标题： 正相关资产的协方差矩阵估计 显示英文标题

标题： Covariance Matrix Estimation for Positively Correlated Assets

摘要： 金融市场中的共同运动现象创造了资产收益正相关的决策场景。 本文研究了在这些条件下协方差矩阵的估计，这是基于因子排序投资组合月度收益中显著正相关性的观察结果。 我们证明，在旋转等变框架内对弱因子相关特征向量进行微调可以产生条件良好的协方差矩阵估计。 我们的特征向量旋转收缩估计器（ERSE）成对旋转特征向量，同时保持正交性，相当于对两个不同的特征值进行多次线性收缩。 对肯弗雷数据库中的因子排序投资组合进行实证分析表明，ERSE在减少样本外投资组合方差方面优于现有的旋转等变估计器，平均风险降低幅度为10.52%相对于线性收缩方法和12.46%相对于非线性收缩方法。 进一步的检验表明，ERSE产生的协方差矩阵具有较低的条件数，生成更集中和稳定的投资组合权重，并在不同子期间和估计窗口中提供一致的改进。 显示英文摘要

摘要： 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.