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Kelly calculates optimal leverage for maximising geometric growth. At the same time, any change in leverage does not lead to a change in a risk-adjusted return (i.e. Sharpe). Therefore Kelly cannot be used to improve risk-adjusted return. Talking about the excess vola, in practive one rarely applies Kelly. The bet is usually Kelly/2, Kelly/4 or even less.


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They are the same. The maximum growth rate is achieved when the Sharpe ratio is maximized. For the proof, see here.



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