Examining the Relationship between Random Matrix Theory and Financial Correlation

This study aims to replicate and extend the methodology of Laloux et al. (1999) by applying Random Matrix Theory (RMT) to a modern dataset comprising the opening prices of S&P 500 constituent stocks from 2013 to 2018. The objective is to determine the extent to which observed correlations in asset returns are driven by genuine market structure versus statistical noise. Standardised log returns were used to construct empirical correlation matrices, and the eigenvalue spectra were compared to the theoretical bounds predicted by the Marčenko-Pastur distribution. With 468 stocks and 1,258 trading days, the empirical ratio Q = T/N ≈ 2.69, yielding a theoretical noise band of [0.15, 2.59]. Out of 468 eigenvalues, 14 exceeded the upper bound. The largest eigenvalue, approximately 133.33, represents a dominant market mode. Spectral filtering was employed to denoise the correlation matrix, and empirical validation shows that portfolio volatility remains stable before and after filtering (0.00791 in both cases, 0.015% reduction), confirming that RMT preserves essential market dynamics while reducing estimation noise.