Multiple Anchor Point Shrinkage for the Sample Covariance Matrix

Covariance estimation for high-dimensional returns is well-known to be impeded by the lack of long data history. We extend the work of Goldberg, Papanicolaou, and Shkolnik (GPS) [14] on shrinkage estimates for the leading eigenvector of a 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 eigenvector shrinkage targets – multiple anchor point shrinkage – that allows the practitioner to incorporate additional information, such as rank ordering or sector separation of equity betas, or prior beta estimates from the recent past. We show that certain rank ordering information can be used to define a consistent estimator of the leading eigenvector. We prove some asymptotic statements and illustrate our results with some numerical experiments.