The fine structure of spectral properties for random correlation matrices: an application to financial markets

TL;DR

This paper investigates the eigenvalue spectra of financial correlation matrices, revealing that large eigenvalue bulks result from superpositions of smaller cross-correlation structures, challenging the idea they are purely noise.

Contribution

It introduces a filtering method to highlight cluster structures in correlation matrices and demonstrates how these structures influence eigenvalue spectra, linking empirical findings to factor models.

Findings

Eigenvalue bulks are superpositions of smaller correlated structures.

Filtering reveals underlying cluster structures in financial data.

Empirical spectra align with predictions from Random Matrix Theory for factor models.

Abstract

We study some properties of eigenvalue spectra of financial correlation matrices. In particular, we investigate the nature of the large eigenvalue bulks which are observed empirically, and which have often been regarded as a consequence of the supposedly large amount of noise contained in financial data. We challenge this common knowledge by acting on the empirical correlation matrices of two data sets with a filtering procedure which highlights some of the cluster structure they contain, and we analyze the consequences of such filtering on eigenvalue spectra. We show that empirically observed eigenvalue bulks emerge as superpositions of smaller structures, which in turn emerge as a consequence of cross-correlations between stocks. We interpret and corroborate these findings in terms of factor models, and and we compare empirical spectra to those predicted by Random Matrix Theory for such models.