Fast and stable portfolios through Huber’s criterion for constrained index tracking

A portfolio with numerous small and illiquid positions typically leads to high transaction costs and the need for frequent rebalancing. To address this issue, one could opt for a sparse portfolio strategy that can effectively track the benchmark index while simplifying portfolio management and reducing transaction costs. However, this approach requires prior specification of the maximum number of assets that can be selected. The computational complexity of cardinality-constrained optimization, particularly in high-dimensional settings, makes the regularization method a more preferable choice to handle such constraints. In this article, we introduce a more efficient index tracking method using penalized Huber loss regression, which automatically selects assets and allocates capital under a set of general convex constraints. Furthermore, we derive a fast algorithm based on coordinate descent to solve the resulting optimization problem. We also empirically evaluate the proposed methodology on real-world data sets. Promising results demonstrate the superiority of the proposed method in terms of tracking error and running time.