Estimating the Sharpe ratio using a Kalman filter

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Estimating the Sharpe ratio using a Kalman filter

edited Feb 2, 2018

Seeking Help Research Statistics

I've gone through all of the lectures and notebooks on Quantopian regarding Kalman filters as well as whatever other material I could find online. While it seems rather straightforward now to "plug in" a linear equation into a Kalman filter to smooth out and estimate the inputs, I'm not quite sure where to start when trying to estimate something like the Sharpe ratio. I was thinking of estimating the mean and standard deviation separately followed by computing the Sharpe ratio, but then I realized the filter should have all the information necessary to compute the ACTUAL Sharpe ratio.

I read this paper on how to create the so-called "fundamental" Sharpe ratio using a Kalman filter, but it's rather complex and maybe even overkill.

My question is how should I go about trying to estimate the Sharpe ratio using a Kalman filter? Any information you might have or resources pointing me in the right direction would go a long way!

Edit: I also want to point out that this was referenced in "Kalman Filters" lecture: "For instance, if we have already computed the moving Sharpe ratio, we can smooth it using a Kalman filter."

2 responses

Note that since the SR is a ratio, if you take the log, you'll end up with difference between two terms. So, if the Kalman filter operates like K(a-b) = K(a) - K(b), then maybe the trick of taking the log would help. A half-baked idea at this point, but I thought I'd share it, regardless.

That's an idea worth exploring for sure. Thank Grant!

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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.