Collective behavior of stock price movements - a random matrix theory approach

We review recent work on quantifying collective behavior among stocks by ap plying the conceptual framework of random matrix theory (RMT), developed in physics to describe the energy levels of complex systems. RMT makes predic tions for "universal" properties that do not depend on the interactions bet ween the elements comprising the system; deviations from RMT provide clues regarding system-specific properties. We compare the statistics of the cros s-correlation matrix C-whose elements C-ij are the correlation coefficients of price fluctuations of stock i and j-against a random matrix having the same symmetry properties. lt is found that RMT methods can distinguish rand om and non-random parts of C. The non-random part of C which deviates from RMT results, provides information regarding genuine collective behavior amo ng stocks. (C) 2001 Published by Elsevier Science B.V.