Improved Estimation of the Covariance Matrix of Stock Returns With an Application to Portfolio Selection

Olivier Ledoit and Michael Wolf


This paper proposes to estimate the covariance matrix of stock returns by an optimally weighted average of two existing estimators: the sample covariance matrix and the single-index covariance matrix. This method is generally known as shrinkage, and it is standard in decision theory and in empirical Bayesian statistics. Our shrinkage estimator can be seen as a way to account for extra-market covariance without having to specify an arbitrary multi-factor structure. For NYSE and AMEX stock returns from 1972 to 1995, it can be used to select portfolios with significantly lower out-of-sample variance than a set of existing estimators, including multi-factor models.

The Matlab code for the estimator proposed in the paper can be downloaded from the website of my co-author Michael Wolf in the Department of Economics of the University of Zurich.

Journal of Empirical Finance, Volume 10, Issue 5, December 2003, pages 603-621

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