -0.078 -0.068 0.017 -0.032 -0.046] | 0.02 | 0.02 | 1322 |
| 2013-01-01 00:00:00 | [-0.000 -0.033 -0.144 -0.140 -0.054 0.073 0.069 -0.065] | 0.07 | 0.06 | 1320 |
| 2013-02-01 00:00:00 | [-0.000 -0.185 -0.144 -0.068 0.033 0.003 0.153 -0.092] | 0.09 | 0.08 | 1404 |
| 2013-03-01 00:00:00 | [0.000 -0.003 -0.007 0.010 0.022 0.072 0.126 -0.083] | 0.03 | 0.03 | 1414 |
| 2013-04-01 00:00:00 | [0.000 0.094 -0.181 -0.169 -0.065 0.043 0.065 0.095] | 0.12 | 0.12 | 1422 |
| 2013-05-01 00:00:00 | [0.000 -0.069 0.008 -0.059 0.078 -0.001 0.176 -0.064] | 0.06 | 0.06 | 1395 |
| 2013-06-01 00:00:00 | [-0.000 0.020 -0.129 -0.121 -0.020 -0.029 0.131 0.101] | 0.09 | 0.09 | 1378 |
| 2013-07-01 00:00:00 | [0.000 -0.052 -0.136 0.191 0.033 0.026 -0.096 -0.037] | 0.08 | 0.08 | 1380 |
| 2013-08-01 00:00:00 | [0.000 -0.030 0.006 -0.065 -0.077 0.038 0.092 0.138] | 0.05 | 0.05 | 1380 |
| 2013-09-01 00:00:00 | [0.000 -0.085 -0.085 0.169 0.074 -0.044 -0.079 -0.120] | 0.08 | 0.08 | 1374 |
| 2013-10-01 00:00:00 | [0.000 0.095 -0.097 -0.063 -0.127 0.041 0.160 -0.035] | 0.1 | 0.09 | 1358 |
| 2013-11-01 00:00:00 | [0.000 -0.088 -0.117 -0.001 0.143 -0.064 -0.036 -0.072] | 0.04 | 0.04 | 1380 |
| 2013-12-01 00:00:00 | [0.000 0.034 -0.105 -0.068 -0.045 0.041 0.365 -0.072] | 0.2 | 0.19 | 1367 |
| 2014-01-01 00:00:00 | [0.000 0.042 -0.178 -0.008 -0.039 -0.062 -0.088 -0.112] | 0.07 | 0.06 | 1371 |
| 2014-02-01 00:00:00 | [0.000 -0.060 -0.104 0.238 0.100 0.004 -0.165 -0.076] | 0.15 | 0.15 | 1415 |
| 2014-03-01 00:00:00 | [0.000 -0.006 0.059 0.018 0.020 0.034 -0.025 -0.027] | 0.01 | 0.01 | 1413 |
| 2014-04-01 00:00:00 | [-0.000 0.053 -0.021 -0.077 -0.159 0.015 0.111 -0.089] | 0.08 | 0.07 | 1371 |
| 2014-05-01 00:00:00 | [-0.000 0.071 -0.060 -0.126 -0.038 -0.005 0.020 -0.100] | 0.06 | 0.05 | 1320 |
| 2014-06-01 00:00:00 | [0.000 -0.059 -0.061 0.149 0.050 -0.016 -0.207 0.074] | 0.11 | 0.1 | 1299 |
| 2014-07-01 00:00:00 | [0.000 -0.016 -0.132 -0.124 -0.135 0.014 0.096 -0.058] | 0.08 | 0.08 | 1298 |
| 2014-08-01 00:00:00 | [0.000 0.058 -0.270 0.109 -0.031 0.013 -0.018 0.034] | 0.09 | 0.08 | 1264 |
| 2014-09-01 00:00:00 | [-0.000 -0.009 -0.059 0.149 0.024 0.050 -0.024 0.006] | 0.02 | 0.02 | 1241 |
| 2014-10-01 00:00:00 | [0.000 -0.007 0.103 0.233 -0.074 0.001 -0.017 0.010] | 0.09 | 0.08 | 1209 |
| 2014-11-01 00:00:00 | [-0.000 0.019 0.333 0.355 0.049 0.025 -0.028 0.119] | 0.37 | 0.37 | 1205 |
| 2014-12-01 00:00:00 | [0.000 0.174 -0.059 -0.210 0.078 0.011 0.027 -0.166] | 0.21 | 0.21 | 1198 |
| 2015-01-01 00:00:00 | [0.000 0.164 0.030 -0.060 -0.016 0.008 0.077 -0.040] | 0.04 | 0.03 | 1181 |
| 2015-02-01 00:00:00 | [0.000 0.117 -0.211 -0.003 -0.016 0.054 0.041 0.049] | 0.07 | 0.06 | 1210 |
| 2015-03-01 00:00:00 | [-0.000 -0.016 -0.041 0.123 -0.019 -0.069 0.100 0.062] | 0.03 | 0.03 | 1229 |
| 2015-04-01 00:00:00 | [0.000 0.111 -0.245 -0.244 -0.013 0.016 -0.007 -0.047] | 0.2 | 0.2 | 1175 |
| 2015-05-01 00:00:00 | [-0.000 -0.315 -0.123 0.220 0.081 -0.038 -0.000 0.054] | 0.2 | 0.2 | 1101 |
| 2015-06-01 00:00:00 | [-0.000 0.281 0.222 -0.008 0.172 -0.046 -0.166 -0.079] | 0.11 | 0.1 | 1081 |
| 2015-07-01 00:00:00 | [-0.000 -0.066 -0.048 0.113 -0.012 -0.080 -0.112 0.087] | 0.08 | 0.07 | 998 |
| 2015-08-01 00:00:00 | [-0.000 0.298 0.005 -0.020 0.083 0.030 -0.076 0.004] | 0.08 | 0.08 | 1007 |
| 2015-09-01 00:00:00 | [0.000 0.227 -0.181 -0.184 -0.123 0.039 0.024 -0.031] | 0.23 | 0.22 | 1007 |
| 2015-10-01 00:00:00 | [0.000 0.203 -0.141 0.051 0.096 0.121 -0.029 0.035] | 0.09 | 0.08 | 969 |
| 2015-11-01 00:00:00 | [0.000 0.024 -0.157 0.017 0.088 -0.013 -0.065 -0.092] | 0.03 | 0.02 | 961 |
| 2015-12-01 00:00:00 | [-0.000 -0.245 0.126 0.153 0.055 0.016 0.026 -0.094] | 0.21 | 0.21 | 989 |
| 2016-01-01 00:00:00 | [0.000 -0.129 -0.090 0.088 -0.011 -0.039 0.036 -0.029] | 0.03 | 0.02 | 995 |
| 2016-02-01 00:00:00 | [-0.000 0.341 -0.078 -0.065 0.091 0.069 -0.142 0.137] | 0.16 | 0.16 | 1037 |
| 2016-03-01 00:00:00 | [-0.000 -0.119 -0.150 0.004 0.061 0.043 0.079 -0.130] | 0.03 | 0.03 | 1068 |
| 2016-04-01 00:00:00 | [0.000 0.130 0.091 -0.095 0.058 -0.011 -0.104 -0.077] | 0.03 | 0.03 | 1076 |
| 2016-05-01 00:00:00 | [-0.000 0.094 -0.166 -0.103 0.035 0.079 0.040 0.011] | 0.1 | 0.09 | 1080 |
| 2016-06-01 00:00:00 | [0.000 -0.276 -0.042 0.112 0.090 -0.104 -0.097 -0.101] | 0.21 | 0.2 | 1088 |
| 2016-07-01 00:00:00 | [-0.000 0.042 -0.104 0.087 -0.028 0.025 -0.044 -0.116] | 0.03 | 0.03 | 1100 |
| 2016-08-01 00:00:00 | [0.000 -0.115 -0.157 0.065 0.070 0.039 -0.030 -0.151] | 0.05 | 0.05 | 1183 |
| 2016-09-01 00:00:00 | [0.000 0.022 -0.046 0.069 -0.068 -0.028 0.113 0.099] | 0.04 | 0.03 | 1213 |
| 2016-10-01 00:00:00 | [-0.000 0.044 0.047 0.243 0.000 -0.024 -0.060 -0.061] | 0.08 | 0.08 | 1250 |
| 2016-11-01 00:00:00 | [-0.000 -0.151 -0.113 0.140 0.014 -0.066 0.067 -0.009] | 0.06 | 0.05 | 1286 |
| 2016-12-01 00:00:00 | [0.000 -0.044 0.110 0.260 0.067 -0.070 0.038 -0.034] | 0.12 | 0.11 | 1324 |
| 2017-01-01 00:00:00 | [0.000 0.070 -0.102 0.076 0.018 0.036 0.063 0.023] | 0.02 | 0.01 | 1350 |
| 2017-02-01 00:00:00 | [-0.000 -0.029 0.009 0.094 0.172 0.056 0.114 -0.046] | 0.05 | 0.05 | 1470 |
| 2017-03-01 00:00:00 | [0.000 -0.048 0.093 0.156 0.153 0.045 -0.037 0.026] | 0.08 | 0.07 | 1497 |
| 2017-04-01 00:00:00 | [0.000 -0.051 0.247 0.089 0.044 -0.018 -0.045 -0.073] | 0.1 | 0.1 | 1527 |
| 2017-05-01 00:00:00 | [-0.000 0.123 0.031 0.049 0.159 -0.056 0.177 -0.166] | 0.09 | 0.09 | 1517 |
| 2017-06-01 00:00:00 | [0.000 0.100 -0.013 0.307 0.101 -0.075 0.081 -0.110] | 0.13 | 0.13 | 1556 |
| 2017-07-01 00:00:00 | [0.000 -0.014 -0.001 -0.117 -0.092 0.026 -0.004 0.040] | 0.02 | 0.01 | 1577 |
| 2017-08-01 00:00:00 | [0.000 0.054 0.066 -0.148 0.015 0.075 -0.070 -0.067] | 0.05 | 0.05 | 1579 |
| 2017-09-01 00:00:00 | [0.000 -0.093 0.187 -0.041 0.130 0.058 0.093 -0.272] | 0.17 | 0.16 | 1594 |
| 2017-10-01 00:00:00 | [-0.000 0.017 0.143 0.149 0.077 -0.055 0.085 0.121] | 0.09 | 0.09 | 1591 |
| 2017-11-01 00:00:00 | [-0.000 -0.011 0.055 -0.030 0.068 0.035 0.138 0.038] | 0.05 | 0.05 | 1643 |
| 2017-12-01 00:00:00 | [0.000 -0.053 0.191 0.261 0.137 -0.033 0.055 -0.095] | 0.16 | 0.16 | 1632 |
| 2018-01-01 00:00:00 | [-0.000 0.091 -0.034 -0.122 0.030 0.073 0.145 0.045] | 0.07 | 0.07 | 1648 |
| 2018-02-01 00:00:00 | [-0.000 0.048 -0.048 -0.321 -0.122 0.068 -0.209 0.004] | 0.18 | 0.17 | 1688 |
| 2018-03-01 00:00:00 | [0.000 -0.013 0.019 -0.062 -0.024 -0.032 0.054 0.008] | 0.01 | 0.0 | 1743 |
| 2018-04-01 00:00:00 | [-0.000 -0.078 0.046 -0.058 0.066 -0.021 0.059 -0.088] | 0.04 | 0.04 | 1759 |
| 2018-05-01 00:00:00 | [0.000 0.005 0.060 0.126 0.156 -0.009 0.193 0.000] | 0.09 | 0.09 | 1773 |
| 2018-06-01 00:00:00 | [-0.000 0.017 -0.001 0.171 0.015 -0.098 -0.030 -0.090] | 0.07 | 0.06 | 1737 |
| 2018-07-01 00:00:00 | [-0.000 -0.090 0.011 0.101 -0.123 -0.060 0.113 -0.150] | 0.06 | 0.06 | 1762 |
| 2018-08-01 00:00:00 | [0.000 0.067 0.190 0.123 0.008 -0.095 -0.094 0.036] | 0.07 | 0.06 | 1835 |
| 2018-09-01 00:00:00 | [-0.000 -0.087 0.033 0.153 -0.035 -0.021 -0.007 -0.024] | 0.05 | 0.04 | 1849 |
| 2018-10-01 00:00:00 | [-0.000 0.210 -0.088 -0.040 -0.050 -0.012 -0.183 -0.046] | 0.12 | 0.12 | 1858 |
| 2018-11-01 00:00:00 | [0.000 -0.055 -0.007 0.020 -0.009 -0.006 0.065 -0.081] | 0.01 | 0.01 | 1900 |
| 2018-12-01 00:00:00 | [0.000 -0.043 0.145 0.072 0.075 -0.087 0.021 -0.098] | 0.07 | 0.07 | 1915 |
| 2019-01-01 00:00:00 | [0.000 0.103 -0.063 -0.160 -0.125 0.008 -0.217 0.145] | 0.12 | 0.12 | 1952 |
| 2019-02-01 00:00:00 | [0.000 0.112 -0.122 0.006 0.022 -0.024 0.117 -0.010] | 0.03 | 0.03 | 1947 |
| 2019-03-01 00:00:00 | [0.000 -0.082 0.008 0.106 0.108 -0.018 0.073 0.016] | 0.04 | 0.03 | 1979 |
| 2019-04-01 00:00:00 | [-0.000 -0.050 -0.054 -0.103 -0.102 -0.041 0.031 -0.045] | 0.02 | 0.02 | 2018 |
| 2019-05-01 00:00:00 | [0.000 -0.021 0.163 -0.004 0.019 0.022 0.027 -0.085] | 0.04 | 0.04 | 2041 |
| 2019-06-01 00:00:00 | [-0.000 -0.062 0.079 -0.086 0.016 0.043 0.007 -0.054] | 0.02 | 0.02 | 2059 |
| 2019-07-01 00:00:00 | [-0.000 -0.023 0.041 -0.245 -0.048 0.016 0.052 0.017] | 0.07 | 0.06 | 2101 |
| 2019-08-01 00:00:00 | [-0.000 0.072 -0.029 -0.064 0.058 0.042 -0.081 -0.009] | 0.02 | 0.02 | 2096 |
| 2019-09-01 00:00:00 | [0.000 0.037 0.055 -0.025 0.018 0.008 0.075 -0.117] | 0.02 | 0.02 | 2108 |
| 2019-10-01 00:00:00 | [0.000 -0.068 0.074 0.022 0.047 -0.018 -0.037 0.004] | 0.02 | 0.02 | 2127 |
| 2019-11-01 00:00:00 | [0.000 0.109 0.011 -0.060 -0.027 0.065 -0.069 0.077] | 0.02 | 0.02 | 2118 |
| 2019-12-01 00:00:00 | [-0.000 0.047 -0.040 -0.231 -0.035 0.051 0.048 0.071] | 0.09 | 0.08 | 2116 |
+---------------------+-----------------------------------------------------------+----------+--------------+---------------+
+-----------+--------+---------+--------+----------+-------------------+----------+-------------------+-----------+---------------+-----------+
| Intercept | beta | Size | BM | ROE(TTM) | asset_growth_rate | momentum | specific_Turnover | Average R | Average adj R | Average n |
+-----------+--------+---------+--------+----------+-------------------+----------+-------------------+-----------+---------------+-----------+
| 0.0 | 0.0078 | -0.0211 | 0.0223 | 0.026 | 0.0049 | 0.0114 | -0.0265 | 0.094 | 0.087 | 1071.59 |
| 1.495 | 0.924 | -2.362 | 2.699 | 4.345 | 1.31 | 1.354 | -4.777 | - | - | - |
+-----------+--------+---------+--------+----------+-------------------+----------+-------------------+-----------+---------------+-----------+
The first dataset **excludes 30% tail **stocks from 2000-01-01 to 2019-12-01. Factors including size factor (Size), value factor (BM), profitability factor (ROE(TTM)) and turnover factor (specific_Turnover) have significant risk premium. Factors including market, investment, and momentum factor have insignificant risk premium.
# %% Fama-Macbeth regression
# dataset : #2
# include tail stocks
# range from 2000-01 ~ 2019-12-01
from fama_macbeth import Fama_macbeth_regress
test_data_2 = return_company[(return_company['Ndaytrd']>=10)]
test_data_2 = test_data_2[['emrwd', 'beta', 'Msmvttl', 'PE1A', 'ROE(TTM)', 'asset_growth_rate', 'momentum', 'specific_Turnover', 'Date_merge']].dropna()
test_data_2 = test_data_2[(test_data_2['Date_merge'] >= '2000-01-01') & (test_data_2['Date_merge'] <= '2019-12-01')]
model = Fama_macbeth_regress(test_data_2)
result = model.fit(add_constant=True)
print(result)
model.summary()
model.summary_by_time()
================================================================================================================================
+-----------+--------+---------+--------+----------+-------------------+----------+-------------------+-----------+---------------+-----------+
| Intercept | beta | Size | BM | ROE(TTM) | asset_growth_rate | momentum | specific_Turnover | Average R | Average adj R | Average n |
+-----------+--------+---------+--------+----------+-------------------+----------+-------------------+-----------+---------------+-----------+
| 0.0 | 0.0107 | -0.0409 | 0.0206 | 0.0224 | 0.006 | 0.0069 | -0.027 | 0.088 | 0.083 | 1429.13 |
| 1.616 | 1.397 | -4.114 | 2.845 | 4.346 | 1.644 | 0.875 | -5.287 | - | - | - |
+-----------+--------+---------+--------+----------+-------------------+----------+-------------------+-----------+---------------+-----------+
The second dataset **contains 30% tail **stocks from 2000-01-01 to 2019-12-01. Factors including size factor (Size), value factor (BM), profitability (ROE(TTM)), turnover factor (specific_Turnover) have significant risk premium. Factors including market, investment, and momentum factor have insignificant risk premium.
# %% Fama-Macbeth regression
# dataset : #3
# exclude tail stocks
# range from 2000-01-01 ~ 2016-12-01
from fama_macbeth import Fama_macbeth_regress
test_data_3 = return_company[(return_company['cap']==True) & (return_company['Ndaytrd']>=10)]
test_data_3 = test_data_3[['emrwd', 'beta', 'Size', 'BM', 'ROE(TTM)', 'asset_growth_rate', 'momentum', 'specific_Turnover', 'Date_merge']].dropna()
test_data_3 = test_data_3[(test_data_3['Date_merge'] >= '2000-01-01') & (test_data_3['Date_merge'] <= '2016-12-01')]
model = Fama_macbeth_regress(test_data_3)
result = model.fit(add_constant=True)
print(result)
model.summary()
model.summary_by_time()
================================================================================================================================
+-----------+--------+---------+--------+----------+-------------------+----------+-------------------+-----------+---------------+-----------+
| Intercept | beta | Size | BM | ROE(TTM) | asset_growth_rate | momentum | specific_Turnover | Average R | Average adj R | Average n |
+-----------+--------+---------+--------+----------+-------------------+----------+-------------------+-----------+---------------+-----------+
| 0.0 | 0.0076 | -0.0326 | 0.0258 | 0.0261 | 0.0062 | 0.0092 | -0.026 | 0.099 | 0.092 | 930.59 |
| 0.632 | 0.778 | -3.225 | 2.93 | 3.93 | 1.466 | 0.971 | -4.276 | - | - | - |
+-----------+--------+---------+--------+----------+-------------------+----------+-------------------+-----------+---------------+-----------+
The third dataset **excludes 30% tail **stocks from 2000-01-01 to 2016-12-01. Factors including size factor (Size), value factor (BM), profitability (ROE(TTM)), turnover factor (specific_Turnover) have significant risk premium. Factors including market, investment, and momentum factor have insignificant risk premium.
# %% Fama-Macbeth regression
# dataset : #4
# include tail stocks
# range from 2000-01-01 ~ 2016-12-01
from fama_macbeth import Fama_macbeth_regress
test_data_4 = return_company[(return_company['Ndaytrd']>=10)]
test_data_4 = test_data_4[['emrwd', 'beta', 'Size', 'BM', 'ROE(TTM)', 'asset_growth_rate', 'momentum', 'specific_Turnover', 'Date_merge']].dropna()
test_data_4 = test_data_4[(test_data_4['Date_merge'] >= '2000-01-01') & (test_data_4['Date_merge'] <= '2016-12-01')]
model = Fama_macbeth_regress(test_data_4)
result = model.fit(add_constant=True)
print(result)
model.summary()
model.summary_by_time()
================================================================================================================================
+-----------+-------+---------+--------+----------+-------------------+----------+-------------------+-----------+---------------+-----------+
| Intercept | beta | Size | BM | ROE(TTM) | asset_growth_rate | momentum | specific_Turnover | Average R | Average adj R | Average n |
+-----------+-------+---------+--------+----------+-------------------+----------+-------------------+-----------+---------------+-----------+
| 0.0 | 0.01 | -0.0541 | 0.0235 | 0.0224 | 0.007 | 0.0053 | -0.027 | 0.094 | 0.089 | 1237.96 |
| 1.223 | 1.125 | -4.807 | 3.053 | 3.84 | 1.722 | 0.595 | -4.857 | - | - | - |
+-----------+-------+---------+--------+----------+-------------------+----------+-------------------+-----------+---------------+-----------+
The fourth dataset **contains 30% tail **stocks from 2000-01-01 to 2016-12-01. Factors including size factor (Size), value factor (BM), profitability (ROE(TTM)), turnover factor (specific_Turnover) have significant risk premium. Factors including market, investment, and momentum factor have insignificant risk premium.
Factor risk premium
This demo constructs factor risk premium, including market system risk premium, SMB, HML, RMW, CMA. Following the convention of Fama-French(1993), the factor mimicking portfolio is constituted first, from which then the factor risk premium is calculated. Details are in the introduction of class Factor_mimicking_portfolio.
In this demo, data are collected from CSMAR dataset. WARNING: Do Not use dataset in this demo for any commercial purpose.
# %% set system path
import sys,os
sys.path.append(os.path.abspath(".."))
Data preprocessing.
# %% import data
import pandas as pd
month_return = pd.read_hdf('.\data\month_return.h5', key='month_return')
company_data = pd.read_hdf('.\data\last_filter_pe.h5', key='data')
trade_data = pd.read_hdf('.\data\mean_filter_trade.h5', key='data')
beta = pd.read_hdf('.\\data\\beta.h5', key='data')
# %% data preprocessing
# forward the monthly return for each stock
# emrwd is the return including dividend
month_return['emrwd'] = month_return.groupby(['Stkcd'])['Mretwd'].shift(-1)
# emrnd is the return including no dividend
month_return['emrnd'] = month_return.groupby(['Stkcd'])['Mretnd'].shift(-1)
# select the A share stock
month_return = month_return[month_return['Markettype'].isin([1, 4, 16])]
# % distinguish the stocks whose size is among the up 30% stocks in each month
def percentile(stocks) :
return stocks >= stocks.quantile(q=.3)
month_return['cap'] = month_return.groupby(['Trdmnt'])['Msmvttl'].apply(percentile)
Construct proxy variable.
# %% Construct proxy variable
import numpy as np
# SMB
# log(Size)
month_return['Size'] = np.log(month_return['Msmvttl'])
# HML
company_data['BM'] = 1 / company_data['PBV1A']
# RMW
# in this demo, the ROE(TTM) are used
# ROE(TTM) = PBV1B/PE(TTM)
company_data['ROE(TTM)'] = company_data['PBV1B']/company_data['PE1TTM']
# CMA
# % calculate the total asset
# asset = debt + equity
# debt = company_value - market_value
# equity = market_value / PB
company_data['debt'] = company_data['EV1'] - company_data['MarketValue']
company_data['equity'] = company_data['MarketValue']/company_data['PBV1A']
company_data['asset'] = company_data['debt'] + company_data['equity']
# asset growth rate
company_data['asset_growth_rate'] = company_data['asset'].groupby(['Symbol']).diff(12)/company_data['asset']
# Momentum
month_return['rolling_12'] = np.array(month_return.groupby(['Stkcd'])['Mretwd'].rolling(12).sum())
month_return['momentum'] = month_return['rolling_12'] - month_return['Mretwd']
# Turnover
trade_data['rolling_Turnover'] = np.array(trade_data['Turnover'].groupby('Symbol').rolling(12).mean())
trade_data['specific_Turnover'] = trade_data['Turnover'] / trade_data['rolling_Turnover']
Merge data.
# %% merge data
from pandas.tseries.offsets import *
month_return['Stkcd_merge'] = month_return['Stkcd'].astype(dtype='string')
month_return['Date_merge'] = pd.to_datetime(month_return['Trdmnt'])
#month_return['Date_merge'] += MonthEnd()
company_data['Stkcd_merge'] = company_data['Symbol'].dropna().astype(dtype='int').astype(dtype='string')
company_data['Date_merge'] = pd.to_datetime(company_data['TradingDate'])
company_data['Date_merge'] += MonthBegin()
trade_data['Stkcd_merge'] = trade_data['Symbol'].dropna().astype(dtype='int').astype(dtype='string')
trade_data['TradingDate'] = trade_data.index.map(lambda x : x[1])
trade_data['Date_merge'] = pd.to_datetime(trade_data['TradingDate'])
#company_data['Yearmonth'] = company_data['Date_merge'].map(lambda x : 1000*x.year + x.month)
trade_data['Date_merge'] += MonthBegin()
# dataset starts from '2000-01'
company_data = company_data[company_data['Date_merge'] >= '2000-01']
month_return = month_return[month_return['Date_merge'] >= '2000-01']
return_company = pd.merge(month_return, company_data, on=['Stkcd_merge', 'Date_merge'])
return_company = pd.merge(return_company, trade_data, on=['Stkcd_merge', 'Date_merge'])
# beta
return_company = return_company.set_index(['Stkcd', 'Trdmnt'])
return_company = pd.merge(return_company, beta, left_index=True, right_index=True)
Generate factor risk premium.
# %% generate factor risk premium
from fama_macbeth import Factor_mimicking_portfolio
import numpy as np
# Size and Value factor risk premium
# select stocks whose size is among the up 30% stocks in each month and whose trading
# days are more than or equal to 10 days
size_bm = return_company[(return_company['Ndaytrd']>=10)]
size_bm = size_bm[['emrwd', 'Size', 'BM', 'Date_merge', 'Size']].dropna()
size_bm = size_bm[(size_bm['Date_merge'] >= '2000-01-01') & (size_bm['Date_merge'] <= '2019-12-01')]
# construct portfolio
size_bm_portfolio = Factor_mimicking_portfolio(np.array(size_bm))
CNSMB, CNHML = size_bm_portfolio.portfolio_return()
CNSMB = - CNSMB
CNSMB = CNSMB.rename('SMB')
CNHML = CNHML.rename('HML')
size_rmw = return_company[(return_company['Ndaytrd']>=10)]
size_rmw = size_rmw[['emrwd', 'Size', 'ROE(TTM)', 'Date_merge', 'Size']].dropna()
size_rmw = size_rmw[(size_rmw['Date_merge'] >= '2004-01-01') & (size_rmw['Date_merge'] <= '2019-12-01')]
# construct portoflio
size_rmw_portfolio = Factor_mimicking_portfolio(np.array(size_rmw))
CNrow, CNRMW = size_rmw_portfolio.portfolio_return()
CNRMW = CNRMW.rename('RMW')
size_cma = return_company[(return_company['Ndaytrd']>=10)]
size_cma = size_cma[['emrwd', 'Size', 'asset_growth_rate', 'Date_merge', 'Size']].dropna()
size_cma = size_cma[(size_cma['Date_merge'] >= '2000-01-01') & (size_cma['Date_merge'] <= '2019-12-01')]
# construct portoflio
size_cma_portfolio = Factor_mimicking_portfolio(np.array(size_cma))
CNrow, CNCMA = size_cma_portfolio.portfolio_return()
CNCMA = CNCMA.rename('CMA')
# generate market portoflio and market risk premium
from portfolio_analysis import Univariate
beta_portfolio = return_company[(return_company['Ndaytrd']>=10)]
beta_portfolio = beta_portfolio[['emrwd', 'Size', 'Date_merge']].dropna()
beta_portfolio = Univariate(np.array(beta_portfolio), number=0)
beta = beta_portfolio.average_by_time()
CNBETA = pd.Series(beta[0], index=np.unique(beta_portfolio.sample[:, 2]))
CNBETA = CNBETA.rename('BETA')
# %% merge data
risk_premium = pd.concat([CNBETA, CNSMB, CNHML, CNRMW, CNCMA], axis=1).shift(1)
Anomaly Portfolio
PCF, Asset growth rate, and turnover rate
This demo exams whether classic asset pricing models can explain some anomaly portfolio return. Anomaly portfolios, including price cash flow, asset growth rate, and turnover rate, are constructed by univariate analysis. Precisely, stocks are grouped by characteristics or proxy variables into 10 groups, and the difference return between the head group and the tail group is taken as anomaly portfolio return. classic asset pricing models include Fama-French 3 factors model, Carhart 4 factors model, and Fama-French 5 factors model, whose factor risk premium is constructed through factor mimicking portfolio.
In this demo, Fama-French 3 factors model and Fama-French 5 factors are used. Data are collected from CSMAR dataset. WARNING: Do Not use dataset in this demo for any commercial purpose.
# %% set system path
import sys,os
sys.path.append(os.path.abspath(".."))
# %% import data
import pandas as pd
month_return = pd.read_hdf('.\\data\\month_return.h5', key='month_return')
company_data = pd.read_hdf('.\\data\\last_filter_pe.h5', key='data')
trade_data = pd.read_hdf('.\\data\\mean_filter_trade.h5', key='data')
beta = pd.read_hdf('.\\data\\beta.h5', key='data')
risk_premium = pd.read_hdf('.\\data\\risk_premium.h5', key='data')
Data preprocessing.
# %% data preprocessing
# forward the monthly return for each stock
# emrwd is the return including dividend
month_return['emrwd'] = month_return.groupby(['Stkcd'])['Mretwd'].shift(-1)
# emrnd is the return including no dividend
month_return['emrnd'] = month_return.groupby(['Stkcd'])['Mretnd'].shift(-1)
# select the A share stock
month_return = month_return[month_return['Markettype'].isin([1, 4, 16])]
# % distinguish the stocks whose size is among the up 30% stocks in each month
def percentile(stocks) :
return stocks >= stocks.quantile(q=.3)
month_return['cap'] = month_return.groupby(['Trdmnt'])['Msmvttl'].apply(percentile)
Construct proxy variable.
# %% Construct proxy variable
import numpy as np
# CMA
# % calculate the total asset
# asset = debt + equity
# debt = company_value - market_value
# equity = market_value / PB
company_data['debt'] = company_data['EV1'] - company_data['MarketValue']
company_data['equity'] = company_data['MarketValue']/company_data['PBV1A']
company_data['asset'] = company_data['debt'] + company_data['equity']
# asset growth rate
company_data['asset_growth_rate'] = company_data['asset'].groupby(['Symbol']).diff(12)/company_data['asset']
# Turnover
trade_data['rolling_Turnover'] = np.array(trade_data['Turnover'].groupby('Symbol').rolling(12).mean())
trade_data['specific_Turnover'] = trade_data['Turnover'] / trade_data['rolling_Turnover']
Merge data.
# %% merge data
from pandas.tseries.offsets import *
month_return['Stkcd_merge'] = month_return['Stkcd'].astype(dtype='string')
month_return['Date_merge'] = pd.to_datetime(month_return['Trdmnt'])
#month_return['Date_merge'] += MonthEnd()
company_data['Stkcd_merge'] = company_data['Symbol'].dropna().astype(dtype='int').astype(dtype='string')
company_data['Date_merge'] = pd.to_datetime(company_data['TradingDate'])
company_data['Date_merge'] += MonthBegin()
trade_data['Stkcd_merge'] = trade_data['Symbol'].dropna().astype(dtype='int').astype(dtype='string')
trade_data['TradingDate'] = trade_data.index.map(lambda x : x[1])
trade_data['Date_merge'] = pd.to_datetime(trade_data['TradingDate'])
#company_data['Yearmonth'] = company_data['Date_merge'].map(lambda x : 1000*x.year + x.month)
trade_data['Date_merge'] += MonthBegin()
# dataset starts from '2000-01'
company_data = company_data[company_data['Date_merge'] >= '2000-01']
month_return = month_return[month_return['Date_merge'] >= '2000-01']
return_company = pd.merge(month_return, company_data, on=['Stkcd_merge', 'Date_merge'])
return_company = pd.merge(return_company, trade_data, on=['Stkcd_merge', 'Date_merge'])
# beta
return_company = return_company.set_index(['Stkcd', 'Trdmnt'])
return_company = pd.merge(return_company, beta, left_index=True, right_index=True)
Construct anomaly portfolios and their return.
# %% construct anomaly portfolio and return
from portfolio_analysis import Univariate
# PCF : Price cash flow ratio
pcf = return_company[(return_company['Ndaytrd']>=10)]
pcf = pcf[['emrwd', 'PCF1A', 'Date_merge']].dropna()
pcf = pcf[(pcf['Date_merge'] >= '2000-01-01') & (pcf['Date_merge'] <= '2019-12-01')]
model_pcf = Univariate(np.array(pcf), number=9)
ret_pcf = model_pcf.print_summary_by_time(export=True)[['Time', 'diff']]
ret_pcf.index = pd.to_datetime(ret_pcf['Time'])
ret_pcf = ret_pcf['diff'].shift(1)
ret_pcf = ret_pcf.rename('PCF')
# Investment: Asset growth rate
inv = return_company[(return_company['Ndaytrd']>=10)]
inv = inv[['emrwd', 'asset_growth_rate', 'Date_merge']].dropna()
inv = inv[(inv['Date_merge'] >= '2000-01-01') & (inv['Date_merge'] <= '2019-12-01')]
model_inv = Univariate(np.array(inv), number=9)
ret_inv = model_inv.print_summary_by_time(export=True)[['Time', 'diff']]
ret_inv.index = pd.to_datetime(ret_inv['Time'])
ret_inv = ret_inv['diff'].shift(1)
ret_inv = ret_inv.rename('INV')
# abnormal turnover rate (one month): abtr1mon
abtr1mon = return_company[(return_company['Ndaytrd']>=10)]
abtr1mon = abtr1mon[['emrwd', 'specific_Turnover', 'Date_merge']].dropna()
abtr1mon = abtr1mon[(abtr1mon['Date_merge'] >= '2000-01-01') & (abtr1mon['Date_merge'] <= '2019-12-01')]
model_abtr1mon = Univariate(np.array(abtr1mon), number=9)
ret_abtr1mon = model_abtr1mon.print_summary_by_time(export=True)[['Time', 'diff']]
ret_abtr1mon.index = pd.to_datetime(ret_abtr1mon['Time'])
ret_abtr1mon = ret_abtr1mon['diff'].shift(1)
ret_abtr1mon = ret_abtr1mon.rename('ABT')
# %% merge data
data = pd.concat([ret_pcf, ret_inv, ret_abtr1mon, risk_premium], axis=1)
data = data['2004':'2019'].dropna()
Fama-French 3 factors model without Newey-West adjustment. Using time series regression, all alphas in regression are significant at 0.05, meaning that the anomaly portfolio return cannot be completely explained by Fama-French 3 factors model. The GRS test presents the same result.
# %% Fama-French 3 factors model
# Without Newey-West adjustment
# import data type: Dataframe
list_data = data.iloc[:, :3]
factor = data.iloc[:, 3:6]
model = TS_regress(list_y=list_data, factor=np.array(factor))
model.fit(newey_west=False)
model.summary()
=====================================================================
+----------+---------+---------+---------+---------+
| Variable | alpha | BETA | SMB | HML |
+----------+---------+---------+---------+---------+
| PCF | -0.0096 | 0.0892 | 0.9127 | -0.7753 |
| t-value | -5.891 | 5.363 | 12.393 | -16.443 |
| p-value | 0.0 | 0.0 | 0.0 | 0.0 |
| INV | 0.0086 | -0.0293 | -0.9563 | -0.7849 |
| t-value | 4.074 | -1.352 | -9.972 | -12.784 |
| p-value | 0.0 | 0.178 | 0.0 | 0.0 |
| ABT | -0.0065 | 0.1271 | -0.067 | 0.3228 |
| t-value | -2.305 | 4.415 | -0.526 | 3.955 |
| p-value | 0.022 | 0.0 | 0.599 | 0.0 |
+----------+---------+---------+---------+---------+
----------------------------------- GRS Test --------------------------------
GRS Statistics: 17.2 GRS p_value: 0.0
-----------------------------------------------------------------------------
Fama-French 3 factors model with Newey-West adjustment. Using time series regression, all alphas in regression are significant at 0.05, meaning that the anomaly portfolio return cannot be completely explained by Fama-French 3 factors model. The GRS test presents the same result.
# %% Fama-French 3 factors model
# With Newey-West adjustment
# import data type: Dataframe
model = TS_regress(list_y=data.iloc[:, :3], factor=data.iloc[:, 3:6])
model.fit(newey_west=True)
model.summary()
=====================================================================
+----------+---------+---------+---------+---------+
| Variable | alpha | BETA | SMB | HML |
+----------+---------+---------+---------+---------+
| PCF | -0.0096 | 0.0892 | 0.9127 | -0.7753 |
| t-value | -4.92 | 6.101 | 8.435 | -11.03 |
| p-value | 0.0 | 0.0 | 0.0 | 0.0 |
| INV | 0.0086 | -0.0293 | -0.9563 | -0.7849 |
| t-value | 5.113 | -1.016 | -8.562 | -8.948 |
| p-value | 0.0 | 0.155 | 0.0 | 0.0 |
| ABT | -0.0065 | 0.1271 | -0.067 | 0.3228 |
| t-value | -2.15 | 3.257 | -0.294 | 1.916 |
| p-value | 0.016 | 0.001 | 0.385 | 0.028 |
+----------+---------+---------+---------+---------+
----------------------------------- GRS Test --------------------------------
GRS Statistics: 17.2 GRS p_value: 0.0
-----------------------------------------------------------------------------
Fama-French 5 factors model with Newey-West adjustment. Using time series regression, all alphas in regression are insignificant, meaning that the anomaly portfolio return can be largely explained by Fama-French 5 factors model. The GRS test presents the same result.
# %% Fama-French 5 factors model
# With Newey-West adjustment
# import data type: Dataframe
model = TS_regress(list_y=data.iloc[:, :3], factor=data.iloc[:, 3:])
model.fit(newey_west=True)
model.summary()
=====================================================================
+----------+---------+---------+---------+---------+---------+--------+
| Variable | alpha | BETA | SMB | HML | RMW | CMA |
+----------+---------+---------+---------+---------+---------+--------+
| PCF | -0.0031 | 0.028 | 0.5858 | -0.9971 | -0.7922 | 0.2925 |
| t-value | -1.486 | 1.767 | 5.303 | -12.079 | -7.24 | 1.975 |
| p-value | 0.07 | 0.039 | 0.0 | 0.0 | 0.0 | 0.025 |
| INV | 0.0008 | -0.0569 | -0.453 | -0.2155 | -0.1186 | 1.6106 |
| t-value | 0.442 | -2.118 | -4.511 | -2.78 | -0.808 | 5.81 |
| p-value | 0.329 | 0.018 | 0.0 | 0.003 | 0.21 | 0.0 |
| ABT | -0.0037 | 0.0932 | -0.2032 | 0.2461 | -0.4225 | 0.2642 |
| t-value | -1.223 | 2.401 | -1.031 | 1.377 | -1.227 | 0.784 |
| p-value | 0.112 | 0.009 | 0.152 | 0.085 | 0.111 | 0.217 |
+----------+---------+---------+---------+---------+---------+--------+
----------------------------------- GRS Test --------------------------------
GRS Statistics: 1.477 GRS p_value: 0.222
-----------------------------------------------------------------------------
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