Screeing Risk Factor Combinations By Marginal Likelihood Function Method Under Bayesian Framework

Factor investing has been a hot topic in the investment community in recent years.Since the capital asset pricing model was proposed,many well-known factor models and anomalous factors have been proposed.Domestic research on multi-factor models has also been hot,but most of the research is an empirical test of foreign factor models in the Chinese market.Since the concept of "factor zoo" was proposed,many scholars have turned their attention to the comparison of factor models.However,the comparison of multi-factor models is limited to the comparison between famous multi-factor models,and does not more comprehensively examine the possible combinations of risk factors.Under the theoretical support of Bayesian framework and stochastic discount factor(SDF),this paper uses the method of comparing the marginal likelihood log value to screen out the risk factors that can enter the SDF from the given factor set,so as to form a multi-factor model of asset pricing.The limiting condition under the SDF framework is non-nested,i.e.the optimal combination of risk factors is not generated by omitting or including variables from the full model.We calculate the logarithmic marginal likelihood function by setting the prior distribution,of factor returns as the t-distribution and the covariance prior distribution of factor returns as the inverse-Wishart distribution.In the sampling process,this paper compares the results of multiple sets of different hyperparameters to investigate the robustness of the likelihood function comparison method and find a better prior hypothesis.The hyperparameter calculation scheme used by the author is larger than the marginal likelihood logarithm value when the hyperparameter value is fixed,that is,the scheme can better fit the actual data.Initially,this paper selects nine traditional common factors {MKT,BAB,SMB,HML,RMW,ROE,CMA,MOM,LIQ} to construct a factor set,and uses the above method to traverse the possible risk factor combinations in the set,and compares the((29-2)× 12=)6120 sets of marginal likelihood logarithmic values to screen the risk factor combinations with the best fitting of the data.In order to construct a more comprehensive set of factors in the category of factors on the basis of traditional factors,three factors {ESG,RSI,LB}are added in this paper,representing governance factors,sentiment factors and technical factors,respectively.Traversing the possible risk factors in the set again,we compared the((212-2)× 6=)24564 sets of marginal likelihood logarithms.This paper draws the following main conclusions:first,under the set of 9 factors,the highest marginal likelihood model we screen out is a multi-factor model with 4 factors set at 64 degrees of freedom;Under the twelve factor set,the highest marginal likelihood model screened out is a multi-factor model with 4 factors set at 4 degrees of freedom.Second,other multi-factor model test methods are used to verify the significant advantages of the optimal risk factor combination selected by the marginal likelihood comparison method.Third,with the advantage of traversing all factor combinations,the explanatory strength of the three traditional factor models in the A-share market is compared.It is found that the Carhart four-factor model performs better than the FF three-factor model,and the first two are better than the FF five-factor model.