Honey, I Shrunk the Sample Covariance Matrix

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.