Summary: Physica A 287 (2000) 374382
A random matrix theory approach to ˙nancial
, P. Gopikrishnan, B. Rosenow,
L.A.N. Amaral, H.E. Stanley
Center for Polymer Studies, Department of Physics, Boston University, Boston, MA 02215, USA
Received 13 May 2000; received in revised form 4 July 2000
It is common knowledge that any two ˙rms in the economy are correlated. Even ˙rms be-
longing to di erent sectors of an industry may be correlated because of "indirect" correlations.
How can we analyze and understand these correlations? This article reviews recent results re-
garding cross-correlations between stocks. Speci˙cally, we use methods of random matrix theory
(RMT), which originated from the need to understand the interactions between the constituent
elements of complex interacting systems, to analyze the cross-correlation matrix C of returns.
We analyze 30-min returns of the largest 1000 US stocks for the 2-year period 19941995. We
˙nd that the statistics of approximately 20 of the largest eigenvalues (2%) show deviations from
the predictions of RMT. To test that the rest of the eigenvalues are genuinely random, we test
for universal properties such as eigenvalue spacings and eigenvalue correlations, and demonstrate