Justifying Mean-Variance Portfolio Selection when Asset Returns Are Skewed

• 成果类型: Article
• 署名作者: Schuhmacher, Frank; Kohrs, Hendrik; Auer, Benjamin R.
• 署名单位: Leipzig University; Brandenburg University of Technology Cottbus; Leibniz Association; Ifo Institut
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.2020.3846
• 发表日期: 2021
• 页码: 7812-7824
• 关键词: PORTFOLIO CONSTRAINTS; location-scale condition; skew-elliptical distributions

摘要

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.