Mean‐variance versus expected utility in dynamic investment analysis

Given the existence of a Markovian state price density process, this paper extends Merton’s continuous time (instantaneous) mean‐variance analysis and the mutual fund separation theory in which the risky fund can be chosen to be the growth optimal portfolio. The CAPM obtains without the assumption of log‐normality for prices. The optimal investment policies for the case of a hyperbolic absolute risk aversion (HARA) utility function are derived analytically. It is proved that only the quadratic utility exhibits the global mean‐variance efficiency among the family of HARA utility functions. A numerical comparison is made between the growth optimal portfolio and the mean‐variance analysis for the case of log‐normal prices. The optimal choice of target return which maximizes the probability that the mean‐variance analysis outperforms the expected utility portfolio is discussed. Mean variance analysis is better near the mean and the expected utility maximization is better in the tails.