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Primary Article

Honey, I Shrunk the Sample Covariance Matrix

Olivier Ledoit and Michael Wolf
The Journal of Portfolio Management Summer 2004, 30 (4) 110-119; DOI: https://doi.org/10.3905/jpm.2004.110
Olivier Ledoit
A managing director in the Equities Division of Credit Suisse First Boston in London, UK.
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  • For correspondence: olivier@ledoit.net
Michael Wolf
A an associate professor of economics and business at the Universitat Pompeu Fabra in Barcelona, Spain.
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  • For correspondence: michael.wolf@upf.edu
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Abstract

The central message of this article is that no one should use the sample covariance matrix for portfolio optimization. It is subject to estimation error of the kind most likely to perturb a mean-variance optimizer. Instead, a matrix can be obtained from the sample covariance matrix through a transformation called shrinkage. This tends to pull the most extreme coefficients toward more central values, systematically reducing estimation error when it matters most. Statistically, the challenge is to know the optimal shrinkage intensity. Shrinkage reduces portfolio tracking error relative to a benchmark index, and substantially raises the manager's realized information ratio.

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The Journal of Portfolio Management
Vol. 30, Issue 4
Summer 2004
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Honey, I Shrunk the Sample Covariance Matrix
Olivier Ledoit, Michael Wolf
The Journal of Portfolio Management Jul 2004, 30 (4) 110-119; DOI: 10.3905/jpm.2004.110

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Honey, I Shrunk the Sample Covariance Matrix
Olivier Ledoit, Michael Wolf
The Journal of Portfolio Management Jul 2004, 30 (4) 110-119; DOI: 10.3905/jpm.2004.110
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