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Honey, I Shrunk the Sample Covariance Matrix

UPF Economics and Business Working Paper No. 691

21 Pages Posted: 18 Sep 2003  

Olivier Ledoit

University of Zurich - Department of Economics

Michael Wolf

University of Zurich - Department of Economics

Date Written: June 2003

Abstract

The central message of this paper is that nobody should be using the sample covariance matrix for the purpose of portfolio optimization. It contains estimation error of the kind most likely to perturb a mean-variance optimizer. In its place, we suggest using the matrix obtained from the sample covariance matrix through a transformation called shrinkage. This tends to pull the most extreme coefficients towards more central values, thereby systematically reducing estimation error where it matters most. Statistically, the challenge is to know the optimal shrinkage intensity, and we give the formula for that. Without changing any other step in the portfolio optimization process, we show on actual stock market data that shrinkage reduces tracking error relative to a benchmark index, and substantially increases the realized information ratio of the active portfolio manager.

Keywords: Covariance matrix, Markovitz optimization, shrinkage, tracking error

JEL Classification: C13, C51, C61, G11, G15

Suggested Citation

Ledoit, Olivier and Wolf, Michael, Honey, I Shrunk the Sample Covariance Matrix (June 2003). UPF Economics and Business Working Paper No. 691. Available at SSRN: https://ssrn.com/abstract=433840 or http://dx.doi.org/10.2139/ssrn.433840

Olivier Ledoit

University of Zurich - Department of Economics ( email )

Wilfriedstrasse 6
Zürich, 8032
Switzerland

Michael Wolf (Contact Author)

University of Zurich - Department of Economics ( email )

Wilfriedstrasse 6
Zurich, 8032
Switzerland

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