This paper presents a study of cross-correlations between price fluctuations of different stocks using random matrix theory (RMT). The authors analyze cross-correlation matrices C of returns from three different time periods and stock sets. They compare the eigenvalues of C with those of a random correlation matrix constructed from mutually uncorrelated time series. They find that most eigenvalues of C fall within the RMT bounds, suggesting a large degree of randomness in the cross-correlation coefficients. However, they also find that eigenvectors corresponding to eigenvalues outside the RMT bounds show systematic deviations, indicating the presence of genuine correlations. These deviating eigenvectors are found to be stable over time and correspond to distinct business sectors. The authors also find that the largest eigenvalue corresponds to a common influence on all stocks. They discuss the implications of these findings for portfolio optimization, suggesting that the deviating eigenvectors can be used to construct portfolios with a stable ratio of risk to return. The study highlights the importance of distinguishing between random and genuine correlations in financial data.This paper presents a study of cross-correlations between price fluctuations of different stocks using random matrix theory (RMT). The authors analyze cross-correlation matrices C of returns from three different time periods and stock sets. They compare the eigenvalues of C with those of a random correlation matrix constructed from mutually uncorrelated time series. They find that most eigenvalues of C fall within the RMT bounds, suggesting a large degree of randomness in the cross-correlation coefficients. However, they also find that eigenvectors corresponding to eigenvalues outside the RMT bounds show systematic deviations, indicating the presence of genuine correlations. These deviating eigenvectors are found to be stable over time and correspond to distinct business sectors. The authors also find that the largest eigenvalue corresponds to a common influence on all stocks. They discuss the implications of these findings for portfolio optimization, suggesting that the deviating eigenvectors can be used to construct portfolios with a stable ratio of risk to return. The study highlights the importance of distinguishing between random and genuine correlations in financial data.