Enhanced Index Tracking with a Two-Stage Mixed Integer Programing Model and Pattern Search Algorithm

Index tracking is an important issue in portfolio theory. Index tracking is a passive approach in the portfolio optimization problem based on which finite stock should be selected to track the benchmark index. Enhanced index tracking is a selection of the portfolio with limited stock so that its return is maximized and track error is minimized without buying all stock in benchmark portfolio. The main aim of this paper was to propose a two-stage mixed integer model for enhancing portfolio performance. In order to show the approach performance, top 50 companies were traced. Return, tracking error, excess return and information ratio were used as Portfolio performance measurement. Genetic Algorithm and Pattern Search Algorithm were also used to solve the models.  The findings showed that the two-stage model was better than one stage model. Likewise, pattern search enjoyed higher performance than Genetic Algorithm in the two-stage model. Therefore, two-stage model had higher performance during pattern search algorithm compared to one stage model or Genetic algorithm.