Research On The Correlation Of Financial Assets Under Different Risk Measures

According to the modern portfolio theory, investment in diversified financial assets is able to reduce the non-systemic risk based on the correlation between various financial assets. Therefore, mere accurate description of the relationship between different financial assets might yield an effective portfolio and achieve the purpose of risk diversification. The classic mean-variance model adopts the linear correlation coefficient to measure the correlation between assets is based on the assumption that financial assets follows the multivariate normal linear correlation. Nevertheless in reality, the financial assets yield sequence reveals a "sharp-peak-and-heavy-tail" and other partial characteristics and is not normally distributed, which greatly constrains the application of the linear correlation coefficient. As an indicator to measure the correlation, the DCCA correlation coefficient could effectively measure the nonlinear relationship between the two time series, which attracts extensive attention of theorists. However, this paper, through empirical studies, finds that both of the covariance matrixes, constructed by the linear correlation coefficient and DCCA correlation coefficient, are filled with plenty of "noise" information, therefore, neither of the two methods could accurately portray the correlation between the financial assets.This paper adopts the random matrix theory to identify and remove the "noise" information of the DCCA correlation coefficient matrix in order to build the true correlation matrix. Through the empirical research, we find both the sample in the data fitting and prediction-sample data prove that the investment portfolio based on the true correlation matrix is more efficient than the linear correlation coefficient and correlation coefficient DCCA, which further proves the validity of the proposed real correlation matrix.Finally, this paper introduces the concept of entropy to optimize variance metrics and constructs a mean-variance-entropy model. It finds that as for each parameter, the model can determine a unique optimal solution through empirical studies. It provides investors with a wider choice of efficient portfolios, which agrees more with the actual state of investors’ minds.