A Random Matrix Theory Approach to Quantifying Collective Behavior Of Stock Price Fluctuations

We review recent work on quantifying collective behavior among stocks by applying the conceptual framework of random matrix theory (RMT), developed in physics to describe the energy levels of complex systems. RMT makes predictions for “universal” properties that do not depend on the interactions between the elements comprising the system; deviations from RMT provide clues regarding system-specific properties. WE compare the statistics of the cross-correlation matrix C—whose elements C i,j are the correlation coefficients of price fluctuations of stock i and j — against a random matrix having the same symmetry properties. It is found that RMT methods can distinguish random and non-random parts of C. The non-random part of C which deviates from RMT results, provides information regarding genuine collective behavior among stocks.

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