cvxportfolio 1.0.3

Portfolio optimization and back-testing.

Cvxportfolio

Cvxportfolio is an object-oriented library for portfolio optimization and back-testing. It implements models described in the accompanying paper.

The documentation of the library is at www.cvxportfolio.com.

Installation

You can install our latest release with

pip install -U cvxportfolio

You can see how this works on our Installation and Hello World youtube video.

Testing locally

After installing you can run our unit test suite in you local environment by

python -m cvxportfolio.tests

Simple Example

In the following example market data is downloaded by a public source (Yahoo finance) and the forecasts are computed iteratively, at each point in the backtest, from past data.

import cvxportfolio as cvx

gamma = 3       # risk aversion parameter (Chapter 4.2)
kappa = 0.05    # covariance forecast error risk parameter (Chapter 4.3)
objective = cvx.ReturnsForecast() - gamma * (
	cvx.FullCovariance() + kappa * cvx.RiskForecastError()
) - cvx.StocksTransactionCost()
constraints = [cvx.LeverageLimit(3)]

policy = cvx.MultiPeriodOptimization(objective, constraints, planning_horizon=2)

simulator = cvx.StockMarketSimulator(['AAPL', 'AMZN', 'TSLA', 'GM', 'CVX', 'NKE'])

result = simulator.backtest(policy, start_time='2020-01-01')

# print back-test result statistics
print(result)

# plot back-test results
result.plot()

At each point in the back-test, the policy object only operates on past data, and thus the result you get is a realistic simulation of what the strategy would have performed in the market. Returns are forecasted as the historical mean returns and covariances as historical covariances (both ignoring np.nan's). The simulator by default includes holding and transaction costs, using the models described in the paper, and default parameters that are typical for the US stock market.

Some Other Examples

We show in the example on user-provided forecasters how the user can define custom classes to forecast the expected returns and covariances. These provide callbacks that are executed at each point in time during the back-test. The system enforces causality and safety against numerical errors. We recommend to always include the default forecasters that we provide in any analysis you may do, since they are very robust and well-tested.

We show in the examples on DOW30 components and wide assets-classes ETFs how a simple sweep over hyper-parameters, taking advantage of our sophisticated parallel backtest machinery, quickly provides results on the best strategy to apply to any given selection of assets.

Development

To set up a development environment locally you should clone the repository (or, fork on Github and then clone your fork)

git clone https://github.com/cvxgrp/cvxportfolio.git
cd cvxportfolio

Then, you should have a look at our Makefile and possibly change the PYTHON variable to match your system's python interpreter. Once you have done that,

make env
make test

This will replicate our development environment and run our test suite.

You activate the shell environment with one of scripts in env/bin (or env\Scripts on Windows), for example if you use bash on POSIX

source env/bin/activate

and from the environment you can run any of the scripts in the examples (the cvxportfolio package is installed in editable mode). Or, if you don't want to activate the environment, you can just run scripts directly using env/bin/python (or env\Scripts\python on Windows) like we do in the Makefile.

Additionally, to match our CI/CD pipeline, you may set the following git hooks

echo "make lint" > .git/hooks/pre-commit
chmod +x .git/hooks/pre-commit
echo "make test" > .git/hooks/pre-push
chmod +x .git/hooks/pre-push

Examples from the paper

In branch 0.0.X you can find the original material used to generate plots and results in the paper. As you may see from those ipython notebooks a lot of the logic that was implemented there, outside of Cvxportfolio proper, is being included and made automatic in newer versions of Cvxportfolio.

Citing

If you use Cvxportfolio in work that leads to publication, you can cite the following:

@misc{busseti2017cvx,
    author    = "Busseti, Enzo and Diamond, Steven and Boyd, Stephen",
    title     = "Cvxportfolio",
    month    = "January",
    year     = "2017",
    note     = "Portfolio Optimization and Back--{T}esting",
    howpublished = {\url{https://github.com/cvxgrp/cvxportfolio}},
}

@article{boyd2017multi,
  author  = "Boyd, Stephen and Busseti, Enzo and Diamond, Steven and Kahn, Ron and Nystrup, Peter and Speth, Jan",
  journal = "Foundations and Trends in Optimization",
  title   = "Multi--{P}eriod Trading via Convex Optimization",
  month   = "August",
  year    = "2017",
  number  = "1",
  pages   = "1--76",
  volume  = "3",
  url     = {\url{https://stanford.edu/~boyd/papers/pdf/cvx_portfolio.pdf}},
}

The latter is also the first chapter of this thesis:

@phdthesis{busseti2018portfolio,
    author    = "Busseti, Enzo",
    title     = "Portfolio Management and Optimal Execution via Convex Optimization",
    school    = "Stanford University",
    address   = "Stanford, California, USA",
    month    = "May",
    year     = "2018",
    url     = {\url{https://stacks.stanford.edu/file/druid:wm743bj5020/thesis-augmented.pdf}},
}

License

Cvxportfolio is licensed under the Apache 2.0 permissive open source license.