Do We Need Higher-Order Comoments to Enhance Mean-Variance Portfolios?

29 Pages Posted: 13 Feb 2020 Last revised: 13 Dec 2020

See all articles by Khaldoun Khashanah

Khaldoun Khashanah

Stevens Institute of Technology

Majeed Simaan

Stevens Institute of Technology - School of Business

Yusif Simaan

Fordham University - Graduate School of Business

Date Written: December 12, 2020

Abstract

We propose a joint distribution that decomposes asset returns into two independent components: an elliptical innovation (Gaussian) and a systematic non-elliptical latent process. The paper provides a tractable approach to estimate the underlying parameters and, hence, the assets' exposures to the latent non-elliptical factor. Additionally, the framework incorporates higher-order moments, such as skewness and kurtosis, for portfolio selection. Taking into account estimation risk, we investigate the economic contribution of the non-elliptical term. Overall, we find weak empirical evidence to support the inclusion of the non-elliptical term and, hence, the higher-order comoments. Nonetheless, our findings support the mean-variance (MV) decision rule that incorporates the elliptical term alone. Excluding the non-elliptical term results in more robust mean-variance estimates and, thus, enhanced out-of-sample performance. This evidence is significant among stocks that exhibit a strong deviation from the Gaussian property. Moreover, it is most pronounced during market turmoils, when exposures to the latent factor are highest. Overall, our paper advocates for shrinking away from the non-elliptical term, which is associated with higher estimation risk.

Keywords: Utility Theory, Non-Elliptical Distributions, Shrinkage, Multivariate Analysis

JEL Classification: C13, C44, C46, G11

Suggested Citation

Khashanah, Khaldoun and Simaan, Majeed and Simaan, Yusif, Do We Need Higher-Order Comoments to Enhance Mean-Variance Portfolios? (December 12, 2020). Available at SSRN: https://ssrn.com/abstract=3523379 or http://dx.doi.org/10.2139/ssrn.3523379

Khaldoun Khashanah

Stevens Institute of Technology ( email )

Hoboken, NJ 07030
United States

Majeed Simaan (Contact Author)

Stevens Institute of Technology - School of Business ( email )

Hoboken, NJ 07030
United States

Yusif Simaan

Fordham University - Graduate School of Business ( email )

113 West 60th Street
Bronx, NY 10458
United States
6462200652 (Phone)

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