Markowitz versus Michaud: portfolio optimization strategies reconsidered

Franziska Becker, Marc Gürtler and Martin Hibbeln

The European Journal of Finance, 2015, vol. 21, issue 4, 269-291

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. Efficient Asset Management: A Practical Guide to Stock Portfolio Optimization and Asset Allocation. Boston: Harvard Business School Press]. We compare the out-of-sample performance of traditional mean-variance optimization by Markowitz [1952. "Portfolio Selection." Journal of Finance 7 (1): 77-91] 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 results. Within the framework of the analyses we consider different estimation periods as well as unconstrained and constrained portfolio optimization problems. The main findings are that Markowitz outperforms Michaud on average but the impact of different estimators and constraints is significantly larger. Precisely, in most situations, the estimator of Frost and Savarino [1988. "For Better Performance: Constrain Portfolio Weights." Journal of Portfolio Management 15 (1): 29-34] proves to work excellent. However, if the variance of estimators is large, for example, for short observation periods or large samples, it is recommendable to additionally implement constraints or to use the estimator of Ledoit and Wolf [2003. "Improved Estimation of the Covariance Matrix of Stock Returns with an Application to Portfolio Selection." Journal of Empirical Finance 10 (5): 603-622].

Date: 2015
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DOI: 10.1080/1351847X.2013.830138

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