Several Equivalent Forms Of The Portfolio Model

In the field of investment, what people are most concerned is the relationship betweenprofit and risk. As we all know, every investor expects greater profits with a lower degree ofrisk. However, the two factors restrict each other. That is to say, when enjoying higher profits,people have to bear higher risk. Therefore, how to deal with the relationship between thembecomes the main point being researched.Firstly, we introduce the definition and intension of the risk. After reviewing someclassical models in the area of portfolio such as Mean-Variance Model, Semi-Variance Model,LPMs Model and VaR Model, we analyze their characteristics separately. The key point isMean-Variance Model, it's the foundation of the investment theory and it was presented byMarkowitz in his doctor essay in 1952. On the assumption that the profit rate obeys normaldistribution, he denotes profit with mean and risk with variance, the this problem change intoquadratic programming.In the chapter 3, firstly we show the equivalence of several models, then we focus on theσ/μmodel under not shot sale restriction. With the augment of profit at the efficientboundary the investors have to shoulder more risk, so we know the mean and variance of theoptimum have relationship each other. We use the ratio of standard variance and mean as theobjective function which represent the augment of risk the investor have to shoulder when theprofit increases one unit, and we change the equation of the constraint into inequation. On thebasis of Mean-Variance model, we can represent theσ/μwith the mean, so we can solvethis problem fluently.