Oops! I Shrunk the Sample Covariance Matrix Again: Blockbuster Meets Shrinkage

Abstract

Existing shrinkage techniques struggle to model the covariance matrix of asset returns in the presence of multiple-asset classes. Therefore, we introduce a Blockbuster shrinkage estimator that clusters the covariance matrix accordingly. Besides the definition and derivation of a new asymptotically optimal linear shrinkage estimator we propose an adaptive Blockbuster algorithm that clusters the covariance matrix even if the (number of) asset classes are unknown and change over time. It displays superior all-around performance on historical data against a variety of state-of-the-art linear shrinkage competitors. Additionally, we find that for small and medium-sized investment universes the proposed estimator outperforms even recent nonlinear shrinkage techniques. Hence, this new estimator can be used to deliver more efficient portfolio selection and detection of anomalies in the cross-section of asset returns. Furthermore, due to the general structure of the proposed Blockbuster shrinkage estimator the application is not restricted to financial problems.

Keywords: Blockbuster, large-dimensional covariance matrix estimation, linear and nonlinear shrinkage, Markowitz portfolio selection

JEL Classification: C13, C30, C53, C58, G11