Crisis detection based on the Marčenko-Pastur law applied to the eigenvalue analysis of the empirical correlation matrix

Accurate separation of genuine factors from noise in financial correlation matrices is essential for effective risk management and asset allocation. We apply Random Matrix Theory (RMT) and the Marčenko–Pastur law (MP) to develop a framework to detect factors driving the price changes in financial markets. Unlike traditional factor models such as the CAPM or the Fama-French, our approach does not rely on predefined factors; instead, it identifies them empirically by analyzing the eigenvalue spectrum of the empirical correlation matrix. This method complements statistical techniques such as Principal Component Analysis (PCA) by offering a robust criterion for determining how many principal components (PCs) are necessary and how the number of factors reduces in times of crisis. Our analysis employs a sliding window methodology to study the eigenvalue structure of the correlation matrices for the returns of stocks in the S&P 500 and Europe STOXX 600 indices. We identify the number of statistically significant factors driving price changes–referred to as Group Modes–and introduce the Group Mode Ratio (GMR) as a novel indicator of market risk. Our findings show that during periods of financial distress – such as the COVID-19 crisis – the GMR declines to zero, signaling increased financial risk and reduced sectoral differentiation. We demonstrate that this RMT-based measure correlates well with traditional risk indicators like the VIX and VSTOXX thereby motivating its potential use as a predictive market risk indicator and as an informative tool for portfolio management decisions. Overall, our framework offers a data-driven approach, independent of option markets, for detecting the evolving factor structure in financial markets and, in particular, to identify periods of increased vulnerability as those in which the number of informative eigenvalues reduces to one, so that there is a breakdown of diversification opportunities.