Research On High-dimensional Investment Portfolio Measurement Based On Time-Varying Factor Copula

The global financial crisis has made it clear that financial risk management plays a pivotal role in the national economic system,even in the national security.Whether it is an individual or a country,it faces financial risks in participating in financial management or investment activities.How to measure risk accurately has always been a hot issue of research for scholars.Due to the complexity of financial data,when modeling the correlation of assets in the portfolio,most scholars choose the Copula function,it makes the classic Copula functions or their derived types widely used in financial portfolios.But for portfolios with dimensions above 20,classic Copula cannot accurately model the dependencies between assets.To solve this problem,we choose the factor Copula model to describe the complex inter-dependence between high-dimensional assets.Through numerical simulation,it is found that the factor Copula can simultaneously describe the upper-tail dependence and the lower-tail dependence of variables,and also characterizes the asymmetric dependence.Based on the factor Copula,we use the GAS model to introduce time-varying into the factor loadings,and then three dependent types of equal-dependence,block-dependence and heterogeneous dependence are established to describe the joint distribution between assets.For the case of a large number of parameters in heterogeneous dependence,we uses two-stage estimation,the GMM is used to estimate some parameters and then introduced them into the maximum likelihood estimation.The numerical simulation shows that the estimation method selected in this paper has better estimation effect.In empirical research part,we select the investment portfolio of 34 stocks in 8 industries included in CSI 100,the AR(1)-GJR-GARCH(1,1)-t model is used to simulate the marginal distribution of stock returns.The results show that each stock has significant spike tail and leverage effect.By introducing the normalized residual sequence fitted by the marginal wave model into the time-varying factor Copula model,we can get the conclusion as follow.The results of the time-varying factor Copula model under the equip-dependence structure show that the interdependence structure between the assets selected in this paper is also changing along with the changes in the financial market.In the period when the stock market volatility is relatively frequent,the dependence between assets is relatively large.The results of the time-varying factor Copula model under the block-dependent structure show that the financial industry is greatly affected by the economic environment,and the connection with other industries is relatively close.As an emerging industry in the entire economic system,the influence of electronic equipment industry has not changed much in the entire economic system,and it is not affected by other industries.It shows excellent anti-risk ability and investment value.By comparing the model's likelihood function value,AIC and BIC,it is found that the time-varying factor Copula in heterogeneous dependence can better model the joint distribution between assets.We use this model to predict the VaR value and ES value of the portfolio income during the observation period.Both the prediction and the test results indicate that the heterogeneous dependent time-varying factor Copula can predict the risk of the portfolio well for a certain period of time.