Research On Efficiency Evaluation For Multi-period Portfolio With Transaction Limits

There are many theoretical and practical researches on the efficiency of portfolio evaluation, While there are few research on multi-period portfolio performance evaluation. Let alone applying DEA to the evaluation of multi-period portfolio.With the review of classical Markowitz portfolio theory and multi-period portfolio optimization model with linear control policies, we established some multi-period portfolio optimization models with transaction limits. On the basis of proving that the real frontier function is concave.We used DEA to evaluate the efficiency of multi-period portfolio model with transaction limits. Different from some other DEA users, we adopted risk measure as input, return measure as output which is conform to the preference of most investors and theory researchers.According to Banker's Approximation theory, we can use DEA frontier to approximate the real frontier. In this thesis, the transaction limits are divided into two aspects. one of the situation is the transactions with lower bound and upper bound.another situation is that the total transactions should less than a constant. Then we adopted DEA model to approximate the real frontier and evaluate the efficiencies of portfolios with transaction limits. In the process of simulation, We took two kinds of policies into account, They are Open-loop policy(the whole sequence of optimal adjustments are freezed at the beginning) and Close-loop policy(the decision maker would “wait and see” what the actual outcome of his/her previous decision is and rethink the course of action accordingly).Finally, we not only got the real frontiers and the DEA frontiers but also computed the DEA efficiency and its real efficiency. Through comparing frontiers and their efficiency,We found their sorting have great correlation, Thus We can say, DEA is a useful tool in evaluating the multi-period portfolio.