arXiv 2 Jul 2025 · Econometrics
arXiv:2507.01545 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Shi, F., Shu, L., Yang, A., and He, F (2020) Improving minimum-variance portfolios by alleviating overdispersion of eigenvalues | 1.000 | 11 | 5 | 100% |
| 2 | Ledoit, O. and Wolf, M (2004) A well-conditioned estimator for large-dimensional covariance matrices | 1.000 | 11 | 3 | 100% |
| 3 | Ledoit, O. and Wolf, M (2017) Nonlinear shrinkage of the covariance matrix for portfolio selection: Markowitz meets goldilocks | 1.000 | 9 | 4 | 100% |
| 4 | DeMiguel, V., Garlappi, L., Nogales, F. J., and Uppal, R (2009) A generalized approach to portfolio optimization: Improving performance by constraining portfolio norms | 1.000 | 8 | 4 | 100% |
| 5 | Ledoit, O. and Wolf, M (2012) Nonlinear shrinkage estimation of large-dimensional covariance matrices | 1.000 | 6 | 3 | 100% |
| 6 | Ledoit, O. and Wolf, M (2003) Improved estimation of the covariance matrix of stock returns with an application to portfolio selection | 0.928 | 4 | 3 | 100% |
| 7 | Ledoit, O. and Wolf, M (2022) The power of (non-)linear shrinking: A review and guide to covariance matrix estimation | 0.843 | 3 | 3 | 100% |
| 8 | Nguyen, V. A., Kuhn, D., and Esfahani, P. M (2022) Distributionally robust inverse covariance estimation: The Wasserstein shrinkage estimator | 0.843 | 3 | 3 | 100% |
| 9 | Barroso, P. and Saxena, K (2022) Lest we forget: Learn from out-of-sample forecast errors when optimizing portfolios | 0.811 | 4 | 2 | 100% |
| 10 | Dai, R., Uematsu, Y., and Matsuda, Y (2024) Estimation of large covariance matrices with mixed factor structures | 0.811 | 4 | 2 | 100% |
Showing the top 10 of 45 scored citations.