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Reconciling mean-variance portfolio theory with non-Gaussian returns

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  • Lassance, Nathan

Abstract

Mean-variance portfolio theory remains frequently used as an investment rationale because of its simplicity, its closed-form solution, and the availability of well-performing robust estimators. At the same time, it is also frequently rejected on the grounds that it ignores the higher moments of non-Gaussian returns. However, higher-moment portfolios are associated with many different objective functions, are numerically more complex, and exacerbate estimation risk. In this paper, we reconcile mean-variance portfolio theory with non-Gaussian returns by identifying, among all portfolios on the mean-variance efficient frontier, the one that optimizes a chosen higher-moment criterion. Numerical simulations and an empirical analysis show, for three higher-moment objective functions and adjusting for transaction costs, that the proposed portfolio strikes a favorable tradeoff between specification and estimation error. Specifically, in terms of out-of-sample Sharpe ratio and higher moments, it outperforms the global-optimal portfolio, and also the global-minimum-variance portfolio except when using monthly returns for which estimation error is more prominent.

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  • Lassance, Nathan, 2022. "Reconciling mean-variance portfolio theory with non-Gaussian returns," European Journal of Operational Research, Elsevier, vol. 297(2), pages 729-740.
    • Handle: RePEc:eee:ejores:v:297:y:2022:i:2:p:729-740
    DOI: 10.1016/j.ejor.2021.06.016
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