Generalized sharpe ratios: Performance measures focusing on downside risk

In this paper, we construct a new measure of fund performance by combining two commonly used measures, namely, the Sharpe ratio and the second-degree stochastic dominance (SSD). For a given fund, we use the SSD criteria to identify an equivalent fund with normal return distribution. The Sharpe ratio of the equivalent fund is referred to as the generalized Sharpe ratio (GSR). The generalized Sharpe ratio not only provides a complete rank of funds but also is consistent with investors' risk aversion. We show that the generalized Sharpe ratio has an intuitively appealing link to various moments of the fund return distribution. In addition, we extend the generalized Sharpe ratio to the left tails of fund return distribution to measure the downside risk of a fund. Applying to a sample of mutual funds, our results show that the ranking based on the new measure can be substantially different from that based on the conventional Sharpe ratio, with our measure directly tying to the distributional features of fund returns.