Maximizing Geometric Returns Under Skew and Tail Risk

Summary

The article examines a performance measure based on the highest geometric return achievable at a strategy's optimal leverage. Under Gaussian returns and unrestricted leverage, it explains why Sharpe ratio can determine the preferred strategy, while a nonzero borrowing rate changes optimal leverage and net returns. A stylized comparison of a trend-following strategy and a fixed-income relative-value strategy illustrates how equal Sharpe ratios can imply equal net geometric returns after borrowing costs.

The article then questions the Gaussian assumption: strategies with negative skew and fat left tails may suffer losses that make high leverage unattractive. It proposes comparing strategies through bootstrapped return samples, holding mean and volatility constant while varying tail characteristics, and using a tail ratio to describe downside fatness. The provided excerpt ends before reporting the results, so it does not establish how tail ratios affect optimal leverage or maximum geometric return. Historical estimates and future regime changes remain important limitations.

Key ideas

• At full Kelly leverage with Gaussian returns and zero financing costs, Sharpe ratio ranks strategies by maximum geometric return.
• Borrowing costs affect optimal leverage and net returns when the risk-free rate is positive.
• Negative skew and fat left tails can make high leverage especially costly to compound wealth.
• Bootstrapping can compare return distributions with matched first and second moments but varying tail properties.
• The excerpt describes the proposed analysis but omits its results.

Tags

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