Nonlinear Factor Analysis Applied In Stock Return Models

Based on nonlinear factor analysis method,this paper uses multifactor model in quan-titative investment.In the article,factors are producted to choose the best stock portfo-lio.Different factor analysis method are compared by analysing their performances.The paper is totally divided into five parts to go on.In the first part,the definitions of quantitative investment and common quantitative stock-choosing models are brief introduced to be prepared for the main part of this paper-multifactor model.In the second part,the theory framework and method of the multifactor model are introduced in detail.Mathmetic formula of factor model and its risk formula are also discussed.In the third part,ordinary linear factor model theory are reviewed.The method of deriving the factor exposure is displayed.The factor rotating method and the factor scoring method are also in troduced.In the fourth part,Nonlinear factor analysis is performed.It will be detailedly dis-cussed that the difference of the two methods in idea and logic.The nonlinear factor analysis theory framework is comleted by proving orthogonal factor theorem and per-forming the definition of the contributing rate.Then the framework can be applied in the practical problems.In the last part,practical anaylsis based on the stock indexs is per-formed.Firstly,indexs are handled.Then linear and nonlinear method are applied sep-arately to derive the common factors.Cluster analysis is applied based on these factors.Then the portfolio with the best expectation return is used to take a backtest from 2014 to 2015.Finally,the effect of two methods are compared.