Mean-Semivariance Optimization: A Heuristic Approach

Abstract

Academics and practitioners optimize portfolios using the mean-variance approach far more often than the mean-semivariance approach, despite the fact that semi-variance is often considered a more plausible measure of risk than variance. The popularity of the mean-variance approach follows in part from the fact that mean-variance problems have well-known closed-form solutions, whereas mean-semivariance optimal portfolios cannot be determined without resorting to obscure numerical algorithms. This follows from the fact that, unlike the exogenous covariance matrix, the semi-covariance matrix is endogenous. This article proposes a heuristic approach that yields a symmetric and exogenous semi-covariance matrix, which enables the determination of mean-semivariance optimal portfolios by using the well-known closed-form solutions of mean-variance problems. The heuristic proposed is shown to be both simple and accurate.