Research On Portfolio With The Lowest Transaction Cost

With the Markowitz Portfolio Model widely used in the asset allocation and investment decisions, how to obtain the optimal portfolio selection, especially with the certain constraints, has become one of the hot issues of concern for many scholars. At present, most models just consider the transaction costs is proportional to the transaction amount and regard the amount of assets as unit 1 without the biggest capital constraints and the lowest transaction costs. In view of that, this paper studies the model with the biggest capital constraint and a complex transaction cost, which is proportional to the amount if and only if it is greater than the lowest transaction cost.First, this paper introduces the classical MV model and the model with the transaction costs which is proportional to the transaction amount.Second, the paper put forward the model with the biggest capital con-straints and a complex transaction cost, which is proportional to the trans-action amount if and only if it is greater than the lowest transaction cost. Then the model is transformed into a convex programming containing only linear constraint conditions, we proved the existence of the optimal solu-tion.Finally, by setting different number of the biggest capital constraints, the paper draws the efficient portfolio frontiers which are respectively before and after the promotion with Matlab. It is concluded that it affects efficient frontiers when the biggest capital constraint is lower; otherwise it has no effect on efficient frontiers when it is big enough.