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Portfolio Selection With Robust Estimation

44 Pages Posted: 28 Jun 2006 Last revised: 4 Nov 2007

Victor DeMiguel

London Business School

Francisco J. Nogales

Universidad Carlos III de Madrid - Department of Statistics; Institute of Financial Big Data UC3M-BS

Date Written: August 2007

Abstract

Mean-variance portfolios constructed using the sample mean and covariance matrix of asset returns perform poorly out-of-sample due to estimation error. Moreover, it is commonly accepted that estimation error in the sample mean is much larger than in the sample covariance matrix. For this reason, practitioners and researchers have recently focused on the minimum-variance portfolio, which relies solely on estimates of the covariance matrix, and thus, usually performs better out-of-sample. But even the minimum-variance portfolios are quite sensitive to estimation error and have unstable weights that fluctuate substantially over time. In this paper, we propose a class of portfolios that have better stability properties than the traditional minimum-variance portfolios. The proposed portfolios are constructed using certain robust estimators and can be computed by solving a single nonlinear program, where robust estimation and portfolio optimization are performed in a single step. We show analytically that the resulting portfolio weights are less sensitive to changes in the asset-return distribution than those of the traditional minimum-variance portfolios. Moreover, our numerical results on simulated and empirical data confirm that the proposed portfolios are more stable than the traditional minimum-variance portfolios, while preserving (or slightly improving) their relatively good out-of-sample performance.

Keywords: Portfolio choice, minimum-variance portfolios, estimation error, robust statistics.

JEL Classification: G11

Suggested Citation

DeMiguel, Victor and Nogales, Francisco J., Portfolio Selection With Robust Estimation (August 2007). Available at SSRN: https://ssrn.com/abstract=911596 or http://dx.doi.org/10.2139/ssrn.911596

Victor DeMiguel (Contact Author)

London Business School ( email )

Sussex Place
Regent's Park
London, London NW1 4SA
United Kingdom

Francisco J. Nogales

Universidad Carlos III de Madrid - Department of Statistics ( email )

Avda. de la Universidad, 30
Leganes, Madrid 28911
Spain
+34 916248773 (Phone)

HOME PAGE: http://www.est.uc3m.es/Nogales

Institute of Financial Big Data UC3M-BS ( email )

CL. de Madrid 126
Madrid, Madrid 28903
Spain

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