Low-Turnover Rebalancing for Sparse Index Tracking

Abstract

Sparse index tracking is often evaluated through rolling reconstruction: a sparse portfolio is fitted on an in-sample window, held over the next period, and rebuilt when the window rolls forward. This can achieve low realised tracking error, but it treats rebalancing primarily as repeated construction and can generate large turnover and frequent substitutions in the selected constituents. We propose a new workflow that separates sparse-tracker construction from sparse-tracker maintenance. A hybrid optimisation-plus-sampling framework provides the metrics operating at the decision level for both layers. The initial tracker is built from a calibrated shrinkage model and uncertainty-aware posterior support screening. Subsequent rebalance dates are handled in the self-financing change variable $\Delta w$. The default action is to preserve the existing tracker; local repairs are implemented only when realised tracking deterioration and posterior directional evidence jointly suggest intervention. In a 2020-2025 S&P 500-style case study, we show that the proposed tracker occupies a distinct low-turnover operating region. Moreover, we demonstrate that the proposed $\Delta w$ maintenance layer can be attached to externally constructed trackers, where it gives consistent improvements over simply holding the initial tracker. Additional diagnostics, sensitivity experiments, and computational details are reported in the companion Supplementary Material. Replication code and logs of several experiments are available at \href{https://github.com/droxanas/Low-Turnover-Rebalancing-for-Sparse-Index-Tracking/}{https://github.com/droxanas/Low-Turnover-Rebalancing-for-Sparse-Index-Tracking/}.