基于动态调整的Copula-非线性分位数回归资产组合优化

Portfolio Optimization Based on Dynamic AdjustmentCopula-Nonlinear Quantile Regression

为优化资产组合方案,考虑单资产分布的非对称性、异方差性、尖峰厚尾性等特征,资产之间的时变非线性相关性,建立了Copula-非线性分位数回归模型。本文的创新与特色,一是通过构建期望超额收益率与考虑动态损失厌恶效应的VaR比率函数,确定了目标函数的表达式,改变了使用超额收益率标准差度量风险,而实证研究中更关注资产的损失风险而非全部风险,未考虑投资者对于收益与损失非对称偏好的不足;二是通过建立基于支持向量机的非线性分位数回归模型,确定了边缘分布函数表达式,解决了普通模型无法处理非对称、非线性,依赖于分布假设的不足;三是通过构建混合Copula函数,确保能够有效捕捉金融市场中的尾部相关、非对称性,完善了刻画资产之间相关关系的模式;四是通过建立风险非线性叠加的资产总风险评价模型,确定了资产组合总风险的表达式,弥补了现有风险评价模型未考虑资产间的相关性的不足。实证结果表明,本文建立的模型预测性能高于其它模型,该模型有更高的VaR比率值,在单位风险下能够获得更高的资产组合效果。

In order to optimize the asset portfolio scheme,considering the characteristics of single asset distribution such as asymmetry,heteroscedasticity,leptokurtosis and fat-tail,and the time-varying nonlinear correlation between assets,the Copula-nonlinear quantile regression model is established.The contributions are as follows.Firstly,the objective function is established by constructing the VaR ratio function that considers the return rate and the effect of dynamic loss aversion,which changes the traditional models measuring the risk using the standard deviation of the excess return,while the empirical research pays more attention to the loss of assets rather than all risks,and failure to consider the lack of investor asymmetry in preferences for gains and losses.Secondly,the quantile regression model based on the support vector machine model is established,and expression of the edge distribution function is obtained,which solves the problem with which that the traditional model can’t deal well with asymmetry and nonlinearity and depends on the distribution hypothesis.Thirdly,a mixture Copula function is established,which can effectively capture the tail correlation and asymmetry in the financial market.Fourthly,an overall risk assessment model based on the non-linear superposition of assets risk is established,which makes up for the existing risk assessment model without considering the correlation between assets,and the total risk of the assets is the simple linear addition of the individual asset.Through comparative analysis,it is found that the prediction performance of the model established in this paper is higher than that of other models.The model can have higher VaR ratio value.