The Distribution Characteristics Of Return Based On The Prospect Theory

The distribution of financial assets yield is one of the most high-profile information, and it has closely related with the vital interests of the investors. So, as one of the observable variables of financial market, the rate of return became the focus of many scholars. Fully understand the characteristics and laws of the distribution of yield can help investors make investment decisions reasonably, and won the best returns in the stock market. The currently research on the return distribution mainly following two aspects:one is based on the perspective of traditional finance theory, using the existing single statistical distribution or a mixture of multiple statistical distribution to described the characters about the yield distribution; another aspect is from the views of behavioral finance, consider some of psychological factors of investors as the reason of the character of yield distribution. Those methods though could depicted the part of the characteristics of yield distribution, but they couldn’t portrays the whole process about how the irrational factors of investors affect the yield distribution.Under the perspective of behavioral finance theory, and based on the prospect theory, this paper through introducing the probability weighting function to describe the influence of the yield distribution by investors’investment behaviors, and build a new subjective yield distribution model. On the basis of the new model, we adopt10representative stocks aggregative index around the world as samples to do empirical study on the characteristics of the distribution of return and the form of the probability weight function at the level of the market. Also try to loosen the assumptions of the subjective yield distribution model, by introducing the concept of value function, extend the new model reasonably, and use the same sample data to do the empirical research on the extension model, at last compare the result of new model and the extension one.The main conclusions of this paper are:from the point of view of investors’ irrational behavior, the subjective yield distribution model can give a reasonable interpretation of the formation process of the real market rate of return, and through the numerical analysis of the new model, the new subjective yield distribution model can reasonably explain the characteristics of real yield like "excess kurtosis and fat tail". The theoretical analysis and empirical results of the new model show that, whether the rate of return is positive or negative, investors will overestimate the probability of small probability events and underestimate the probability of high probability events, the complete probability weighting function is connected by two similar anti-S-shaped curves. The nonlinear least square regression results of the new model indicate that, the model with biparametric probability weighting function can characterize the features of the stock return distribution well, and under the condition of the positive and negative return, the parameter estimates of every weighting function are different. Through the comparison of adj-R2, this issue found that, the new subjective yield distribution model used the GE probability weighting function usually can depict the distribution characteristics of the real rate of return on the market well. This paper also empirical analysis the subjective yield distribution expansion model, found that the conclusions obtained by the extended model and the new model is roughly the same, from another angle, which also proved the rationality and stability of the new subjective yield distribution model.