A robust optimization framework for the enhanced index tracking problem

Abstract Enhanced index tracking (EIT) problem seeks to construct a portfolio that not only mirrors the market index movements but also delivers superior returns. In formulating this problem, historical data are typically treated as scenarios. However, this view may lead to information loss, as historical patterns are not guaranteed to recur in the future. To account for potential deviations from historical scenarios, this paper presents a robust formulation for the EIT problem. Two error functions are considered to quantify the deviation of the portfolio return from the index return: the mean‐squared deviation (MSD) and the mean‐squared downside deviation (MSDD). The robust formulation of the problem for the MSD tracking error presents significant challenges. This paper, first, discusses the difficulties associated with incorporating the MSD error and clarifies why the methods used for the MSDD‐based formulation cannot be directly applied to the MSD‐based model. Then, the problem with the MSD error is formulated as a bi‐level optimization model and is solved with a decomposition‐based heuristic, employing a least‐absolute‐shrinkage‐and‐selection‐operator (LASSO)‐based technique to handle the cardinality constraint. To assess the robustness of the proposed model under extreme market conditions, we evaluate its performance on the 2008 financial crisis and the Corona‐virus‐desease‐2019 (COVID‐19) pandemic. Experimental results on major international stock market data highlight the superiority of the MSD‐based model over MSDD‐based robust models. Furthermore, the proposed model is also compared with three recently developed and well‐established EIT models, and the results demonstrate that the proposed approach delivers good performance in comparison to other models as well.