Random matrix approach to cross correlations in financial data
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- 27 June 2002
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 65 (6), 066126
- https://doi.org/10.1103/physreve.65.066126
Abstract
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 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 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.
Keywords
This publication has 60 references indexed in Scilit:
- Universal and Nonuniversal Properties of Cross Correlations in Financial Time SeriesPhysical Review Letters, 1999
- Noise Dressing of Financial Correlation MatricesPhysical Review Letters, 1999
- Physicists attempt to scale the ivory towers of financeComputing in Science & Engineering, 1999
- Random-matrix theories in quantum physics: common conceptsPhysics Reports, 1998
- Random-matrix physics: spectrum and strength fluctuationsReviews of Modern Physics, 1981
- Statistical Theory of the Energy Levels of Complex Systems. IVJournal of Mathematical Physics, 1963
- Statistical Theory of the Energy Levels of Complex Systems. VJournal of Mathematical Physics, 1963
- Statistical Theory of the Energy Levels of Complex Systems. IJournal of Mathematical Physics, 1962
- On the statistical distribution of the widths and spacings of nuclear resonance levelsMathematical Proceedings of the Cambridge Philosophical Society, 1951
- On a Class of Analytic Functions from the Quantum Theory of CollisionsAnnals of Mathematics, 1951