Genetic algorithm versus classical methods in sparse index tracking

The main objective in index tracking is to replicate the performance of a target index by using a small subset of its constituents. Non-convex regularization techniques, such as the \(\ell _q\) and the log penalization, which are able to enhance portfolio sparsity by selecting a low number of active weights, recently proved to perform remarkably well in index tracking problems. The resulting non-convex optimization is NP-hard and deterministic optimization methods, such as interior point and gradient projection algorithms, may not efficiently reach the optimal solution due to the presence of multiple local optima and discontinuities in the search space. Therefore, heuristic approaches can be more helpful and easy to implement, thanks to recent hardware development. In this paper, we compare three state-of-the-art estimation techniques, i.e., the interior point, the gradient projection and the coordinate descent algorithms, to a popular heuristic method, the genetic algorithm, in index tracking optimization. We show and evaluate the performance of the four methods in a penalized framework on different simulated settings and on real-world financial data.