Research On Evaluation Methods And Applications For Multi-period Portfolios On Considering Transaction Costs

Financial market is a very complex system in the modern economy market system, its healthy development has a pivotal role for the sustainable development of national economy. As an important part in financial markets, the essence of securities investment is for effective allocation of resources. Markowitz explained how the efficient frontier of portfolios is constructed to select the optimal portfolio, thus laying a solid foundation for the development of portfolio theory. On this basis, accurately and scientifically evaluate the investment portfolios become an important and hot topic in the current research.Based on the Markowitz portfolio theory and combined with the actual situation of the securities market, we establish multi-period portfolio optimization models in the Open-loop strategy and Close-loop strategy considering the transaction costs (mainly consider three convex transaction costs, namely, linear transaction costs, the ?-shape transaction costs and the piece-wise linear transaction costs). Based on the real frontier, we define the efficiency of the portfolios and the corresponding nonlinear model is established to evaluate the efficiency of portfolios. Due to the lack of analytical solutions of frontier and difficulties in solving the nonlinear model, we prove that the real frontier is concave function. Then, we use DEA efficient frontier to approximate real frontier and propose the DEA model based on the data to evaluate the efficiency of multi-period portfolios.The simulation results show that there is a strong correlation between the sorting of using the method of definition (based on the real frontier) and the method of Data Envelopment Analysis (based on the DEA efficient frontier) to evaluate the portfolios. When the number of decision making units big enough, the DEA frontier infinite close to real frontier. This illustrates the feasibility of efficiency evaluation of multi-period portfolios by using DEA efficient frontier to approximate the real frontier, namely, the validity and rationality of using DEA models based on the data to evaluate multi-period portfolios considering the transaction cost is illustrated in the end.