Research On Stock Enhanced Index Based On Robust Regression And Return-Risk Model

In recent years,enhanced indexing funds have developed rapidly.The so-called enhanced index refers to the use of a partial replication strategy to track the trend of the benchmark index while obtaining excess returns that exceed the benchmark index.Enhanced indexing funds have the dual advantages of passive investment and active management,with outstanding allocation value.In the long run,the yield of index funds is actually higher than that of most active funds.Therefore,this article aims to build an enhanced index that outperforms the benchmark index and assist in the development of enhanced indexing funds and related financial derivatives.Unlike index tracking investment strategies,enhanced index investment strategies have only recently been proposed as a new research area.The core of the former is to control tracking error,while the core of the latter is to obtain an absolute return that deviates from the index.This article is based on a return-risk model,in which the return model is used to calculate the expected return on stocks,and the risk model calculates the expected risk of the portfolio,using an optimization model to solve the portfolio weight allocation,including linear programming and quadratic programming.In the return model,when calculating the historical return rate series of factors,this article abandons the commonly used multiple linear regression,because the actual data is difficult to meet the basic assumptions of the multiple linear regression model,and innovatively uses a linear regression method under model uncertainty for estimation,which can achieve robust estimation of parameters,so it is referred to as robust regression for short;In the risk model,the risk prediction for Nstocks is transformed into a risk prediction for K factors,greatly reducing the prediction workload.When calculating the covariance matrix of factors based on the historical series of factor returns,the half life exponential weighting method is used instead of the equal weight method,making recent data have a higher weight,thereby quickly capturing changes in volatility.This article selects CSI 300 constituent stocks from 2014-2022 as the research sample,uses 2014-2019 data as the data within the sample,conducts effective factor screening,and uses 2020-2022 data as the data outside the sample for model solving and performance backtesting.In terms of factor selection,this article has identified 73 factors and their specific calculation methods based on the comprehensive analysis of factor databases of domestic and foreign securities companies and Barra style factors.Based on Tushare’s original data,it has conducted factor generation,data preprocessing,single factor testing,factor screening,factor collinearity processing,and other operations.After obtaining the expected returns of stocks and the expected risks of portfolios,first,with the goal of maximizing returns and the constraints of market capitalization neutrality and industry neutrality,the weights of portfolio positions are solved through linear programming methods,and performance backtesting is conducted.The initial enhanced index obtained performs well;Then,in order to further control risk,a risk neutral constraint is added to the linear programming algorithm,and it is found that this strategy can effectively reduce losses in the bear market stage;Finally,by adding portfolio expected risk to the objective function and solving the portfolio weight using a quadratic programming method that maximizes the difference between expected returns and risk,it is found that this strategy can significantly improve excess returns during the bull market stage.Under the above three sets of enhanced index investment strategies,the effect of robust regression is basically superior to ordinary regression.During the 2020-2022 backtesting period,when the optimization model is quadratic programming,robust regression has a cumulative excess return of 8.4%compared to ordinary regression.Therefore,different strategies have different application scenarios.If it is a bull market,then choose the income risk quadratic programming model,and if it is a bear market,then choose the linear programming model with risk constraints.Finally,this article constructs the CSI 800 Enhanced Index based on this,which has achieved outstanding enhancement effects during the back testing period,achieving an annualized excess return of 14.9%,a Sharpe ratio of 1.1,an information ratio of 2.6,tracking error of 5.6%,and an annualized fluctuation of 20.9%.