Mean-Variance Analysis in a Finite World

Abstract

Despite the enormous attention received by the single-period mean-variance model in the literature, its structural relationship to the empirical world is still largely unexplored. The purpose of this note is to show that when certain consistency requirements and equilibrium conditions in the financial markets are taken into account, the collective judgment of the present literature concerning the mean-variance approach is in some respects too lenient and in other respects too harsh. In addition, it will be noted that the mean-variance model can only achieve consistency with the von Neumann-Morgenstern postulates and absolute preference (also known as first-order stochastic dominance) at the price of a severe upper bound on the risk aversion that can be possessed by the decision maker.