I'm currently comparing empirically the differences between Markowitz and Kelly portfolios. I calculated the Kelly weights for monthly return observations over 10 years for a sample of 50 stocks from the S&P 500. Without constraints, I received a highly levered Kelly portfolio of weights summing up to 23 with mean of 85% and std. deviation of 91%. I then de-levered the portfolio proportionally and received the same tangency portfolio with the exact same weights as in the Mean-Variance-Optimization case. I was surprised by this result and wanted to ask you if someone knows why this could be the case or made similar observations.

I’m very grateful for any kind of advice on this subject.


1 Answer 1


They are the same.

The maximum growth rate is achieved when the Sharpe ratio is maximized.

For the proof, see here.

  • 1
    $\begingroup$ Are they the same in every circumstance when you de-lever Kelly? Why is make such a big fuss about Kelly if its just the tangency portfolio? $\endgroup$
    – User1111
    Sep 3, 2015 at 16:33
  • $\begingroup$ The formula at the beginning of the cited post is bogus. What if the covariance matrix is singular? You get what we professionals call "junk on a stick". $\endgroup$
    – Igor Rivin
    Mar 28, 2017 at 20:11

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