Brewing Index Tracking Analysis Based On Mean And Quantile Reversion

With the development of the securities market,more investors and listed companies are turning their attention to index tracking.However,the return of the stock market cannot be achieved through active investment,so how to build a tracking portfolio is very practical for investors and fund companies.In this thesis,we firstly organize the theories related to index tracking,followed by the basic theories of mean regression and quantile regression;then we introduce the traditional subset selection method and canonical method based on these two regressions,respectively,and set index tracking evaluation index.In this thesis,the brewery index and 37 constituent stocks of the Shanghai-Shenzhen Jing Minute Line from July 1,2022 to October 25,2022 are selected as samples from the Golden Point Money Terminal of Southwest Securities,and their 5-minute line closing prices are taken as the data set,which is divided into training and testing sets according to the ratio of 8:2.Then,based on two different stock selection methods:optimal stock selection and maximum correlation coefficient selection,mean regression models and quantile regression models are built for tracking the brewery index and their index tracking effects are evaluated to obtain the model with better tracking effects.Under the mean regression model,the least squares regression model,stepwise regression model,Lasso regression model,elasticity constraint estimation regression model,and non-negative constraint estimation regression model are established.The results show that the explanatory variables Hainan Yedao(4),Huizhuan Beer(13),Jinfeng Liquor(14),Weilong(22),~*ST Xifa(25),and Tianyoude Liquor(37)are insignificant in the least squares regression model;the stepwise regression models based on the AIC criterion informativeness and BIC criterion informativeness retain 33 variables and 28 variables,respectively;Based on Lasso,37 variables were retained and no variables were excluded;based on elasticity constraint estimation,the best λ value of 0.008 was obtained,and 12 variables were retained for both elasticity constraint estimation and non-negative constraint estimation.The index tracking metrics of these models are calculated: tracking error,mean error sum of squares.The results show that the stepwise regression index tracking model based on the BIC criterion is the best for the brewery index,when 28 constituents are retained;secondly,in the case of the least retained variables,i.e.,the elasticity-constrained estimation and the non-negative-constrained estimation,both of which retain only 12 constituents,the index tracking models in both cases also track the brewery index better.Therefore,for comparison purposes,the mean reversion index tracking models with 12 and 28 constituents were chosen under the maximum correlation coefficient selection method,and the corresponding index tracking indicators were calculated.Under the quantile regression model,stepwise regression models,Lasso quantile regression models,and SCAD quantile regression models were established at the five quantile points of 0.1,0.25,0.5,0.75,and 0.9.The results showed that the number of variables retained in the stepwise regressions based on the AIC and BIC criteria at the five quartiles of 0.1,0.25,0.5,0.75,and 0.9 were the same,34,35,32,33,and 33,respectively;the number of variables retained in the Lasso quantile regressions at the five quartiles was the same,14;the number of variables retained in the SCAD quantile regressions at the five quartiles was 35,36,and 36,respectively.The number of variables retained in the SCAD quantile regression at the five quantile points are 35,36,34,36,37.Calculating the index tracking indicators for all models: tracking error,mean error sum of squares,we obtain: the index tracking effect of the quantile regression model established by the SCAD quantile regression at the quantile point of 0.5 is better,and at this time,34 constituent stocks are retained.Thus,under the maximum correlation coefficient stock selection method,the quantile regression model is established with 34 constituent stocks and the corresponding index tracking index is calculated.Finally,the index tracking indexes of all models were analyzed together,and the results showed that:(1)the tracking error and the mean error sum of squares of the brewery index tracking model established by the optimal stock selection method were smaller than those of the brewery index tracking model established by the maximum correlation coefficient selection method under both mean regression and quantile regression;(2)the stepwise regression brewery index tracking model established based on the BIC criterion worked best under mean regression;(3)Under quantile regression,the brewing index tracking model obtained by SCAD at the 0.5 quantile is the best.