基于R-Vine Copula与均值–熵的金融市场投资组合优化

Portfolio Optimization in Financial Markets Based on R-Vine Copulas and a Mean-Entropy Framework

摘要: 为构建一个面向金融资产收益非正态性与高维复杂相依结构的投资组合优化框架，本文以全球七大主要股票市场指数为样本，首先采用ARMA-APARCH-sstd模型刻画各资产收益的边缘分布并获得条件均值与条件波动的一期预测，其次引入R-vine Copula对多资产间非线性、非对称及尾部相依结构进行建模。基于估计得到的联合分布，通过蒙特卡洛模拟生成未来收益情景，并在熵风险度量下求解静态最优权重；进一步结合动态边缘预测开展蒙特卡洛VaR回测，并构造压力情景以检验组合稳健性。实证结果显示：R-vine Copula能有效捕捉混合型尾部相关结构；与CVaR相比，基于均值–熵风险的组合在风险控制、回撤与尾部覆盖率方面表现稳健，尤其在极端情形下具有更强的风险刻画能力。

Abstract: To develop a portfolio optimization framework that accommodates non-normal asset returns and complex dependence structures in high dimensions, this study uses seven major global stock market indices as the sample. First, the ARMA-APARCH-skewed sstd model is employed to characterize the marginal distributions of individual returns and to generate one-step-ahead forecasts of conditional means and conditional volatilities. Next, an R-vine copula is introduced to model nonlinear, asymmetric, and tail dependence among multiple assets. Based on the estimated joint distribution, future return scenarios are generated via Monte Carlo simulation, and static optimal portfolio weights are obtained under an entropy-based risk measure. Furthermore, dynamic marginal forecasts are incorporated to conduct Monte Carlo VaR backtesting, and stress scenarios featuring “mean shifts downward” and “volatility amplification” are constructed to assess portfolio robustness. Empirical results indicate that the R-vine copula effectively captures mixed tail-dependence patterns. Compared with CVaR, portfolios optimized under the mean-entropic risk criterion demonstrate robust performance in risk control, drawdown mitigation, and tail coverage, exhibiting particularly strong capability in characterizing risk under extreme market conditions.