ON THE ROLE OF SKEWNESS, KURTOSIS, AND THE LOCATION AND SCALE CONDITION IN A SHARPE RATIO PERFORMANCE EVALUATION SETTING

Abstract

In recent years, researchers and practitioners have invested considerable effort in the development of new investment fund performance measures that account for mean, variance and the higher moments of the return distribution. To justify the application and necessity of the new performance measures in decision-making, some authors argue that the theoretical conditions required to use the Sharpe ratio are violated by high skewness and kurtosis in empirical asset return data. In this note, we highlight that high levels of skewness and kurtosis and even cross-sectional variations in skewness and kurtosis do not allow a decision-theoretic rejection of the Sharpe ratio. However, we also point out that while it is hard to discard the measure on decision-theoretic grounds, it can be challenged on technical grounds because it has several undesirable properties.