Untangling Universality and Dispelling Myths in Mean-Variance Optimization

Posted: 3 Apr 2024 Last revised: 13 May 2024

See all articles by Elie Benveniste

Elie Benveniste

New York University (NYU) - Courant Institute of Mathematical Sciences

Petter N. Kolm

New York University (NYU) - Courant Institute of Mathematical Sciences

Gordon Ritter

New York University (NYU) - Courant Institute of Mathematical Sciences; City University of New York (CUNY) - Weissman School of Arts and Sciences; Columbia University - Department of Mathematics; University of Chicago - Department of Mathematics; Columbia University - School of Professional Studies

Date Written: March 3, 2024

Abstract

Following Markowitz's pioneering work on mean-variance optimization (MVO), such approaches have permeated nearly every facet of quantitative finance. In the first part of the article, we argue that their widespread adoption can be attributed to the universality of the mean-variance paradigm, wherein the maximum expected utility and mean-variance allocations coincide for a broad range of distributional assumptions of asset returns. Subsequently, we introduce a formal definition of mean-variance equivalence, and present a novel and comprehensive characterization of distributions, termed mean-variance-equivalent (MVE) distributions, wherein expected utility maximization and the solution of an MVO problem are the same. In the second part of the article, we address common myths associated with MVO. These myths include the misconception that MVO necessitates normally-distributed asset returns, the belief that it is unsuitable for cases with asymmetric return distributions, the notion that it maximizes errors, and the perception that it underperforms a simple 1/n portfolio in out-of-sample tests. Furthermore, we address misunderstandings regarding MVO's ability to handle signals across different time horizons, its treatment of transaction costs, its applicability to intraday and high-frequency trading, and whether quadratic utility accurately represents investor preferences. Finally, we present a contemporary and practically feasible method for leveraging value functions to solve multi-period optimization with a mean-quadratic-variation objective.

Keywords: Investment management, Mean-variance optimization, Mean-variance equivalent distributions, Portfolio optimization, Portfolio theory, Robust portfolio management, Trading, Universality

JEL Classification: C51, C53, C61, G11, G12

Suggested Citation

Benveniste, Elie and Kolm, Petter N. and Ritter, Gordon, Untangling Universality and Dispelling Myths in Mean-Variance Optimization (March 3, 2024). Available at SSRN: https://ssrn.com/abstract=4747461 or http://dx.doi.org/10.2139/ssrn.4747461

Elie Benveniste

New York University (NYU) - Courant Institute of Mathematical Sciences ( email )

New York University
New York, NY 10012
United States

Petter N. Kolm (Contact Author)

New York University (NYU) - Courant Institute of Mathematical Sciences ( email )

251 Mercer Street
New York, NY 10012
United States

Gordon Ritter

New York University (NYU) - Courant Institute of Mathematical Sciences ( email )

New York University
251 Mercer Street
New York, NY 10012
United States

City University of New York (CUNY) - Weissman School of Arts and Sciences ( email )

One Bernard Baruch Way
New York, NY 10010
United States

Columbia University - Department of Mathematics ( email )

New York, NY
United States

University of Chicago - Department of Mathematics ( email )

5734 S. University
Chicago, IL 60637
United States

Columbia University - School of Professional Studies ( email )

203 Lewisohn Hall
2970 Broadway, MC 4119
New York, NY 10027
United States

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