Random Matrix Theory and a Precise Definition of Correlation in Financial Markets

     Galina Korotkikh
     Faculty of Informatics and Communication
     Central Queensland University
     Mackay, Queensland, 4740, Australia
     g.korotkich@cqu.edu.au

Recent results based on random matrix theory suggest that some commonly used financial methods find correlations that are not real. This raises serious doubts on the blind use of empirical correlation matrices for risk management.
Motivated by these results a different approach is considered in the talk. The approach combines random matrix theory and a precise definition of correlation to develop solid methods for differentiating real trends from randomness in financial markets. In particular, this allows to define a metric on the space of  stocks and a distance between pairs of them.