A bacterial foraging optimization approach for the index tracking problem

Index tracking is a popular passive portfolio management strategy which invests in a subset of stock market index constituents to reproduce the performance of the index. In this paper we apply a heuristic approach based on bacterial foraging optimization (BFO) to the index tracking problem. BFO is a swarm intelligence technique which mimics the foraging behavior of bacteria with three important movements, i.e., chemotaxis, reproduction, and elimination-dispersal. It has strong capability in both global search and local search, and thus has been successfully applied in several problems, but not yet in index tracking. To make our model more realistic, we consider transaction cost when revising the tracking portfolio, and include cardinality and bounding constraints. The BFO approach is compared with a genetic algorithm which is widely adopted as the benchmark in the index tracking problem. Empirical experiments with HangSeng, DAX, FTSE, S&P and Nikkei indexes indicate that, our BFO achieves significantly better overall objective function value under a wide range of tracking error/excess return tradeoffs. Furthermore, rolling window tests show that, our BFO leads to significantly smaller out-of-sample tracking error under a wide range of transaction cost constraints.