推广的高阶CAPM理论模型及其实证检验

Generalized High Order CAPM Model and Empirical Test

本文设投资者的效用函数可由n阶泰勒展开式近似表达,在此基础上构建的推广的高阶CAPM理论模型显示,当风险资产市场达到均衡点(不动点)时,投资的净效用与市场组合收益率的1阶矩、2阶矩、3阶矩、……、n阶矩有关。同一时刻不同风险资产的预期收益率差异由其收益率与市场组合收益率、市场组合收益率的2次方、……、市场组合收益率的(n-1)次方的协方差的差异共同决定。选择兼具期货和现货投资基础的沪深300指数、上证50指数、中证500指数进行实证检验,结果发现,投资者投资某一资产组合的效用受到资产组合收益率1阶矩的正向影响、2阶矩的负向影响、3阶矩的正向影响、4阶矩的负向影响,由此逐一验证了标准偏好的四个性质:不满足、风险厌恶、绝对风险厌恶递减(审慎)、绝对审慎递减(克制)。

In this paper,we assume that the utility function can be approximately expressed by n-order Taylor expansion.On this basis,the generalized higher-order CAPM model shows that when the risk asset market reaches the equilibrium point(fixed point),the net utility of investment is determined by the first moment,the second moment,the third moment,and so on,n-order moment of the market portfolio yield.At the same time,the difference of the expected return of different risk assets is determined by the difference of the covariance of its rate of return with the market portfolio yield,the second power of market portfolio yield,and so on,the(n-1)power of market portfolio return respectively.This paper selects Shanghai and Shenzhen 300 index,Shanghai Stock Exchange 50 index and China Securities 500 index as examples for empirical test.The results show that the most explanatory independent variables for the rise and fall of component stocks are the covariance between the rise and fall of constituent stocks and the rise and fall of the index,and the utility of investors'investment in a portfolio is positively affected by the first moment of portfolio return,negatively affected by the second moment of portfolio return,positively affected by the third moment of portfolio return,and negatively affected by the fourth moment of portfolio return.Thus,four properties of standard preference are verified one by one:dissatisfaction,risk aversion,diminishing absolute risk aversion(prudence)and diminishing absolute prudence(temperance).