CORRELATION MATRIX OF EQUI-CORRELATED NORMAL POPULATION: FLUCTUATION OF THE LARGEST EIGENVALUE, SCALING OF THE BULK EIGENVALUES, AND STOCK MARKET

Given an [Formula: see text]-dimensional sample of size text] form a correlation matrix text]. Suppose that and tend to infinity with converging fixed finite constant If the population is factor model, then eigenvalue distribution almost surely converges weakly Marčenko–Pastur such index scale parameter limiting ratio specific variance text]th variable For normal equi-correlation coefficient text], which one-factor for largest we prove surely. These results suggest important role equi-correlated model in Laloux et al. [(2000) Random theory financial correlations, International Journal Theoretical Applied Finance 3 (3), 391–397]: histogram returns stock prices fits density Moreover, provide covariance population. We discuss phase transition as decay rate