fuzzy variable

Index tracking is one of the most important passive strategies which describes the process of attempting to track the performance of some specified benchmark indexes. Most recent studies determined security returns in conventional models by the precise historical data. However, such precise data are not always available and it is hard to forecast security returns with stochastic values. Therefore, to handle such imprecise uncertainty, considering security returns as variables with imprecise distributions, i.e., fuzzy variables are recommended. In these studies, researchers have studied and experimented with various risk-measure methods for index tracking portfolio selection. Models which were extended based on Markowitz portfolio selection model have used the single period variance of returns as a risk measure. Since forecasting future returns of portfolio is uncertain, we consider these returns as fuzzy variables in this study. We also apply Value-at-Risk as the risk measure whichhas not yet been established as risk measure in index tracking portfolio selection problems. The model is tested, using Tehran Price Index (TEPIX) and computational results are presented at the end.