An Empirical Study Of The Improved Fama-French Four-Factor Model Under Uncertainty In Chinese Second-Board Market

With the development of Chinese financial market,capital investment in the stock market has gradually become one of the important investment methods for Chinese residents.The investment return rate of stocks(or stock portfolios),as one of the core indicators for people to consider stock investment,has been increasingly concerned and intensively studied in the financial theory and practice field.It is of great theoretical and practical significance to study the factors affecting the yield of stocks(or stock portfolios)and the formation mechanism.As is well known,for the mature securities market,the Fama-French three-factor model has been successfully applied to the fitting and prediction of the rate of return,and has achieved a series of fruitful and meaningful research results.For some emerging securities markets,researches on yield fitting and prediction based on Fama-French three-factor model are relatively lagging behind,and the breadth and depth of research are relatively limited.In particular,model construction analysis and empirical research involving factors other than three factors that affect the rate of return with a certain universality are still in the process of exploring research.On the other hand,for models such as the Fama-French regression model,people often assume that the residual distribution is certain for the convenience of research.For example,the residual is assumed to have a constant mean and a certain variance distribution! However,due to the complexity and uncertainty of financial markets,assumptions of certain distribution of the residual are often not confirmed by the market.In view of this,based on the complexity and uncertainty of financial markets,this paper considers and deeply studies the extended modeling and empirical analysis of the Fama-French three-factor model with uncertainty in the distribution of residual terms.That is to say,starting from the angles of the selection of the influence factors affecting the rate of return and the expansion of the Fama-French regression model,this paper constructs the improved Fama-French four-factor model under uncertainty by selecting a reasonable residual uncertainty distribution set and using the basic theory and method of nonlinear expectation.After which,this paper gives an empirical analysis in the Chinese Second-board market.Firstly,this paper studies the heterogeneous fluctuation characteristics of securities(combination)in the Second-board market,constructs a Fama-French four-factor model with heterogeneous volatility factor,and verifies its rationality and effectiveness in the Second-board market;Secondly,aiming at the uncertainty of the occurrence and change of various factors in the financial market,this paper conducts the Fama-French four-factor model under uncertainty.Then,combined with the nonlinear expectation theory,using the weighted expectation regression method,this paper gives the identification,consistency and asymptotic normality and related proofs of the Fama-French four-factor model under uncertainty;Finally,using the data of the Second-board market securities(or portfolio)to empirically analyze the model proposed in this paper,and the empirical results show that the improved Fama-French four-factor model with the weighted expectation method has better explanatory power.