Noise Dressing of Financial Correlation Matrices

We show that results from the theory of random matrices are potentially of great interest to understand the statistical structure of the empirical correlation matrices appearing in the study of multivariate time series. The central result of the present study, which focuses on the case of financial price fluctuations, is the remarkable agreement between the theoretical prediction (based on the assumption that the correlation matrix is random) and empirical data concerning the density of eigenvalues associated to the time series of the different stocks of the S&P 500 (or other major markets). In particular, the present study raises serious doubts on the blind use of empirical correlation matrices for risk management.