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 is covMarket.m. Or, alternatively, download it from the website of my co-author Michael Wolf at the Institute for Empirical Research in Economics of the University of Zurich.
More generally, you can estimate the covariance matrix by a weighted average of the sample covariance matrix with any other structured estimator. Examples of other structures that are intuitively appealing but are not in the paper include: the diagonal covariance matrix and the two-parameter covariance matrix. The corresponding Matlab functions are: shrinkDiag.m and cov2para.m respectively.
Journal of Empirical Finance, Volume 10, Issue 5, December 2003, pages 603-621
Download full paper (Acrobat PDF - 198KB)
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