Index tracking problem solving using metaheuristic firefly algorithm

Index tracking portfolio is a form of investment that is faced with popularity. This problem is the choice of a portfolio that replicates the performance of a stock market index by purchasing a subset of the stocks included in the index. Due to the large number of companies that create the index, the choice of limited number of stocks is a combinatorial problem that cannot be solved in polynomial time. There is a cardinality constraint, includes the number of stocks in portfolio and also minimum and maximum holding level for every stock is a constraint in this problem. In order to solve NP-Hard optimization problems, metaheuristic algorithms have proven their efficiency. In this study, an intelligent metaheuristic, which utilizes the firefly algorithm, is presented for solving the index tracking problem. Proposed approach was applied to the S&P500 index, the Hang Seng and the Tehran Stock Exchange. The results indicate the efficiency of the scheme.