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 (Laloux et al., 1999). The data comprises the opening prices of S&P 500 constituent stocks from 2013 to 2018 (Kaggle, 2018). The objective of the research paper is to determine the extent to which observed correlations in asset returns are driven by genuine market structure versus the anomalies that are present. Standardised log returns will be used to construct empirical correlation matrices. The eigenvalue spectra will be compared to the theoretical bounds predicted by the Marčenko–Pastur distribution (Marčenko & Pastur, 1967). This provides the theoretical eigenvalue density for large random correlation matrices under the assumption of Gaussian distributed and uncorrelated time series (Wigner et al., 1955). There is a limited number of significant outliers (Laloux et al., 1999). It is most notably a dominant market mode (Plerou et al., 2002). Spectral filtering has been employed to denoise the correlation matrix, leading to improved clarity in identifying systematic components (Bun et al., 2017). Empirical validation shows that portfolio volatility remains stable before and after spectral filtering (Allez & Bouchaud, 2012). Therefore, it confirms that RMT preserves essential market dynamics while reducing estimation outliers (Potters et al., 2005). These findings support the continued relevance of Random Matrix Theory in financial modeling and risk analysis (Potters et al., 2005). This is particularly relevant for volatility forecasting and robust portfolio construction in high dimensional environments (Allez & Bouchaud, 2012).