  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 price fluctuations. The central
result of the present study 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&P500 (or other major markets). In
particular the present study raises serious doubts on the blind use of
empirical correlation matrices for risk management.
