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Given return of a portfolio or a single asset modeled as a continuous, but not necessarily gaussian, probability distribution, what's the Kelly criterion equation?

I've heard that it's simply the the ratio of the sharpe ratio to the standard deviation. Is it true?

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    $\begingroup$ This was already discussed here quant.stackexchange.com/a/7199 $\endgroup$ – RRG Apr 3 '17 at 9:08
  • $\begingroup$ This is discussed (among other places) in the book Investment Science by Luenberger $\endgroup$ – noob2 Apr 3 '17 at 13:55
  • $\begingroup$ It is only true if there is a second moment in the distribution. Given the data and papers on the topic, that claim would be very dubious. $\endgroup$ – Dave Harris Apr 4 '17 at 4:39
  • $\begingroup$ The Sharpe Ratio is a rough but good approximation. In regard to approximating optimal bet size, the world of professional gambling is ahead of canonical portfolio managers. For a good essay on how this works, I recommend: wizardofodds.com/gambling/kelly-criterion. $\endgroup$ – David Addison Apr 19 '17 at 23:42

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