Regularizing stock return covariance matrices via multiple testing of correlations
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.
Cite
@article{arxiv.2407.09696,
title = {Regularizing stock return covariance matrices via multiple testing of correlations},
author = {Richard Luger},
journal= {arXiv preprint arXiv:2407.09696},
year = {2024}
}