Covariance Matrix Estimation for Positively Correlated Assets

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.