Mean-Variance Approximations to Expected Logarithmic Utility

In this paper, we investigate how closely functions of means and variances can approximate Von Neumann-Morgenstern expected utility modeled as a logarithmic utility-of-wealth function. Using historical security return data, we computed portfolios maximizing expected logarithmic utility and compared them to those maximizing appropriate mean-variance formulations. In all cases the approximations were very good, and in many cases the optimal portfolios were virtually identical. We conclude that the mean-variance model can serve as a useful surrogate to at least one popular alternative investment strategy.