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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?

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  • $\begingroup$ 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
    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
    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
    Apr 5, 2022 at 17:24

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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.

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  • $\begingroup$ 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
    Jan 26 at 16:30

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