Regularizing stock return covariance matrices via multiple testing of correlations

Richard Luger

Papers from arXiv.org

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.

Date: 2024-07
New Economics Papers: this item is included in nep-ecm and nep-ets
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Journal Article: Regularizing stock return covariance matrices via multiple testing of correlations (2025)
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