Probability Weighting Function and Distribution of Stock Return
Zhang Ting-tin · Systems Engineering · 2013
Based on the cumulative prospect theory,this paper introduces the cumulative probability weighting function to describe the influence of subjective factors upon the objective distribution of returns,and establishes a new model of the distribution of subjective return.On the basis of the new model,we take the aggregative index of 10 typical stocks around the world as samples to empirically study the characteristics of the distribution of returns and the form of the probability weight function at the level of the market.The results show that:(1) the new model can generally depict the characteristics of the probability density curve of return,such as excess kurtosis and fat tail;(2) the whole probability weight function is connected by tow of the similar curve which presented as the shape of inverse-S whether the returns are positive or negative.The nonlinear least square regression results indicate that,the model with biparametric probability weighting function can characterize the features of the stock return distribution well,and the function which given by Goldstein and Einhorn can do the job better,and the probability weighting functions are different under the condition of positive or negative returns.