Linear Programming Model For Portfolio Selection And Its Application

Portfolio selection is based on the level of risk and the annual profitability.It is a low-risk investment strategy according to certain principles of the right choices.The purpose of securities investment income is getting profit.However,portfolio investment is accompanied by the high-yield and high-risk economic activities.Yield and risk are the two core issues of the portfolio selection.The basic principle of investment securities is to pursue the maximization of return and the minimization of risk and find a balance from the interaction of income and risk.The key of portfolio selection is carrying out decentralized investment effectively to disperse the risks and reduce the total risk through diversified investment.Portfolio Investment Theory is one of the finance areas with fastest growing and broadest application and attracts the attention from many scholars at home and abroad. 1952,Markowitz proposed the model of mean - variance to measure income and risk in portfolio selection.However,this model is seldom applied in practice because the efficient frontier deduced by it is difficult to calculate.Later,Kormo put forward absolute deviation risk function with the feature of linear function.When the proceeds meet the conditions of normal distribution,the nature of absolute deviation risk function and variance risk function are the same.Moreover,the portfolio selection models based on the absolute risk of deviation function can be solved through a linear programming.It is proved that this model not only keeps the excellent nature of mean-variance model but also avoids the calculating difficulties in the process of solving the Markowitz model.This study includes two parts..The first part is recalling the classic models bY firstly introducing the basic theory of the portfolio and the classical mean - variance model and secondly presenting a class of models which can be transformed into linear programming, such as mean - absolute deviation model,mean - semi-absolutedeviation model,meanabsolute deviation model with transaction costs and mean - semi-absolute deviation model with transaction costs.Besides,the first part detailedly states the forming and transformation process of several linear models.The second part is to compare the typical stocks selected from Chinese securities market.Selecting five representative stocks from the finance,real estate,steel,electricity and other stocks to analyses,the study focuses on the impact of different types of stocks,the proceeds model and the combination of risk and the transaction costs on the investment portfolio.Through data analysis and comparative study,we found the risk measured by MAD is bigger than the one measured by SMAD. The risk of the investment portfolio is increasing with the growing of the expectant yield. Transaction costs almost have no effects on the risks and the proportion of the investment portfolio in the long-term investment.Besides,the investment ratio varies with the change of the expected profit.Generally speaking,the investment ratio of the stocks with higher average monthly return goes up with expected yield's increase.Similarly,the investment ratio of the stocks with lower average monthly return goes down with expected yield's decrease.High,medium and low yield stocks exist in most investment portfolio,but their proportions are different.