Estimation Risk and Shrinkage in Vast-Dimensional Fundamental Factor Models

Abstract

We investigate covariance matrix estimation in vast-dimensional spaces of 1,500 up to 2,000 stocks using fundamental factor models (FFMs). FFMs are the typical benchmark in the asset management industry and depart from the usual statistical factor models and the factor models with observed factors used in the statistical and finance literature. Little is known about estimation risk in FFMs in high dimensions. We investigate whether recent linear and non-linear shrinkage methods help to reduce the estimation risk in the asset return covariance matrix. Our findings indicate that modest improvements are possible using high-dimensional shrinkage techniques. The gains, however, are not realized using standard plug-in shrinkage parameters from the literature, but require sample dependent tuning.