The Power of (Non-)Linear Shrinking: A Review and Guide to Covariance Matrix Estimation

University of Zurich, Department of Economics, Working Paper No. 323 (2019)

42 Pages Posted: 1 Jun 2019

See all articles by Olivier Ledoit

Olivier Ledoit

University of Zurich - Department of Economics

Michael Wolf

University of Zurich - Department of Economics

Date Written: May 2019

Abstract

Many econometric and data-science applications require a reliable estimate of the covariance matrix, such as Markowitz portfolio selection. When the number of variables is of the same magnitude as the number of observations, this constitutes a difficult estimation problem; the sample covariance matrix certainly will not do. In this paper, we review our work in this area going back 15+ years. We have promoted various shrinkage estimators, which can be classified into linear and nonlinear. Linear shrinkage is simpler to understand, to derive, and to implement. But nonlinear shrinkage can deliver another level of performance improvement, especially if overlaid with stylized facts such as time-varying co-volatility or factor models.

Keywords: dynamic conditional correlations, factor models, large-dimensional asymptotics, Markowitz portfolio selection, rotation equivariance

JEL Classification: C13, C58, G11

Suggested Citation

Ledoit, Olivier and Wolf, Michael, The Power of (Non-)Linear Shrinking: A Review and Guide to Covariance Matrix Estimation (May 2019). University of Zurich, Department of Economics, Working Paper No. 323 (2019). Available at SSRN: https://ssrn.com/abstract=3384500 or http://dx.doi.org/10.2139/ssrn.3384500

Olivier Ledoit (Contact Author)

University of Zurich - Department of Economics ( email )

Wilfriedstrasse 6
Z├╝rich, 8032
Switzerland

Michael Wolf

University of Zurich - Department of Economics ( email )

Wilfriedstrasse 6
Zurich, 8032
Switzerland

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