Mean-Variance Utility Functions and the Demand for Risky Assets: An Empirical Analysis Using Flexible Functional Forms

In a recent study, Levy and Markowitz [15] demonstrate that, at least for some utility functions, expected utility can be approximated by a judiciously chosen function defined over mean and variance. In addition to resurrecting mean-variance analysis from the limbo into which it was placed by the criticisms of Borch [10] and others, the analysis by Levy and Markowitz yields a more direct approach to portfolio analysis than that provided by the current empirical literature. The current portfolio literature is concerned with notions of efficient sets and systematic risk rather than with utility functions and mean-variance. While much has been gained from a utility-free methodology, it is ultimately predicated upon a separation theorem and, hence, an environment with zero transactions costs. But security markets are not costless and the separation theorem may not hold. In that event, a utility-dependent approach to portfolio analysis could potentially lead to more powerful results especially if such an approach could be empirically implemented.