A0946
Title: James-Stein for eigenvectors
Authors: Alexander Shkolnik - University of California, Santa Barbara (United States)
Alec Kercheval - Florida State University (United States)
Lisa Goldberg - University of California, Berkeley (United States) [presenting]
Abstract: Estimated covariance matrices are widely used to construct portfolios with variance-minimizing optimization, yet the embedded sampling error produces portfolios with systematically underestimated variance. This effect is especially severe when the number of securities greatly exceeds the number of observations. In this high dimension low sample size (HL) regime, we show that a dispersion bias in the leading eigenvector of the estimated covariance matrix is a material source of distortion in the minimum variance portfolio. We correct the bias with the data-driven GPS (Global Positioning System) shrinkage estimator, which improves with the size of the market, and which is structurally identical to the James-Stein estimator for a collection of averages. We illustrate the power of the GPS estimator with a numerical example, and conclude with open problems that have emerged.
