Portfolio selection under different attitudes in fuzzy environment

This paper studies stock portfolio selection problem based on varying conservative-neutral-aggressive attitudes. The return rates of stocks are characterized by fuzzy variables. The Pareto-optimal solutions are obtained by maximizing the return and minimizing the risk subject to constraints of transaction cost and value at risk. Since investors with different attitudes may have different understanding of the likelihoods of occurrence, measure Me with the ability of reflecting varying conservative-neutral-aggressive attitudes is adopted. Based on Me, the expected value of fuzzy return and the lower absolute deviation are used to quantify the return and risk levels of a portfolio respectively. Then the ɛ-constraint method is employed to obtain the efficient frontier. Finally, an empirical study is carried out using the data of 10 stocks in Chinese stock market. Sensitivity comparisons are conducted to demonstrate the effectiveness of the proposed model. The results show that different frontiers can be obtained under different attitudes, confidence levels and values at risk.