Skip to main content

Portfolio optimization and back-testing.

Project description

CVXportfolio on PyPI linting: pylint Coverage Status Documentation Status Apache 2.0 License Anaconda-Server Badge

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


Since end of 2023 we’re running daily example strategies using the development version (master branch); each day we commit target weights and initial holdings to the repository. All the code that runs them, including the cron script, is in the repository.


Cvxportolio is written in Python and can be easily installed in any Python environment by simple:

pip install -U cvxportfolio

You can see how this works on our Installation and Hello World youtube video. Anaconda installs are also supported.

Cvxportfolio’s main dependencies are Cvxpy for interfacing with numerical solvers and Pandas for interfacing with databases. We don’t require any specific version of our dependencies and test against all recent ones (up to a few years ago).


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

python -m cvxportfolio.tests

We test against recent python versions (3.8, 3.9, 3.10, 3.11, 3.12) and recent versions of the main dependencies (from pandas 1.4, cvxpy 1.1, …, up to the current versions) on all major operating systems. You can see the automated testing code.

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

# plot back-test results

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.

Other examples

Many examples are shown in the documentation website, along with their output and comments.

Even more example scripts are available in the code repository.

The original examples from the paper are visible in a dedicated branch, and are being translated to run with the stable versions (1.0.0 and above) of the library. The translations are visible at this documentation page.

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.

Similar projects

There are many open-source projects for portfolio optimization and back-testing. Some notable ones in the Python ecosystem are Zipline, which implements a call-back model for back-testing very similar to the one we provide, Riskfolio-Lib which implements (many!) portfolio optimization models and also follows a modular approach like ours, VectorBT, a back-testing library well-suited for high frequency applications, PyPortfolioOpt, a simple yet powerful library for portfolio optimization that uses well-known models, YFinance, which is not a portfolio optimization library (it only provides a data interface to Yahoo Finance), but used to be one of our dependencies, and also CVXPY by itself, which is used by some of the above and has an extensive set of examples devoted to portfolio optimization (indeed, Cvxportfolio was born out of those).


We welcome contributors and you don’t need to sign a CLA. If you don’t have a Github account you may also send a git patch via email to the project maintainer.

Bug fixes, improvements in the documentations and examples, new constraints, new cost objects, …, are good contributions and can be done even if you’re not familiar with the low-level details on the library. For more advanced contributions we recommend reading the TODOs and roadmap file.


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

git clone
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

Code style and quality

Cvxportfolio follows the PEP8 specification for code style. This is enforced by the Pylint automated linter, with options in the Pyproject configuration file. Pylint is also used to enforce code quality standards, along with some of its optional plugins. Docstrings are written in the Sphinx style, are also checked by Pylint, and are used to generate the documentation.

Versions and releases

Cvxportfolio follows the semantic versioning specification. No breaking change in its public API will be introduced until the next major version (2.0.0), which won’t happen for some time. New features in the public API are introduced with minor versions (1.1.0, 1.2.0, …), and only bug fixes at each revision.

The history of our releases (source distributions and wheels) is visible on our PyPI page.

Releases are also tagged in our git repository and include a short summary of changes in their commit messages.

We maintain a document listing the planned changes and target releases.


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

    author    = "Busseti, Enzo and Diamond, Steven and Boyd, Stephen",
    title     = "Cvxportfolio",
    month    = "January",
    year     = "2017",
    note     = "Portfolio Optimization and Back--{T}esting",
    howpublished = {\url{}},

  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{}},

The latter is also the first chapter of this PhD thesis:

    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{}},


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

Project details

Download files

Download the file for your platform. If you're not sure which to choose, learn more about installing packages.

Source Distribution

cvxportfolio-1.3.2.tar.gz (336.8 kB view hashes)

Uploaded Source

Built Distribution

cvxportfolio-1.3.2-py3-none-any.whl (352.9 kB view hashes)

Uploaded Python 3

Supported by

AWS AWS Cloud computing and Security Sponsor Datadog Datadog Monitoring Fastly Fastly CDN Google Google Download Analytics Microsoft Microsoft PSF Sponsor Pingdom Pingdom Monitoring Sentry Sentry Error logging StatusPage StatusPage Status page