Previous empirical studies have shown that correlation matrices in financial markets usually have dominant eigenvalues. This paper applies a classic eigenvector–eigenvalue identity to analyze the properties of financial correlation matrices with super-dominant eigenvalues. Empirical analysis shows that there is an approximate relationship between the maximum eigenvalue and the eigenvector component. If the correlation matrix has a super eigenvalue, we can estimate the maximum eigenvalue of the sub-matrix from the maximum eigenvalue of the large-dimensional correlation matrix. Conversely, we can also estimate the maximum eigenvalue of the correlation matrix of a large number of stocks from the maximum eigenvalues corresponding to a few stocks. In addition, we find that different stock sets constructed based on the components of the eigenvector generate different predicted values, and the most accurate estimates can be obtained by selecting stocks at equal intervals. This paper reveals that eigenvector–eigenvalue identity helps to analyze the spectrum of financial correlation matrix in depth.

先前的经验研究表明，金融市场中的相关矩阵通常具有主导特征值。本文应用经典的特征向量-特征值恒等式来分析具有超主要特征值的金融相关矩阵的性质。实证分析表明，最大特征值与特征向量分量之间存在近似关系。如果相关矩阵具有超特征值，则可以从大尺寸相关矩阵的最大特征值估计子矩阵的最大特征值。相反，我们也可以根据与几只股票相对应的最大特征值来估计大量股票的相关矩阵的最大特征值。此外，我们发现，基于特征向量成分构建的不同股票集会产生不同的预测值，并且可以通过以相等间隔选择股票来获得最准确的估计。本文揭示了特征向量-特征值一致性有助于深入分析金融相关矩阵的频谱。