Regularizing stock return covariance matrices via multiple testing of correlations

TL;DR

This paper introduces a novel large-scale inference method for regularizing stock return covariance matrices by testing correlations and applying adaptive thresholding, which improves estimation accuracy and portfolio optimization.

Contribution

It develops a new correlation testing and regularization framework that handles heavy tails and GARCH effects, ensuring positive definite covariance matrices with controlled error rates.

Findings

Outperforms existing estimators in simulations

Enhances portfolio optimization accuracy

Ensures positive definiteness and sparsity in covariance estimates

Abstract

This paper develops a large-scale inference approach for the regularization of stock return covariance matrices. The framework allows for the presence of heavy tails and multivariate GARCH-type effects of unknown form among the stock returns. The approach involves simultaneous testing of all pairwise correlations, followed by setting non-statistically significant elements to zero. This adaptive thresholding is achieved through sign-based Monte Carlo resampling within multiple testing procedures, controlling either the traditional familywise error rate, a generalized familywise error rate, or the false discovery proportion. Subsequent shrinkage ensures that the final covariance matrix estimate is positive definite and well-conditioned while preserving the achieved sparsity. Compared to alternative estimators, this new regularization method demonstrates strong performance in simulation experiments and real portfolio optimization.