Research on Mean-Variance-Efficiency Portfolio of Fuzzy DEA Based on Possibility Theory

The actual financial market is complicated and volatile, in which most investment portfolio models include the historical return of stock as an important indicator while overlooking the impact of stock efficiency. Meanwhile we have noticed that the specific indicators of fuzzy input and fuzzy output enable the fuzzy DEA model to effectively measure stock efficiency. Accordingly, this paper uses fuzzy DEA model to analyze the stock efficiency, with equity multiplier, price earnings ratio and beta value as fuzzy input, total assets turnover, earning per share and net profit growth rate as fuzzy output. Secondly, this paper takes the possibility mean and possibility variance as the measurement of portfolio return and risk, so as to build the mean-variance-efficiency portfolio model. And the genetic algorithm of exponential fitness function is applied to the model in order to satisfy the requirement of fitness values being non-negative. At the end, an empirical example is given to verify the feasibility of the model and improved algorithm, and we also prove that there is a certain correlation between stock efficiency and return. As shown by the results, it is quite indispensable to consider the portfolio efficiency in the actual financial market, which can provide investors with more comprehensive, scientific and effective decision-making scheme.