Theoretical analyses of stock correlations affected by subprime crisis and total assets: Network properties and corresponding physical mechanisms**Project supported by the National Natural Science Foundation of China (Grant Nos. 11705042 and 71874172), the China Postdoctoral Science Foundation (Grant Nos. 2018T110040 and 2016M590041), the Fundamental Research Funds for Central Universities, China (Grant No. JZ2018HGTB0238), Curriculum Planning and Design Research Project, China

Abstract

In the field of statistical mechanics and system science, it is acknowledged that the financial crisis has a profound influence on stock market. However, the influence of total asset of enterprise on stock quote was not considered in the previous studies. In this work, a modified cross-correlation matrix that focuses on the influence of total asset on stock quote is introduced into the analysis of the stocks collected from Asian and American stock markets, which is different from the previous studies. The key results are obtained as follows. Firstly, stock is more greatly correlated with big asset than with small asset. Secondly, the higher the correlation coefficient among stocks, the larger the eigenvector is. Thirdly, in different periods, like the pre-subprime crisis period and the peak of subprime crisis period, Asian stock quotes show that the component of the third eigenvector of the cross-correlation matrix decreases with the asset of the enterprise decreasing. Fourthly, by simulating the threshold network, the small network constructed by 10 stocks with large assets can show the large network state constructed by 30 stocks. In this research we intend to fully explain the physical mechanism for understanding the historical correlation between stocks and provide risk control strategies in the future.