Research On The Dependence And Risk Of Stock Returns Of Large Listed Firms In China With Factor Copula Models

With the further deepening of reform and opening-up and economic development,China's financial market gradually improved and got perfect,and dependencies of financial markets and financial assets' price synergistic effect were getting more and more significant.In the stock market which was an important part of financial markets,dependence of different markets,different plates,different industries and different stocks existed and volatility of a market or an asset often brought the volatility of other markets or assets leading to the risk spreaded,infection,enlarge to other markets or assets quickly.With the further development of Chinese stock market,The connection and dependence of the different listed companies are getting more and more stronger.The correlation of the different stocks is becoming more and more obvious.To analyze the correlation and investment risk of stock returns of large listed companies in our country is of great significance to the portfolio construction,market risk management and healthy development of the stock market.Based on the theory of copulas,this article used the one-factor copula model and the nested Frank copula model of structured factor copula models to analyze the sequences of returns of the Hushen 300 stocks in China and calculated Spearman rank correlation coefficient and tail-weighted measures of dependence between stock returns of the different industries as well as the VaR and ES of the portfolio to analyze the correlation and investment risk of stock returns of listed companies and the investment risk of the whole market of all the Hushen 300 stocks.This article choose the logarithmic return rate sequences of recent five years of Hushen 300 stocks,eliminating the stocks which were less than 5 years from IPO.We used the two stages maximum likelihood estimation method to estimate GARCH(1,1)-Gaussian model,GARCH(1,1)-t model respectively to fit each stock return sequences,and used the AIC information criterion to chose a better fitted model.Through the K-S test and Ljung-Box autocorrelation test of standard residual error sequences,we found that GARCH(1,1)-Gaussian model,GARCH(1,1)-t model could better fit the return sequences.And we used the one-factor copula model to fit the standard residual error sequences of stock returns and chose a better linking copula by AIC criterion.We found that the stocks of insurance,materials,real estate,energy,auto parts,food,banking,transportation,capital markets had a better fitting effect with one-factor BB1 copula model and the stocks of utilities,retail,media,durable clothing,software,hardware,pharmaceutical,biological,capital goods had a better fitting effect with one-factor Rotated Gumbel copula model of all 17 secondary industries.We obtained the parameters by maximum likelihood estimation and calculated Spearman rank correlation coefficient,tail-weighted measures of dependence to analyse the correlation and tail correlation respectively of the stock returns,and we found that most of the rank correlation coefficients of stock returns were in the range from 0.3 to 0.8 indicating the correlations were significant positive.The mean rank correlation coefficients of the stock returns of capital market,insurance,energy,transportation were greater than 0.5 indicating the whole correlation is stronger,and the correlation of stock returns of food,hardware were weaker.In terms of the tail correlation,we found that the tail correlation of the stock returns in all 17 industries by using the average of tail measures.Except the bank industry the upper tail correlation coefficients of industries were greater than lower tail correlation and the tail correlation coefficients of bank and capital market were greater than 0.6 indicating the stronger tail correlation.At last we used the monte carlo simulation technique with the one-factor model and the nested Frank copula model to calculate the VaR and ES of the equal weighed market portfolios and found that VaR and ES of retail,bank,hardware,capital market,medicine,insurance,etc.were greater in the confidence level of 99%,97.5% and 95%.We found the risk of retail industry was greatest because which has only two stocks and the dispersion is lower and the overall risk of the whole market was lowest which VaR and ES were significantly lower under the special confidence level due to the highest dispersion.