Extreme Eigenvector Analysis of Global Financial Correlation Matrices

The correlation between the 31 global financial indices from American, European and Asia-Pacific region are studied for a period before, during and after the 2008 crash. A spectral study of the moving window correlations gives significant information about the interactions between different financial indices. Eigenvalue spectra for each window is compared with the random matrix results on Wishart matrices. The upper side of the spectra outside the random matrix bound consists of the same number of eigenvalues for all windows where as significant differences can be seen in the lower side of the spectra. Analysis of the eigenvectors indicates that the second largest eigenvector clearly gives the sectors indicating the geographical location of each country i.e. the countries with geographical proximity giving similar contributions to the second largest eigenvector. The eigenvalues on the lower side of spectra outside the random matrix bounds changes before during and after the crisis. A quantitative way of specifying information based on the eigenvectors is constructed defined as the “eigenvector entropy” which gives the localization of eigenvectors. Most of the dynamics is captured by the low eigenvectors. The lowest eigenvector shows how the financial ties changes before, during and after the 2008 crisis.