Fuzzy Index Tracking Portfolio Selection Model

In financial markets, investment strategies can be divided into two classes: passive investment strategies and active investment strategies. Investors adopting active investment strategies trade in securities actively, so that they can find profit opportunities on a running basis. Active investors take it for granted that they can beat markets continuously. Investors who adopt passive investment strategies consider that the securities market is efficient. Therefore, they cannot go beyond the average return level of the market continuously. Index tracking investment is a kind of passive investment strategy, i.e., investors purchase all or some securities which are contained in a securities market index and construct an index tracking portfolio. The securities market index is considered as a benchmark. The investors want to obtain a return similar to that of the benchmark, through index tracking investment.

The chapter is organized as follows. In Section 2, we present a bi-objective programming model for the index tracking portfolio selection problem. In Section 3, regarding investors’ vague aspiration levels for the excess return and linear tracking error as fuzzy numbers, we propose a fuzzy index tracking portfolio selection model. In Section 4, a numerical example is given to illustrate the behavior of the proposed fuzzy index tracking portfolio selection model. Some concluding remarks are given in Section 5.