TY - JOUR

T1 - Random matrix approach to cross correlations in financial data

AU - Plerou, Vasiliki

AU - Gopikrishnan, Parameswaran

AU - Rosenow, Bernd

AU - Amaral, Luís A Nunes

AU - Guhr, Thomas

AU - Stanley, H. Eugene

PY - 2002/6/27

Y1 - 2002/6/27

N2 - We analyze cross correlations between price fluctuations of different stocks using methods of random matrix theory (RMT). Using two large databases, we calculate cross-correlation matrices C of returns constructed from (i) 30-min returns of 1000 US stocks for the 2-yr period 1994–1995, (ii) 30-min returns of 881 US stocks for the 2-yr period 1996–1997, and (iii) 1-day returns of 422 US stocks for the 35-yr period 1962–1996. We test the statistics of the eigenvalues [formula presented] of C against a “null hypothesis” — a random correlation matrix constructed from mutually uncorrelated time series. We find that a majority of the eigenvalues of C fall within the RMT bounds [formula presented] for the eigenvalues of random correlation matrices. We test the eigenvalues of C within the RMT bound for universal properties of random matrices and find good agreement with the results for the Gaussian orthogonal ensemble of random matrices—implying a large degree of randomness in the measured cross-correlation coefficients. Further, we find that the distribution of eigenvector components for the eigenvectors corresponding to the eigenvalues outside the RMT bound display systematic deviations from the RMT prediction. In addition, we find that these “deviating eigenvectors” are stable in time. We analyze the components of the deviating eigenvectors and find that the largest eigenvalue corresponds to an influence common to all stocks. Our analysis of the remaining deviating eigenvectors shows distinct groups, whose identities correspond to conventionally identified business sectors. Finally, we discuss applications to the construction of portfolios of stocks that have a stable ratio of risk to return.

AB - We analyze cross correlations between price fluctuations of different stocks using methods of random matrix theory (RMT). Using two large databases, we calculate cross-correlation matrices C of returns constructed from (i) 30-min returns of 1000 US stocks for the 2-yr period 1994–1995, (ii) 30-min returns of 881 US stocks for the 2-yr period 1996–1997, and (iii) 1-day returns of 422 US stocks for the 35-yr period 1962–1996. We test the statistics of the eigenvalues [formula presented] of C against a “null hypothesis” — a random correlation matrix constructed from mutually uncorrelated time series. We find that a majority of the eigenvalues of C fall within the RMT bounds [formula presented] for the eigenvalues of random correlation matrices. We test the eigenvalues of C within the RMT bound for universal properties of random matrices and find good agreement with the results for the Gaussian orthogonal ensemble of random matrices—implying a large degree of randomness in the measured cross-correlation coefficients. Further, we find that the distribution of eigenvector components for the eigenvectors corresponding to the eigenvalues outside the RMT bound display systematic deviations from the RMT prediction. In addition, we find that these “deviating eigenvectors” are stable in time. We analyze the components of the deviating eigenvectors and find that the largest eigenvalue corresponds to an influence common to all stocks. Our analysis of the remaining deviating eigenvectors shows distinct groups, whose identities correspond to conventionally identified business sectors. Finally, we discuss applications to the construction of portfolios of stocks that have a stable ratio of risk to return.

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U2 - 10.1103/PhysRevE.65.066126

DO - 10.1103/PhysRevE.65.066126

M3 - Article

C2 - 12188802

AN - SCOPUS:33646976588

SN - 1063-651X

VL - 65

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

IS - 6

ER -