Market Correlation Structure Changes Around the Great Crash: A Random Matrix Theory Analysis of the Chinese Stock Market

Abstract

-We perform a comparative analysis of the Chinese stock market around the occurrence of the 2008 crisis based on the random matrix analysis of high-frequency stock returns of 1228 stocks listed on the Shanghai and Shenzhen stock exchanges. Both raw correlation matrix and partial correlation matrix with respect to the market index in two time periods of one year are investigated. We find that the Chinese stocks have stronger average correlation and partial correlation in 2008 than in 2007 and the average partial correlation is significantly weaker than the average correlation in each period. Accordingly, the largest eigenvalue of the correlation matrix is remarkably greater than that of the partial correlation matrix in each period. Moreover, each largest eigenvalue and its eigenvector reflect an evident market effect, while other deviating eigenvalues do not. We find no evidence that deviating eigenvalues contain industrial sectorial information. Surprisingly, the eigenvectors of the second largest eigenvalues in 2007 and of the third largest eigenvalues in 2008 are able to distinguish the stocks from the two exchanges. We also find that the component magnitudes of the some largest eigenvectors are proportional to the stocks' capitalizations.Introduction. -Financial markets evolve in a selforganized manner with the interacting elements forming complex networks at different levels, including international markets [1][2][3][4], individual markets [5][6][7][8], and security trading networks [9][10][11][12][13][14][15][16]. There are well-documented stylized facts of stock return time series within individual markets unveiled by the random matrix theory (RMT) analysis [6,17]: (1) The largest eigenvalue reflects the market effect such that its eigenportfolio returns are strongly correlated with the market returns; (2) Other largest eigenvalues contain information of industrial sectors; and (3) The smallest eigenvalues embed stock pairs with large correlations. However, for stock exchange index returns [1] and housing markets [18,19], the largest eigenvalues can be used to extract geographic traits. Moreover, the signs of eigenvector components contain information of local interactions [18,20,21].

A pre-crisis vs. crisis analysis of peripheral EU stock markets by means of wavelet transform and a nonlinear causality test

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Information Transfer between Stock Market Sectors: A Comparison between the USA and China

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