Copula函数在多因子模型系数估计中的应用

Application of Copula functions in the factor coefficient estimation

主要研究用多因子模型刻画金融资产收益率时,因子载荷系数的合理估计问题.以因子系数的金融意义为出发点,并结合Copula的相关理论,提出了一种新的因子系数估计方法.新方法用Copula函数描述各个因子与金融资产收益所服从的联合分布;从因子系数的正负及其发生的概率,金融资产收益率随因子波动的大小两方面来估计因子系数的值.在此基础上,对因子系数新的估计公式做了进一步调整,强调了尾部相关性对因子系数取值的影响.基于中国证券市场的交易数据,对不同估计方法进行了实证研究.通过分别计算统计量R-square的值,随机误差项的均方偏差,尾部均方偏差以及投资组合的在险价值与条件在险价值等方法,实际论证了文中所提新的因子系数估计的改进方法优于因子系数估计的新的Copula方法,而后者又明显好于传统的线性回归方法.

This paper studied the reasonable estimation of factor coefficients when the multi-factor model is used to describe the return rates of financial assets. New methods to estimate factor coefficients were proposed by examining financial implication of factor coefficients and utilizing the Copula theory. Through modeling the joint distribution of each factor and the return rate of the financial asset with the Archimedean Copula function, the new method estimated factor coefficients in two steps： the sign of the coefficient and its occurring probability were first determined by the Kendall＇s tau; the fluctuation scale of the factor coefficient was then calculated as the ratio of the variation of the financial asset＇s return rate with respect to the change of each factor. Moreover, the above method was further improved by emphasizing the influence of distribution tails on the factor coefficient, which was done by introducing the tail correlation. Empirical tests were carried out with trading data from Chinese stock markets. The practicality and advantage of our new methods were demonstrated by calculating the R-square value, the mean-square deviation of the random error term, and the corresponding tail mean-square deviation of the determined multi-factor models with different factor coefficient estimation methods, as well as their application to the value-at-risk and conditional value-at-risk calculations of the portfolio. Empirical results show that the improved new method is the best, while the new method is obviously better than the traditional linear regression method.