Kelly Leverage Maximizes Geometric Growth, Not Sharpe Ratio

Summary

The document asks whether the Kelly criterion can be adjusted to maximize risk-adjusted returns because full Kelly sizing can produce substantial volatility. The answer explains that Kelly chooses leverage to maximize expected geometric growth. Scaling leverage, however, does not improve the Sharpe ratio under the framing given, so the criterion is not a way to optimize that risk-adjusted measure.

To manage the volatility associated with full Kelly bets, the response says practitioners often use a fraction of the calculated Kelly allocation. It gives examples of fractional sizing but does not derive a formula or provide performance comparisons. The discussion is brief and rests on the stated relationship between leverage and Sharpe; it does not address estimation error, changing return distributions, drawdown preferences, or other definitions of risk-adjusted performance.

Key ideas

• Kelly sizing targets geometric growth rather than a higher Sharpe ratio.
• Changing leverage alone does not improve the risk-adjusted return as described in the answer.
• Full Kelly exposure can produce volatility that investors may find excessive.
• Fractional Kelly sizing is presented as a practical way to reduce exposure.

Tags

# Risk Adjusted Kelly Ratio?


# Risk Adjusted Kelly Ratio?












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?

## Answer by Bogdan Levchenko (score 1)

https://quant.stackexchange.com/a/22592

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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.