基于Vine Copula的中国股市风格资产相依结构特征及组合风险测度研究

An Empirical Study on Dependency Structure and Risk Measure of Style Portfolio in Chinese Stock Market Based on Vine Copula Model

本文首先采用AR(1)-GJR(1,1)-SkT(v,λ)模型来刻画中国股市风格资产(大盘成长、大盘价值、中盘成长、中盘价值、小盘成长、小盘价值)的边缘分布,接着结合各边缘分布的残差系列,针对传统二元Copula函数面临的"维度诅咒"问题及多元Copula函数在刻画多变量联合分布时缺乏灵活性和精确性等局限,重点引入C-Vine Copula和D-Vine Copula函数来分析这六种风格资产之间的相依结构和联合分布,然后通过拟合效果比较选出最佳Vine Copula模型,运用蒙特卡洛模拟方法预测风格资产组合的VaR,最后通过Kupiec和Christoffersen返回检验方法测试其预测效果。研究结果表明:中国股市各风格资产之间的相依性存在结构性差异,最适合用D-Vine Copula模型来刻画各风格资产之间的相依结构。总体上来看,同类型的风格资产之间的相依程度比不同类型之间的相依程度要高;在同一类型的风格资产中,资产规模差距越大的风格资产之间的相依系数就越小。无条件的风格资产收益系列之间的相关性要显著大于有条件的风格资产收益系列之间的相关性;基于Student-t Copula、Clayton-Gumbel Copula具有尾部分布特征的Copula作为构建模块的D-Vine Copula模型能够有效地预测中国股市风格资产组合的VaR,有利于提升投资组合的风险管理能力。

In this paper, we firstly describe the marginal distribution of style assets in Chinese stock market based on AR（ 1 ） -GJR（ 1,1 ） -SkT（ u,λ ） model. The kind of style assets in this analysis include large-cap growth, large-cap value, median-cap growth, median-cap value, small cap growth and small-cap value. And then, we introduce C-Vine Copula and D-Vine Copula functions to analyze the inter-dependence of these style assets under the condition that traditional bivariate Copula faces the problem of ＂dimensional curse＂ and muhi- variate Copula functions lack precision and flexibility in characterizing the multivariate joint distribution. Finally, we make a comprehen- sive comparison between C-Vine Copula and D-Vine Copula model according to their fitting effect in order to select the best Vine Copula. The VaR of the style portfolio is calculated by Monte Carlo method and the VaR forecast efficiency of Vine Copula model is baektested through Kupiec and Christoffersen backtesting. The result shows that in Chinese stock market the inter-dependence of these style assets are of structural differences, which can be best depicted by D-Vine Copula model. On the whole, the dependence between the same kind of style assets is larger than that between different kinds of style assets. Among the same kind of style assets, the greater gap in size of style assets, the less dependent they are of each other. Unconditional dependence is larger than that of the conditional dependence among Vine Copula model. The D-Vine Copula, which passes the backtesting, can effectively predict VaR of style portfolio in Chinese stock market, and therefore is useful to the risk management.