Index Tracking: A Stock Selection Model Using Particle Swarm Optimization

Index tracking has long been of interest for both industry of fund management and academia. Various methods have been proposed and tested and various issues are discussed throughout the past 30 years. Yet one issue remains unresolved is how to perform stock selection optimally. In this article, I propose to use an artificial intelligent method—particle swarm optimization (or PSO) to select the most effective stocks to track a target index most closely. I track the S&P 500 index using a small number of its constituents from 1990 till 2019. Practical constraints such as liquidity (in a form of bid-ask spread), transaction costs (commission), and capital requirement are considered. The overall out-of-sample error is consistent with the literature and shown to be greatly reduced if the rebalancing horizon is shorter and the number of stocks is increased. Also, turnovers are lower if rebalancing is more frequent and if more stocks are chosen. Hence, there is a clear tradeoff between rebalancing cost and tracking accuracy.