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Resampled Efficiency using CVXOPT
Michael Doherty
posted
Portfolio Optimization Asset Allocation Risk Management

Hello All,

I am attempting to implement a resampled portfolio optimization using the expected returns and covariances from JPM 2018 outlook, but when I use CVXOPT to solve for the efficient frontier, it is not arriving at the global minimum variance solution. I can tell its not by the space between the randomly generated portfolios and the calculated efficient frontier. When I run the same code on historical data of more correlated assets such as stocks the line fits perfectly to the random weight portfolio.

Any insight as to why this may be occurring? I realize it must be because of the data's structure or how I am calculating the mu vector.

I have attached the notebook for reference.

Thanks,
Mike

7 responses
Thomas Wiecki

This looks quite interesting.

I suppose you expect the efficient frontier to tangent the point cloud?

Where did you get the covariance matrix from?

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The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by Quantopian. In addition, the material offers no opinion with respect to the suitability of any security or specific investment. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. If you are an individual retirement or other investor, contact your financial advisor or other fiduciary unrelated to Quantopian about whether any given investment idea, strategy, product or service described herein may be appropriate for your circumstances. All investments involve risk, including loss of principal. Quantopian makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances.

Michael Doherty

Correct. I backed into it using the correlation matrix from JPM

https://am.jpmorgan.com/us/institutional/our-thinking/2018-long-term-capital-market-assumptions?show-nav=true&nav=pageSection&navId=1383479160209&has-pdf=true

Thomas Wiecki

That could definitely cause some discrepancy to the real data. What happens if you estimate cov from returns directly?

Michael Doherty

If I use real returns the parabola fits tangent to the cloud.

Michael Doherty

Think I figured it out. Just not enough of random portfolios generated to reach frontier due to number of asset combinations. Here is my implementation of resampled efficiency.

Thomas Wiecki

That's a really neat plot!

Care to write up a bit more motivation and explanation? I'm sure others would be curious as well.

Michael Doherty

Sure thing! I think the method is patented but I am not even sure this is the right way to do it! Would be curious to see if this method backtested is more robust than just one optimization on the underlying data.

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The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by Quantopian.

In addition, the material offers no opinion with respect to the suitability of any security or specific investment. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. If you are an individual retirement or other investor, contact your financial advisor or other fiduciary unrelated to Quantopian about whether any given investment idea, strategy, product or service described herein may be appropriate for your circumstances. All investments involve risk, including loss of principal. Quantopian makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances.