VaR风险度量下的β系数:估计方法和实证研究

Beta coefficient based on value-at-risk:estimation methods and empirical analysis

传统资本资产定价模型得出的β系数受到正态分布假设的约束。为了更好地反映金融现实,对VaR-β系数的估计问题(VaR-β系数是一种在Value-at-Risk风险度量下的β系数,可以在各种概率分布假设下应用)进行了研究。在一些常用VaR估计方法的基础上,发展了三种VaR-β系数估计方法:核密度方法、高阶矩方法和Copula方法,并得出了相应的解析表达式。最后,使用香港证券市场中的数据对核密度方法的应用进行了实证研究,并论证了置信度水平可以做为反映投资者情绪的一个指标。

In the traditional Capital Asset Pricing Model （CAPM）, theβ coefficient is estimated with an implicit normality assumption. To reduce the gap to the reality, this paper studies the issue of estimating VaR-β, an alternative type ofβ coefficient based on Value-at-Risk （VaR） with a distribution-free specification. Based on some common VaR calculation models, we propose three different estimation methods for VaR- β： kernel density method, higher moments method and copula method. And we also derive analytical expressions for the VaR-βs under these estimation methods. Finally, an empirical analysis of kernel density method is given for Hong Kong stock market, in which we demonstrate that the confidence level can be taken as a measurement of investors＇ sentiment.