Using, Taming or Avoiding the Factor Zoo? A Double-Shrinkage Estimator for Covariance Matrices

Abstract

Existing factor models struggle to model the covariance matrix for a large number of stocks and factors. Therefore, we introduce a new covariance matrix estimator that first shrinks the factor model coefficients and then applies nonlinear shrinkage to the residuals and factors. The estimator blends a regularized factor structure with conditional heteroskedasticity of residuals and factors and displays superior all-around performance against various competitors. We show that for the proposed double- shrinkage estimator, it is enough to use only the market factor or the most important latent factor(s). Thus there is no need for laboriously taking into account the factor zoo. Supplementary material for this article is available online.