Research On Efficiency Evaluation For Multi-Period Portfolios With V-shaped And The Secondary Transaction Costs

With the rapid development of China's financial market, More and more investors can choose a variety of financial products. And these products are essentially portfolios, so it is a very important to evaluate these portfolios accurate and reasonable, which not only can guide investors to choose right products, but also improve the efficiency of capital markets.Based on the Markowitz mean-variance theory, we consider the different types of transaction costs in real financial market, and establish multi-period portfolio optimization models in the V-shaped transaction costs and the secondary trading costs. Based on the real frontier, we define the efficiency of the portfolios in the same scale and the corresponding nonlinear model is established to evaluate the efficiency of portfolios. Meantime, Referring to previous scholars'research, we devide investment strategies into the Open-loop strategy and the Close-loop strategy, and apply convex programming algorithm calculate the analytical solutions. Due to the lack of analytical solutions of frontier and difficulties in solving the nonlinear model. Then, Based on DEA, we use network DEA to evaluate the efficiency of multi-period portfolios.We evaluate multi-period portfolios which considering of transaction costs with three methods:the method of definition?DEA model and network DEA model. The simulation results show that the network DEA model is closer to real efficiency than DEA model; Network DEA model is the same with the portfolio optimization model in essence, they have a strong correlation.