Sharpe Ratio for skew-normal distributions: a skewness-dependent performance trade-off?

Main academic criticism on the Sharpe ratio concerns its lack in incorporating skewness in performance evaluation. In this note we rewrite the classical Sharpe ratio for skew normal distributions. This new skew-normal Shape ratio consistently moves with skewness and no distorted information on performance is provided. An empirical investigation illustrates skew-normality of mutual and hedge fund returns. When investors are concerned about skewness, the use of the skewnormal
Sharpe ratio thus seems a proper choice for making performance rankings.