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The Kelly Ratio maximises the expected cumulative return.

However, it has been criticised for leading to excessive volatility.

Is there a version of the kelly formula that maximises the risk adjusted return?

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    $\begingroup$ What is the Kelly ratio and the risk adjusted Kelly ratio? They might be well known, but it is still good to write them down specifically so that people can start with your question without references. $\endgroup$ – Gordon Nov 2 '15 at 14:40
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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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