偏度对资产定价影响的实证研究
Empirical Test of Skewness in Asset Pricing
石改香
指导教师姓名：陈灯塔副教授
专业名称：金融学
摘要
传统CAPM 对上海A 股市场的实证研究发现， β 不能很好地解释截面资的收益率差异；三因素模型的截面回归分析同时表明， P h 比较显著， P s 出现了混合的结果而且模型的拟合度也不够好。但是在SKS 的单因素检验中， P γ 显著，R2较高，说明它能解释大部分的截面资产收益率差异。
本文基于上面的实证分析一方面放松了CAPM 中资产收益率服从正态分布的假设，认为投资者具有非增的绝对风险，偏好正偏度的资产，对于负偏度的资产会要求较高的回报率；另一方面引入被CAPM 忽略的其它公司特征因素：规模、账值市值比。基于前述两方面，本文考察了在Fama 和French 三因素模型基础上加入偏度定价因子的四因素模型，并检验它在上海A 股市场的实证结果，即分析资产超额收益率与市场超额收益率、公司规模、账值市值比、偏度的关系。
为了分析偏度对资产定价的影响，本文依股票的协偏度构建了两个套期保值组合，并用其收益差作为度量偏度的定价因子（SKS）。文章采用沪市A 股1997年7 月至2009 年6 月的月交易数据对四因素模型进行实证检验。四因素模型的横截面回归结果显示：R2明显提高，而且SKS λ 也显著为正，这比市场超额收益率的单因素模型和Fama-French 三因素模型都有了改进。此外，从SKS 的构造方法可知，显著为正的SKS λ 意味着资产收益率与偏度有负向的线性关系：偏度越小，资产收益率越高。对于负偏度的资产，偏度降低导致投资者所面临的风险增加，因此他们将要求较高的回报率，即偏度的风险溢价是负的。
通过模型的对比分析得出，在Fama-French 三因素模型基础上引入偏度定价因子的四因素模型能更好地解释截面资产的收益率差异，偏度也表现出了统计上的显著性。而且，四因素模型的结论并不因加权方式的不同而有所变化，因此，偏度对资产定价起着重要的作用，四因素模型能更充分地解释资产收益变化。
关键词：协偏度；偏度因子；因素模型
Abstract
Empirical test of Traditional CAPM in Shanghai A-share market demonstratesβ can not account for differences in cross-section return; Fama-French three-factor model also shows that P h is significant, P s has mixed results and fitting degree is not good enough. However, the results in single factor cross-section model of SKS indicate that SKS has significant power in explaining differences for cross-section return.
Based on the above empirical analysis, on the one hand, we relax the assumption that rates of return of assets follow a normal distribution in CAPM. This paper considers that investors have a non-increasing absolute risk aversion and prefer to positive skewness. Therefore, they will require higher return for assets with negative skewness. On the other hand, we introduce other factors that are overlooked by CAPM, such as size, book-to-market ratio. In view of the above two, this paper establishes four-factor model based on Fama-French three-factor model and pricing
factor SKS, then test it in the Shanghai A share market.
In order to analyze the impact of skewness on asset pricing, this paper constructs SKS factor. Cross-sectional regression analysis of four factors model shows R2 markedly increases and SKS λ is significantly positive, which has been improved compared to single factor model of market excess return and Fama-French three-factor model. According to structure of SKS, we know significantly positive estimator means return on assets has a negative linear relationship with skewness: the more negative skewness, the higher return. If the assets have negative skewness, then investors will face more risk, therefore, they will also require higher return.
Through the comparative analysis of FF model and four-factor model, we find the latter can better explain the difference in cross-section rerun. In addition, the four-factor model basically has the same conclusion whether total market value-weighted or circulating market value-weighted, which further demonstrates the robustness of the model.
Key words：Coskewness; SKS; Factor Model
