The Sharp Razor: Performance Evaluation with Non-Normal Returns

Abstract

Because the Sharpe ratio only takes into account the first two moments, it wrongly “translates” skewness and excess kurtosis into standard deviation.

As a result: It deflates the skill measured on “well-behaved” investments (positive skewness, negative excess kurtosis). It inflates the skill measure on “badly-behaved” investments (negative skewness, positive excess kurtosis).

Sharpe ratio estimates need to account for Higher Moments, even if you assume that investors only care about two moments (Markowitz framework).

Keywords: Portfolio selection, Normality, Serial Correlation, Probabilistic Sharpe Ratio, Minimum Track Record Lenght, Sharpe Ratio Efficient Frontier

JEL Classification: C02, G11, G14, D53