Abstract
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.
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MacLean, L.C., Zhao, Y. & Ziemba, W.T. Mean-variance versus expected utility in dynamic investment analysis. Comput Manag Sci 8, 3–22 (2011). https://doi.org/10.1007/s10287-009-0106-7
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DOI: https://doi.org/10.1007/s10287-009-0106-7