Markowitz versus Michaud: Portfolio Optimization Strategies Reconsidered

Abstract

Several attempts have been made to reduce the impact of estimation errors on the optimal portfolio composition. On the one hand, improved estimators of the necessary moments have been developed and on the other hand, heuristic methods have been generated to enhance the portfolio performance, for instance the "resampled efficiency" of Michaud (1998). We compare the out-of-sample performance of traditional Mean-Variance optimization by Markowitz (1952) with Michaud's resampled efficiency in a comprehensive simulation study for a large number of relevant estimators appearing in the literature. In addition, we perform an empirical study to confirm the simulation re-sults. Within the framework of the analyses we consider different estimation periods as well as unconstrained and constrained portfolio optimization problems. The main find-ings are that Markowitz outperforms Michaud on average but the impact of different estimators and constraints is significantly larger. Precisely, in most situations, the esti-mator of Frost/Savarino (1988) proves to work excellent. However, if the variance of estimators is large, e.g. for short observation periods or large samples, it is recommend-able to additionally implement constraints or to use the estimator of Ledoit/Wolf (2003).

Keywords: portfolio selection, estimators of moments, simulation study, capital market study, mean-variance optimization, resampled efficiency

JEL Classification: G11, C15