Eigenvalue density of cross-correlations in Sri Lankan financial market

Abstract

We apply the universal properties with Gaussian orthogonal ensemble (GOE) of random matrices namely spectral properties, distribution of eigenvalues, eigenvalue spacing predicted by random matrix theory (RMT) to compare cross-correlation matrix estimators from emerging market data. The daily stock prices of the Sri Lankan All share price index and Milanka price index from August 2004 to March 2005 were analyzed. Most eigenvalues in the spectrum of the cross-correlation matrix of stock price changes agree with the universal predictions of RMT. We find that the cross-correlation matrix satisfies the universal properties of the GOE of real symmetric random matrices. The eigen distribution follows the RMT predictions in the bulk but there are some deviations at the large eigenvalues. The nearest-neighbor spacing and the next nearest-neighbor spacing of the eigenvalues were examined and found that they follow the universality of GOE. RMT with deterministic correlations found that each eigenvalue from deterministic correlations is observed at values, which are repelled from the bulk distribution.