Justifying Mean-Variance Portfolio Selection when Asset Returns Are Skewed

Frank Schuhmacher (), Hendrik Kohrs () and Benjamin R. Auer ()
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Frank Schuhmacher: Department of Finance, University of Leipzig, 04109 Leipzig, Germany
Hendrik Kohrs: University of Leipzig, Department of Finance, 04109 Leipzig, Germany; Department of Risk Management and Quantitative Analysis, VNG Handel and Vertrieb GmbH, 04347 Leipzig, Germany
Benjamin R. Auer: University of Leipzig, Department of Finance, 04109 Leipzig, Germany; Chair of Finance, Brandenburg University of Technology Cottbus-Senftenberg, 03046 Cottbus, Germany; Research Network Area Macro, Money and International Finance, CESifo Munich, 80539 Munich, Germany

Management Science, 2021, vol. 67, issue 12, 7812-7824

Abstract: We show that, in the presence of a risk-free asset, the return distribution of every portfolio is determined by its mean and variance if and only if asset returns follow a specific skew-elliptical distribution. Thus, contrary to common belief among academics and practitioners, skewed returns do not allow a rejection of mean-variance analysis. Our work differs from Chamberlain's [Chamberlain G (1983) A characterization of the distributions that imply mean-variance utility functions. J. Econom. Theory 29(1):185–201.] by focusing on the returns of portfolios, where the weights over the risk-free asset and the risky assets sum to unity. Furthermore, it extends Meyer's [Meyer J, Rasche RH (1992) Sufficient conditions for expected utility to imply mean-standard deviation rankings: Empirical evidence concerning the location and scale condition. Econom. J . (London) 102(410):91–106.] by introducing elliptical noise into their generalized location-scale framework. To emphasize the relevance of our skew-elliptical model, we additionally provide empirical evidence that it cannot be rejected for the returns of typical portfolios of common stocks or popular alternative investments.

Keywords: portfolio constraints; location-scale condition; skew-elliptical distributions (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:67:y:2021:i:12:p:7812-7824

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