Research on improvement of Chinese portfolio quality based on random matrix theory

Abstract

In this paper, from the perspective of prediction of future optimal portfolio, a method for evaluating investment portfolio quality is proposed. Based on the definition of portfolio quality, after making assumptions on the ‘true’ correlation matrix, we theoretically analyze adverse influence of correlation noise on portfolio quality. The method from random matrix theory (RMT) can be used for denoising the correlation matrix in such a way that only statistically relevant information is used. Theoretically portfolio quality can be improved by noise filtering of correlation matrix based on RMT which is empirically proved in many different stock markets. Despite the fact that much noise exists for correlation matrices of Chinese stock returns, whether better portfolios can be achieved from Chinese stock market by application of RMT for removing the noise of correlation matrices is seldom studied. We apply the method based on random matrix theory to cleaning correlation matrices of 102 Chinese stocks and on this basis construct portfolios. Comparison of portfolios with different number of eigenvalues kept in correlation matrices of two different estimation periods shows that the denoising technique from RMT is an effective method of improving portfolio quality in Chinese stock market by successfully cleaning the correlation matrix.