Cross-correlation Analysis Of Chinese Stock Market Based On Random Matrix Theory

The research on the correlation of stock returns has its theoretical value andpractical value as well.The former can be shown in that the stock market,a complexdynamic system,can be better known;and the latter can be shown in its importance inasset allocation and investment risk estimates.However,it is difficult to get acorrelation matrix which is reliable and can stand the test of practice.Marketconditions chang over time,and this will cause changeable correlation between twostocks.Meanwhile the finite length of time series available to estimate crosscorrelations will introduces “measurement noise”.Due to the reasons above,there ismuch uncertainty and a great deal of noise information in the empirical correlationmatrix.Therefore,the study of the properties of the correlation matrices is verymeaningful.The paper analyzes the statistic properties of correlation matrices for stockreturns first and finds that there is a great deal of noise information in empiricalcorrelation matrices.In order to distinguish noise information from true information,499stocks areselected from the Shanghai A-share assample and the daliy return of the499stocks insix years(2008.1-2014.1) are used to calculate the correlation matrix of theirreturn.And then the statistical difference between the empirical correlation matrix ofreturn and the random correlation matrix is tested.By calculating the eigenvalues ofcorrelation matrix,it is found that most eigenvalues fall into the predictive scope ofrandom matrix theory,and about6.46%of them are above the upper limit of thepredicted value,and there is a strong linear relationship between the largest eigenvalueand the correlation coefficient.Then the nature of the eigenvectors of the Correlationmatrix is discussed and it is found that the distribution of all the other eigenvectorelements is relatively close to the normal distribution except several eigenvectorswhich are corresponding with large eigenvalue and there is a strong relationshipbetween the vector element which is corresponding with the largest eigenvalue and the correlation coefficient.Finally,the application of random matrix theory in portfolio is discussed.And theempirical correlation matrix is filtered with the random matrix method.We use PG+and LCPB method to filter the noise information of mutual experience matrix basedon the random matrix theory.The conclusions of the dissertation are asfolloes:（1）In the A share market,there is much noise information in the correlationmatrix of stock returns and the largest eigenvalue reflects the main information of themarket.（2）The correlation coefficient of the A share market as a whole is relativelylarge,and the consistency of the volatility of the stock market as a whole is muchobvious:the prices rise and fall together,and the effectiveness of the market isrelatively poor and the ability to spread risk is relatively weak.（3）The optimizing of portfolio risk have achieved some results with PG+andLCPB method.LCPB method have a better effect. When N and Lchange,riskoptimization results relatively large differences.