Random Matrix Theory and Cross-Correlations of Stock Prices
We use methods of random matrix theory to analyze the cross-correlation matrix C of price changes of the largest 1000 US stocks for the 2-year period 1994–95. We find that the statistics of most of the eigenvalues in the spectrum of C agree with the predictions of random matrix theory, but there are deviations for a few of the largest eigenvalues. The eigenvectors whose eigenvalues deviate from the random matrix bound contain information about business sectors and are stable in time. Finally, we demonstrate that the sectors we identify are useful for the practical goal of finding an investment which earns a given return without exposure to unnecessary risk.
KeywordsPrice Change Large Eigenvalue Optimal Portfolio Business Sector Random Matrix Theory
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