We analyze cross-correlations between price fluctuations of different stocksusing methods of random matrix theory (RMT). Using two large databases, wecalculate cross-correlation matrices C of returns constructed from (i) 30-minreturns of 1000 US stocks for the 2-yr period 1994--95 (ii) 30-min returns of881 US stocks for the 2-yr period 1996--97, and (iii) 1-day returns of 422 USstocks for the 35-yr period 1962--96. We test the statistics of the eigenvalues$\lambda_i$ of C against a ``null hypothesis'' --- a random correlation matrixconstructed from mutually uncorrelated time series. We find that a majority ofthe eigenvalues of C fall within the RMT bounds $[\lambda_-, \lambda_+]$ forthe eigenvalues of random correlation matrices. We test the eigenvalues of Cwithin the RMT bound for universal properties of random matrices and find goodagreement with the results for the Gaussian orthogonal ensemble of randommatrices --- implying a large degree of randomness in the measuredcross-correlation coefficients. Further, we find that the distribution ofeigenvector components for the eigenvectors corresponding to the eigenvaluesoutside the RMT bound display systematic deviations from the RMT prediction. Inaddition, we find that these ``deviating eigenvectors'' are stable in time. Weanalyze the components of the deviating eigenvectors and find that the largesteigenvalue corresponds to an influence common to all stocks. Our analysis ofthe remaining deviating eigenvectors shows distinct groups, whose identitiescorrespond to conventionally-identified business sectors. Finally, we discussapplications to the construction of portfolios of stocks that have a stableratio of risk to return.
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