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?
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.