Performance evaluation, portfolio selection, and HARA utility

Our main goal is the generalization of the approach of Jobson and Korkie(1984) for funds performance evaluation. Therefore, we consider the portfolio selection problem of an investor who faces short sales restrictions when choosing among F different investment funds and assume the investor's utility function to be of the HARA type. We develop a performance measure and discuss its relationships to Treynor(1965), Sharpe(1966), Jensen(1968), Prakash and Bear(1986), and Grinblatt and Titman(1989). Particular attention is given to the special case of cubic utility implying skewness preferences. Our findings are illustrated by an empirical example.