许启发1,2，张世英1

（1．天津大学 管理学院，天津 300072；2．山东工商学院 统计学院，山东烟台 264005）

摘 要：为改进传统Beta系数测量系统风险的不足，反映系统风险的动态特征，讨论了四阶矩的资本资产定价模型（CAPM）并将小波分析引入到高阶矩CAPM模型研究中。利用小波多分辨分析的特点，给出了小波高阶中心矩和高阶混合中心矩的定义，基于此给出了多分辨系统风险测度Beta、Gamma、Theta的计算方法和多分辨CAPM。实证结果支持了多分辨系统风险假说和多分辨CAPM的成立，为构建动态投资组合分散金融风险的动态影响提供了经验性证据。

关键词：高阶矩；CAPM；小波变换；多分辨

Research on Moment CAPM based on Multiresolution Analysis of Wavelet

Xu Qi-fa1,2, Zhang Shi-ying1

(1.School of Management, Tianjin University, Tianjin 300072, China;

2.School of Statistics, Shandong Institute of Business & Technology, Yantai Shandong 264005, China;)

Abstract: To advance Betas for measuring systematic risk and reflect dynamic character of risk, four moments CAPM and wavelet analysis are discussed at the same time in the paper. Based on multiresolution analysis, the definition of wavelet high central moments and high mix central moments are put forward by us. Further more, methods for calculating Betas, Gammas and Thetas and multiresolution CAPM are established also. The empirical results sustain the hypothesis of multiresolution systematic risk and multiresolution CAPM, which provide experienced evidence for dynamic portfolio to disperse risk.

Key words: High Moments; CAPM; Wavelet Transform; Multiresolution

0 引言

Markowitz(1952)的均值-方差理论和Sharpe(1964)、Lintner(1965)提出并发展的资本资产定价模型（CAPM）构成了现代投资组合理论的基础。然而，他们的讨论都是集中在收益分布的前两阶矩（一阶矩：均值和二阶矩：方差）基础上进行，假定投资者不在乎高阶矩的存在。事实上，大量的实证研究表明金融资产收益的分布与正态分布相比，不仅是有偏的而且具有高峰特征。忽略这样的典型特征必将导致CAPM的实证表现较差，这促使众多学者将高阶矩引入到投资组合的研究中去（如Samuelson,1970; Ingersoll,1975; Kraus和Litzenberger,1976; Fang和Lai,1997; Dittmar,1999; Soosung和Stephen,1999; Rohan和Mukesh,2001等的工作）[1~3]，分别得到三阶矩的CAPM和四阶矩的CAPM，扩展了传统的二阶矩CAPM。