Journal of Data Science

Abstract: We analyze the cross-correlation between logarithmic returns of 1108 stocks listed on the Shanghai and Shenzhen Stock Exchange of China in the period 2005 to 2010. The results suggest that the estimated distribution of correlation coefficients is right shifted in the tumble time of Chinese stock market. Due to the large share of maximum eigenvalue, the principal correlation component in Chinese stock market is dominant and other components only have trivial effects on the market condition. The same-signed corresponding vector elements enable us to propose the maximum eigenvalue series as an indicator for collective behavior in the equity market. We provide the evidence that the largest eigenvalue series can be used as an effective indicative parameter to describe the collective behavior of stock returns, which is found to be positively correlated to market volatility. By using time-varying windows, we find the positive correlation diminishes when the market volatility reaches both highest and lowest level. By defining a stability rate, we display that the collective behavior of stocks tends to be more homogeneous in the context of crisis than the regular time. This study has implications for the arising discussions on correlation risk.