Performance Evaluation for Mutual Funds, Skewness Preferences, and Two-Fund Separation

We consider investors with mean-variance-skewness preferences who aim at select-ing one out of F different funds and combining it optimally with the riskless asset and directstock holdings. Direct stock holdings are either exogenously or endogenously determined. Inour theoretical section, we derive and discuss several performance measures for the investor’sdecision problems with a central role of Kimball’s (1990) prudence and of several variants ofSharpe and Treynor measures. In our empirical section, we show that the distinction betweenexogenous and endogenous stock holding is less important than the issue of skewness prefer-ences. The latter are most relevant for fund rankings, when an investor’s skewness prefer-ences are not derived from cubic HARA utility so that the two-fund separation theorem is notvalid.