Time-varying Capital Asset Pricing Model

As the hinge theory of modern financial theory.The financial asset pricing theory has always been studied,since Arrow et al proposed the random discount model.From the first which was limited to theoretical research to the Sharp created the classic CAPM model.There is a relationship between the yield rate of a security and the systemic market risk of the market.The existence of this relationship makes it possible to determine the yield rate of the security using the yield rate of the market portfolio and the relationship between the risk of the security and the market risk.The classical capital asset pricing model is a model with the only one factor.After this,.Fama created the efficient market hypothesis.It is that in the effective capital market the price of the financial asset is all of the related market information's completely accurate response,therefore there are many classical capital asset pricing model is used to test the actual financial market is effective research,the results of the study,however,is not in conformity with the effective financial market expectations,there are many financial abnormal phenomena.In order to rationally explain these financial unusual phenomenon,behavioral finance tries to make a rational explanation for the financial anomalies by studying the psychology of investors from the point of view of psychological theories.However,Fama et al.tried to construct a more practical and effective capital asset pricing model by creating a three-factor model,that is,by increasing some risk factors,and the coefficient of risk factors in this model was the beta coefficient.And shall be presumed beta coefficient is a constant in the model,and then there are also some scholars who do research on the beta coefficients' feature of time-varying.Most of the methods used are to characterize the time-varying model of the beta coefficient as a variable of time,or to assume that the relationship between the instrumental variables related to the time-varying coefficient and the beta coefficient is linear.Therefore,parametric or non-parametric methods were used to characterize the time-varying in the past,and there were few studies considering macroscopic factors.In this paper,A conditional Fama-French three-factor empirical research of China's A-share market is finished.It mainly use the single-index semi-parametric estimation method,which takes macro information into consideration.The semiparametric method avoids the risk of error setting in parametric models and the curse of dimension in nonparametric estimation,which make the model more economical.At the same time,considering the possibility that not all the macro variables used in this paper have the ability to influence the beta coefficient,this paper chooses the SCAD method to compress and screen the macro variables,trying to make the model more concise.At the same time,based on the results of Liu and Stambaugh's research on the Chinese market value factor,the model is more proper for the Chinese market to use the E/P ratio as the criterion for dividing value groups.The conditional three-factor model which is using a single index semiparametric model is contrast to Ferson and Harvey's,which also consider the use of non-time instrumental variables as the linear model to describe the time variation of the beta coefficient.Finally,through empirical analysis,it is found that the classical capital asset pricing model has a certain interpretation degree for the Chinese stock market,but through the analysis of the significance of 25 portfolios' pricing errors,it is considered that this model does not fully capture the risk factors.And unconditional three factor model of interpretation degree contrast to classical capital asset pricing model has a larger increase,at the same time in the 25 portfolios' coefficients of scale factors and value factors are significant,seconhand shows that the stock market does exist in China scale effect and value effect,but for the price of the model error analysis can be found that this model is still somewhat less than on the risk characterization.By comparing the conditional three-factor model created by Ferson and Harvey,it can be found that the explanatory power of this model is improved to some extent compared with that of the unconditional three-factor model.When using a single index semiparametric model conditions of three factor model in this paper,the four macro variables are used by the variable selection,at the same time,the explanatory power of the model in comparison with the explanatory power of three factor model with linear conditions is further improved.Besides it further passed the test proved that using single index semiparametric model depicting the degeneration in contrast to the linear model is more matchable for the real market.In order to further analyze the beta coefficient of our country's market,this paper choose the single index semiparametric model used in the beta coefficient of different industry analysis,finally found four macroeconomic variables by the same choice,In terms of the applicability of the single index semiparametric model in all sectors of China's stock market,it is also superior to the linear assumption of timevarying capital asset pricing model.