Covariance Matrix Estimation for Positively Correlated Assets

TL;DR

This paper introduces ERSE, a new covariance matrix estimator tailored for positively correlated assets, which improves portfolio risk estimation by better eigenvector adjustment, outperforming existing methods in empirical tests.

Contribution

The paper proposes ERSE, an eigenvector rotation shrinkage estimator that enhances covariance matrix estimation for positively correlated assets, outperforming existing rotation-equivariant estimators.

Findings

ERSE reduces out-of-sample portfolio variance by over 10%.

ERSE produces covariance matrices with lower condition numbers.

ERSE yields more stable and concentrated portfolio weights.

Abstract

The comovement phenomenon in financial markets creates decision scenarios with positively correlated asset returns. This paper addresses covariance matrix estimation under such conditions, motivated by observations of significant positive correlations in factor-sorted portfolio monthly returns. We demonstrate that fine-tuning eigenvectors linked to weak factors within rotation-equivariant frameworks produces well-conditioned covariance matrix estimates. Our Eigenvector Rotation Shrinkage Estimator (ERSE) pairwise rotates eigenvectors while preserving orthogonality, equivalent to performing multiple linear shrinkage on two distinct eigenvalues. Empirical results on factor-sorted portfolios from the Ken French data library demonstrate that ERSE outperforms existing rotation-equivariant estimators in reducing out-of-sample portfolio variance, achieving average risk reductions of 10.52\% versus linear shrinkage methods and 12.46\% versus nonlinear shrinkage methods. Further checks indicate that ERSE yields covariance matrices with lower condition numbers, produces more concentrated and stable portfolio weights, and provides consistent improvements across different subperiods and estimation windows.