Enhanced optimal tracking error portfolio via quantile regression with SSD constraints

Constructing an index-tracking portfolio involves closely replicating the performance of a benchmark index while minimizing deviations from it. In this paper, we propose a novel enhanced index tracking model that combines a quantile-regression-based deviation measure with linear second-order stochastic dominance (SSD) constraints. The objective is to control the tail risk of the tracking error while guaranteeing an enhancement of the portfolio return distribution relative to the benchmark. The proposed formulation leads to a linear optimization problem that remains computationally tractable under realistic portfolio constraints. The model is empirically evaluated using real-world data to assess the contribution of SSD constraints and to compare its performance with that of classical quantile regression. The empirical results show that both models outperform the benchmark index. However, when the investable universe is restricted through preselection, the proposed model delivers significant improvements in risk-return performance and tail-risk control.