Analysis of Portfolio Efficient Frontier Based on Copula-APD-GARCH Model

According to the risk measures ES(Expected Shortfall),Markowitz's portfolio model which is based on mean and variance is expanded and the problem of portfolio optimization is researched in this paper.The multivariate copula function can capture the dependency structure of multi-dimensional random variables and APD describes the marginal distribution and the GARCH model describes the volatility,hence the Copula-APD-GARCH model is established to construct the joint distribution of financial assets.With this model,the efficient frontier based on mean-ES is studied and compared under different dependency structures such as Gauss copula,t-copula and Clayton copula.The empirical result indicates that the normal copula can lead to a significant overestimation of portfolio risk in efficient portfolio set;the risk value based on t-copula is minimum when the expected return is smaller and the efficient frontier based on Clayton copula is best accompanied with the increase of expected return.