基于扭曲混合Copula函数的均值-ES模型的构建与应用

Construction and Application of Mean-ES Model Based on Distorted Mixed Copula Function

考虑到金融资产间的极端尾部相依结构对投资组合风险优化的影响,构建基于扭曲混合Copula函数的均值-ES模型,通过扭曲函数来刻画金融资产间的极端尾部特征,获得一定预期收益下的投资组合优化策略。首先,将均值-ES模型中用于刻画相依结构的协方差矩阵扩展为可以描述极端尾部相依结构的扭曲混合Copula函数,构建了基于扭曲混合Copula函数的均值-ES模型;其次,提出了基于该模型的ES估计算法;最后,通过数值模拟和实证研究说明了该模型用于刻画极端尾部相依结构特征并进行投资组合优化的效果。数值模拟的结果表明,基于扭曲混合Copula函数的均值-ES模型适用于具有极端尾部相依结构特征的数据集;利用该模型进行投资组合优化后收益明显提升,风险显著降低。实证研究的结果表明,该模型能显著提升最优投资组合的样本外策略表现,同时返回检验的结果也验证了使用该模型对投资组合优化进行风险预测的准确性。因此,基于扭曲混合Copula函数的均值-ES模型弥补了传统投资组合风险优化模型中忽略极端尾部风险的不足,推动了扭曲混合Copula函数在投资组合风险优化中的应用研究。

Considering the profound tail dependence structure among financial assets,which exerts a substantial impact on portfolio risk optimization,a mean-ES model is constructed based on distorted mixed copula functions to derive an investment portfolio optimization strategy with a specific expected return by capturing the extreme tail characteristics of financial assets through distortion functions.Firstly,extend the covariance matrix employed in the mean-ES model to depict the extreme tail dependence structure of the distorted mixed copula function,thereby constructing a mean-ES model based on it.Secondly,an ES estimation method is proposed based on this model.Finally,the efficacy of this model is demonstrated in investment portfolio optimization for datasets exhibiting extreme tail dependence structure through numerical simulation and empirical studies.The results from numerical simulation indicate that,the mean-ES model relying on distorted mixed copula function is suitable for datasets characterized by extreme tail dependence structure.Upon optimizing the investment portfolio using this model,both returns and risks are significantly improved.Empirical study results further confirm that the model substantially enhances out-of-sample performance of optimal investment portfolios and validate its accuracy in predicting risk during portfolio optimization.Consequently,mean-ES model based on distorted mixture copula function fills a crucial gap in traditional portfolio risk optimization models by addressing extreme tail risks and propels research into applying distorted mixture copula function in portfolio risk optimization.