Heuristic methods for stock selection and allocation in an index tracking problem

Index tracking is one of the most popular passive strategy in portfolio management. However, due to some practical constrains, a full replication is difficult to obtain. Many mathematical models have failed to generate good results for partial replicated portfolios, but in the last years a data driven approach began to take shape. This paper proposes three heuristic methods for both selection and allocation of the most informative stocks in an index tracking problem, respectively XGBoost, Random Forest and LASSO with stability selection. Among those, latest deep autoencoders have also been tested. All selected algorithms have outperformed the benchmarks in terms of tracking error. The empirical study has been conducted on one of the biggest financial indices in terms of number of components in three different countries, respectively Russell 1000 for the USA, FTSE 350 for the UK, and Nikkei 225 for Japan.