Random matrix theory and a definition of correlations in financial markets

Recent results based on Random Matrix Theory (RMT) suggest that commonly used methods to find correlations in financial markets are not adequate. They suggest that stocks may have collective behaviour that cannot be described by the classical approach. This raises doubts on the blind use of empirical variance-covariance matrices and needs a new understanding of correlations that goes beyond the linear one. This motivates us to propose a definition of correlations to describe and explain this collective behaviour. Computational experiments in the paper show that these correlations reproduce the character of the RTM results and reveal themselves by symmetries in eigenvector distributions of variance-covariance matrix.