Reconciling mean-variance portfolio theory with non-Gaussian returns

European Journal of Operational Research, 2021, 297(2):729-740.

36 Pages Posted: 15 Sep 2020 Last revised: 15 Dec 2021

Date Written: June 9, 2021

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.

Keywords: Mean-variance portfolio, Higher moments, Estimation risk

JEL Classification: C1,G11

Suggested Citation

Lassance, Nathan, Reconciling mean-variance portfolio theory with non-Gaussian returns (June 9, 2021). European Journal of Operational Research, 2021, 297(2):729-740., Available at SSRN: https://ssrn.com/abstract=3664049 or http://dx.doi.org/10.2139/ssrn.3664049

Nathan Lassance (Contact Author)

LFIN/LIDAM, UCLouvain ( email )

151 Chaussée de Binche
Mons, 7000
Belgium

Do you have negative results from your research you’d like to share?

Paper statistics

Downloads
117
Abstract Views
686
Rank
427,613
PlumX Metrics