Chapter 11 Future Research
The variants of the Particle Swarm Optimization were examined for their efficacy in solving the index tracking problem. The local PSO and the self-adaptive velocity PSO were found to be particularly effective, as they increase the diversity within the swarm and prevent premature convergence in local minima. Additionally, the self-adaptive velocity PSO offers the advantage of reducing the number of hyperparameters, making it capable of solving a wide range of problems without the need for extensive fine-tuning. The implementation of the self-adaptive velocity PSO, as described in (Fan & Yan, 2014), was found to be effective, but further research is needed to determine whether it can be improved by combining it with the local variant.
A backtesting study was conducted in the final chapter, evaluating the practical application of the index tracking problem for retail investors. The results were promising, but further evaluation is necessary to confirm the stability of the results, given the path-dependent nature of the portfolios.