基于Copula-APD-GARCH模型的投资组合有效前沿分析

根据ES风险度量方法,拓展了马克维茨均值-方差资产组合模型,研究均值-ES准则下的资产组合问题.用APD-GARCH模型刻画风险资产收益率序列,以多元Copula函数描述风险资产间的相关结构信息,构造灵活的Copula-APDG-ARCH模型.利用该模型,借助Monte Carlo模拟,分别研究相关结构是多元正态Copula函数、多元t-Copula函数和多元Clayton Copula函数的风险资产组合的均值一ES有效前沿,并进行比较.实证研究表明,在有效组合范围内,正态Copula函数明显高估了资产的组合风险;当期望收益较小时,t-Copula函数对应的风险值最小,但随着期望收益的增加,多元Clayton Copula函数时应的有效前沿表现最好.

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.