Mean‐Variance Versus Direct Utility Maximization

Abstract

Levy and Markowitz showed, for various utility functions and empirical returns distributions, that the expected utility maximizer could typically do very well if he acted knowing only the mean and variance of each distribution. Levy and Markowitz considered only situations in which the expected utility maximizer chose among a finite number of alternate probability distributions. The present paper examines the same questions for a case with an infinite number of alternate distributions, namely those available from the standard portfolio constraint set.

Commissioned Paper: Capacity Management, Investment, and Hedging: Review and Recent Developments

“…Levy and Markowitz (1979), and Kroll et al (1984) studied this question in the following sense: If you know the expected value and variance of a probability distribution of return on a portfolio, can you guess fairly closely its expected utility? They found that the correlation between the predicted expected utilities and the actual expected utilities was extremely high, usually exceeding 0.99.…”

Mean-Variance Analysis of Supply Chain Contracts

“…However, it is shown in Van Mieghem (2003) that maximizing a utility function with a constant coefficient of risk aversion is equivalent to maximizing a mean-variance performance measure (also see Luenberger 1998, Choi et al 2008 for some supplementary discussions). There are also evidences in the literature which demonstrate that the mean-variance approach yields a solution which is close to the optimal solution under the utility function approach (see Levy & Markowitz 1979, Kroll et al 1984, and Van Mieghem 2003. Moreover, some meaningful and applicable objectives, such as the safety first objective (Roy 1952), can be formulated under the mean-variance framework.…”

An asymptotic analysis of the mean-variance portfolio selection

“…Grauer [9] compared the logoptimal strategies and the mean-variance analysis in the one-period model for various specifications of the state return distributions and his experiments revealed that these two portfolios have almost the same performance when the returns come from the normal distribution. Kroll, Levy and Markowitz [15] conducted a similar study. Merton [17] developed a continuous time mean-variance analysis and showed that log-optimal portfolio is instantaneously mean-variance efficient when asset prices are log-normal.…”