The Random Matrix-based informative content of correlation matrices in stock markets

Abstract

Studying and comprehending the eigenvalue distribution of the correlation matrices of stock returns is a powerful tool to delve into the complex structure of financial markets. This paper deals with the analysis of the role of eigenvalues and their associated eigenvectors of correlation matrices within the context of financial markets. We exploit the meaningfulness of Random Matrix Theory with the specific aspect of the Marchenko-Pastur distribution law to separate noise from true signal but with a special focus on giving an interpretation of what mean these signals in the financial context. We empirically show that the highest eigenvalue serves as a proxy of market spillover. Furthermore, based on an analysis of portfolio betas, we prove that the eigenvector associated with this eigenvalue is the market portfolio. These analyses of portfolio betas also reveal that the second and third-highest eigenvalues, and their associated eigenvectors, result in some cases of counter-behavior that makes them suitable to be a safe haven during high-volatility periods. The analysis is performed on a set of indices coming from developed and emerging countries over a time period ranging from 2015 to 2024.

Keywords: Econophysics, Random Matrix Theory, Marchenko-Pastur distribution, Eigenvalue distribution, Financial Markets, Spillover