Research On Performance Evaluation Methods For Portfolios With Margin Requirements

Markowitz portfolio optimization theory laid a foundation for modern financial research. Also, this theory opened a new epoch in quantitative analysis of portfolios.In short, a portfolio is the distribution of wealth among different assets, in order to achieve the goal of diversifying risk and ensuring profits. As an important measure of controlling risk, margins are indispensable to the futures markets as well as the whole capital market. However, the research on portfolio selection with margin requirements is limited.This thesis is concerned with single-period and multi-period portfolio selection problems under the allowance of short selling with cash as well as security margins.The objective is to maximize the expected return and minimize the variance of the terminal wealth. Based on the real frontier, the definition of portfolio efficiency with margin requirements is given. Then the corresponding nonlinear models to evaluate the efficiencies of the portfolios are constructed. Since the nonlinear models are difficult to solve and the analytical solutions of the frontiers are hard to obtain. Under the assumption that the real frontier is a concave function, we adopt DEA models to evaluate portfolios efficiencies with margin requirements. In the simulation analysis,we use the definitions(based on the real frontier) and the DEA models(based on DEA efficient frontier) to evaluate portfolio efficiencies with margin requirement,respectively. The results show that the correlations of efficiencies from the two approaches are very high. The more the samples, the closer the DEA frontier and real frontier.This thesis indicates that using DEA models to evaluate portfolio efficiencies with margin requirements is feasible and the results are reasonable. What’s more, this research enhances the development of modern financial markets; it provides supports for implementing short selling mechanism with margin requirements too.