The CAPM Study Based On Copula Entropy

Investment portfolio is taken at the foremost position in the financial research and the capital asset pricing model is considered as one of the modern financial core contents. The CAPM keeps developing from the moment it born through many years. My dissertation includes three issues.First of all, the dissertation proposes the method which builds the market factor with joint distribution of the local stock index before we choose the investment field. The method solves the problem and we can build a market factor completely. We define the copula entropy which is considered as the measure index of correlation and the risk within the market. Comparing copula entropy with correlation coefficient and the mutual information, we can find that copula entropy is reasonable and has many advantages about measuring dependence. The copula entropy is used as the correlation index to measure the time-varying characteristics of the correlation and the risk within the market. In economic theory analyses, we also find out that the copula entropy is very significant.Second, we build the joint entropy optimization model to solve the fund investment portfolio, in which we propose two steps approach:constituent stocks analysis and fund portfolio analysis. There are two methods to solve the different joint entropy optimization models named dual joint entropy approach and copula entropy approach. We extend Jaynes's maximization entropy principle. The dual theory is taken to get the solution of both the maximum joint entropy model and the minimum relative joint entropy model. The ideas of the copula entropy let us to transfer the joint entropy model to copula entropy model in entropy optimization problem. The copula entropy approach is proposed. The application to the fund portfolio is broadened. The packaged financial product such as the fund investment is still the new financial product and the history data are probably limited in China. The method we propose can build the possible strategy base on the constituent stocks of the fund.The last part of the dissertation, we propose the Bayesian copula estimation to get the posterior distribution of the parameters of the system risk beta and the investment horizon lambada. We find out the data are correlated each other strongly and choose Seemingly Unrelated Regressions method to get the result of the parameter estimation. The Bayesian copula estimation is chosen to consider the correlation of the data instead of regular Bayesian estimation. The reason we chose SUR is concerning the affect of the correlation of residuals and the Bayesian copula estimation using copula function as the likelihood function is proposed with the similar argument. The experiment analyzes the interaction of the system risk and the investment horizon in six different industries.