I was wondering how Kelly criterion can be used for portfolio optimisation in the case one would like to optimise the portfolio for minimum variance. I understand how the Kelly criterion can be used to decide the allocation for a certain stock, but what if I also would like to make sure I am diversified (= I want to set a certain portfolio variance). In other word is there a way to combine Kelly with mean-variance, or something like that?

  • $\begingroup$ Hi: It's an interesting question but my guess is no since you haven't gotten any responses. Note that the two concepts are kind of at odds with each other. Kelly, on an intuitive level, is trying to minimize your chance of bankruptcy in the long term while, in mean variance, one is trying to maximize return with a minimum variance. So, one would expect that combining the concepts would be difficult. Still, I would google because people are always trying to do interesting things so one never knows what attempts might be out there. $\endgroup$
    – mark leeds
    Commented Apr 3, 2022 at 17:21
  • $\begingroup$ Hi: Maybe you've already seen this. Don't know how relevant it is to your case. researchgate.net/profile/Zachariah-Peterson/publication/… $\endgroup$
    – mark leeds
    Commented Apr 3, 2022 at 17:24
  • $\begingroup$ I haven't read it but I saw this today on quantocracy and you might be interested. raposa.trade/blog/… $\endgroup$
    – mark leeds
    Commented Apr 5, 2022 at 17:24

1 Answer 1


After careful study I found that Kelly portfolio composition and the tangent portfolio composition are proved to be the same using matrix algebra. Namely the portfolio composition that maximize the Sharpe ratio is the same as the one that maximize growth rate. But empirical papers show that they are different. Kelly portfolio is condensed and has higher mean and variance than tangent portfolio. I deeply wonder why this happens!!! This is the critical point that is simply ignored and misunderstood in the literature.

  • $\begingroup$ You might want to spell out your argument in detail (and how your result differs from the literature) so that other users can benefit. $\endgroup$
    – John
    Commented Jan 26 at 16:30
  • $\begingroup$ There is a simple formula for Kelly on a continuous distribution of returns,published by the pioneers ,Ed Thorp and William Ziemba,and in their exhaustive book,The Kelly Criterion for Investment ( sic,not the exact title,I am writing from memory). The formula often quoted is mainly for gambling and is meant for discrete distributions and not continuous samples like share trading. The Kelly criterion by the way very rarely coincides with the mean variance portfolio on empirical data,it is a rare example in reality. $\endgroup$ Commented May 26 at 21:37
  • $\begingroup$ It is not exactly the Sharpe ratio you have misinterpreted it,crucially and critically wrong ,whereas the divisor of the Sharpe ratio is the standard deviation of the investment,for the Kelly criterion it is the variance not the standard deviation,and there is also a normalising and/ or scaling factor ,which I will check later and print here. $\endgroup$ Commented May 26 at 21:42
  • $\begingroup$ Jim Simmons,Warren Buffet, both learned the Kelly criterion and applied it to their investing after consulting with a dialogue with either both, and Ed Thorp or one might have also discussed it ,with William Ziemba,my recollections of their memoirs are hazy now. $\endgroup$ Commented May 26 at 21:46
  • $\begingroup$ You are almost certainly guaranteed to lose money with the the Markovitz or sharpe-lintner, mean variance portfolios,not always so with Kelly criterion and with half Kelly virtually never. $\endgroup$ Commented May 26 at 21:48

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