Portfolio Selection Via Expectile Regressions

With the deepening of financial theory research,large-scale portfolio investment decision-making has become one of the hot issues of research.In order to achieve the goal of minimizing investment risk under the established conditions of expected returns,the quantitative model and the selection of risk measurement indicators are all crucial.The mean-variance model based on the assumption of normality can no longer meet the needs of modern portfolio investment decisions.It is necessary to consider new risk measurement methods and establish new portfolio investment decision models.The risk measurement index has experienced changes from the moment risk measure to the distribution(tail)risk measure.Among them,ES(Expected Shortfall)has better mathematical properties,which not only overcomes the shortcomings of VaR but also has the advantages of VaR.In addition,the portfolio investment decision model based on regression analysis has received more and more attention.To this end,this paper discusses the problem of portfolio investment decision based on Expectile regression.In this paper,the mean-ES portfolio investment model is established.In order to solve its computational difficulties,it is theoretically transformed into an Expectile regression problem,and then a new method for Expectile regression is given.The method has two advantages: First,the objective function of Expectile regression is a quadratic loss function,which has continuous and smooth characteristics,and its optimization and calculation process is simple and easy,and has good scalability.Second,optimizing the Expectile regression objective function to obtain Expectile,and using the correspondence between Expectile and ES,can accurately obtain the ES risk value of the optimal portfolio investment.Furthermore,considering the need of large-scale portfolio investment,we add weight constraints in the mean-ES portfolio investment decision model based on Expectile regression,and establish a minimum ES portfolio investment decision model with weight constraints,and study LASSO,adaptive LASSO or Minimum ES high-dimensional portfolio investment decisions such as elastic network penalty.In the empirical aspect,five stocks with industry representativeness in the Shanghai and Shenzhen 300 Index are selected for empirical research.The mean-ES model based on Expectile regression is compared with the mean-VaR model and the mean-variance model.It is found that the former can be well decentralized portfolio investment tail risk size,significantly improve portfolio investment performance.The stock daily return rate of the Shanghai and Shenzhen 300 Index was selected as the research object,and the 300 constituent stocks were combined to make investment decisions.The financial assets were selected from a large number of financial assets for portfolio investment,which greatly improved the portfolio investment management effectiveness.In this paper,the mean-ES portfolio investment model is theoretically transformed into an Expectile regression problem,and its solution scheme is given,which enriches the research content of portfolio investment decision.In practice,the model established in this paper can deal with large-scale portfolio investment decision-making problems,select assets with larger contributions to make portfolio investment,reduce asset management costs,improve management efficiency,and achieve higher yield-to-risk ratio.Institutional investors have a certain reference value for decision making.