Multi Anchor Point Shrinkage for the Sample Covariance Matrix

Abstract: 

Estimation of the covariance of a high-dimensional returns vector is well-known by practitioners to be impeded by the lack of long data history. We extend the work of Goldberg, Papanicolaou, and Shkolnik (GPS) [6] on shrinkage estimates for the leading eigenvector of the covariance matrix in the high dimensional, low sample-size regime, which has immediate application to estimating minimum variance portfolios. We introduce a more general framework of shrinkage targets { multi anchor point shrinkage { that allows the practitioner to incorporate additional information { such as sector separation of equity betas, or prior beta estimates from the recent past { to the estimation. We prove some precise asymptotic statements and illustrate our results with some numerical experiments.

Author: 
Hubeyb Gurdogan
Publication date: 
September 6, 2021
Publication type: 
Journal Article