The Empirical Analysis Of A-share Market On The Collinearity Problem Of Multi-factor Stock Selection Model

The multi-factor selection model has become the most important strategy for quantifying equity investment in A-shares.The factor-colinearity problem has a fundamental and important impact on the effectiveness and robustness of the strategy.If the problem of factor collinearity can be reasonably solved,it will help improve the robustness of the multi-factor stock selection model and better control the risk exposure of the portfolio.This article focuses on a variety of collinear processing methods,using a number of classic factors,conducted an empirical analysis in the A-share market,in order to explore a practical method that can reasonably solve factor collinearity.This paper first introduces the related background of multi-factor model and the research status of multicollinearity problem,and expounds the influence of multicollinearity problem on multi-factor model.In terms of theoretical models,this article focuses on the basic principles and ideas of principal component analy-sis,kernel principal component analysis,Schmidt orthogonal,regular orthogonal,symmetric orthogonal,and stepwise regression orthogonal methods including the related proofs and derivation.At the same time,this paper proves theequiva-lence of Schmidt s orthogonalization method and stepwise regression orthogonal method.At the stage of empirical analysis,the paper examines and analyzes the problem of collinearity between the selected factors,and the result shows that there is a certain degree of collinearity between the factors.This paper first uses the tradi-tional data dimension reduction algorithm principal component analysis method to process the original factor data and analyzes each principal component as a new factor after the conversion.The results show that the principal component analysis can solve the factor collinearity problem,but there is no way to maintain the correspondence between the main components and the original factor,and the actual backtesting effect is poor.In terms of nuclear principal component analy-sis,compared with the principal component method,the effect of nuclear principal component analysis has been improved,and there is room for optimization,but it is still difficult to clearly defeat the market.Then the paper adopts the regu-larization orthogonalization method which is similar to the principal component principle.The results show that the regularization orthogonalization method is slightly better than the principal component analysis,but it still underperforms the entire market equal weighted portfolio.Further,the Schmidt orthogonaliza-tion method is used to orthogonalize the original factors.The results show that the Schmidt orthogonalization method can maintain the corresponding relation-ship before and after factor transformation to a certain extent,but depends on the orthogonality of the factors.The results of historical backtesting show that Schmidt's orthogonalization method can solve the problem of repeated exposure of factors caused by factor collinearity to a certain extent,and has a good application effect.Finally,the symmetry orthogonalization method is used for further analy-sis.The results show that before and after factor symmetry orthogonal processing can maintain a good correspondence,and does not depend on the orthogonal order,which is conducive to the essence of the maintenance factor,The results of history backtesting show that the symmetric orthogonal multifactorial portfolio achieves good historical backtesting performance after symmetrical orthogonal processing.The results of the empirical analysis show that Schmidt orthogonal and sym-metric orthogonal methods have good effects on the processing factor collinear problem,but the symmetry orthogonal is not dependent on the orthogonal order,and it can better maintain the essential meaning of the factor,and the historical back test also shows the more stable performance of the phase.Principal com-ponent analysis and kernel principal component analysis and regular orthogonal algorithm are not good enough.On the one hand,it is impossible to maintain the corresponding relationship before and after processing.On the other hand,the actual retest analysis is not effective.Finally,based on the symmetric orthog-onal method,the multi-factor selection model was constructed using the GBDT algorithm.The results show that the performance of the symmetric orthogonal portfolio under each training cycle is superior to the portfolio without symmetri-cal orthogonality.On the basis of symmetry orthogonality,this paper separately trains the GBDT model under shorter and longer training cycles,and then pro-ceeds to equalize the yield prediction results of both of them and construct GBDT long-short equilibrium stock selection model,the model has more stable perfor-mance and stronger market adaptability.Therefore,the content and methods studied in this paper have certain positive significance for improving the multi-factor selection model and improving its performance robustness.