Most serious investors use mean-variance optimization to form portfolios, in part, because it requires knowledge only of a portfolio’s expected return and variance. Yet this convenience comes at some expense, because the legitimacy of mean-variance optimization depends on questionable assumptions. Either investors have quadratic utility or portfolio returns are normally distributed. Neither of these assumptions is literally true. Quadratic utility assumes that investors are equally averse to deviations above the mean as they are to deviations below the mean and that they sometimes prefer less wealth to more wealth. Moreover, asset returns have been shown to exhibit significant departures from normality. The question is: does it matter? Levy and Markowitz (1979) demonstrate that mean-variance approximations of utility based on plausible utility functions and empirical return distributions correlate very strongly with true utility. Samuelson (2003) argues that investors now have sufficient computational power to maximize expected utility based on plausible utility functions and the entire distribution of returns from empirical samples, and he introduces a different metric to determine the robustness of mean-variance approximation. We apply Samuelson’s metric to measure the approximation error of mean-variance optimization based on a sample of representative asset returns. Moreover, we apply Samuelson’s metric to compare the sampling error of these alternative approaches. Finally, we introduce a hybrid approach to portfolio formation, which enables investors to maximize expected utility based on plausible utility functions, but which relies on theoretical rather than empirical return distributions.

2016-08-31T10:45:36+00:00