Highlights
A multi-period MILP formulation extends single-period index tracking models.
- At least one multi-period specification achieves a lower out-of-sample RMSE than both benchmarks in seven of the eight configurations.
- The optimal transaction cost limit varies across portfolio cardinalities, sample lengths, and market indices.
- Tracking performance is highly sensitive to the permitted rebalancing degree. Furthermore, no universally optimal parameter value exists.
- Portfolio managers should calibrate rebalancing limits to specific portfolio configurations rather than applying uniform rules.
- Intermediate transaction cost constraints achieve an optimal balance between static buy-and-hold and unrestricted dynamic rebalancing.
- The MILP framework provides a computationally tractable foundation for dynamic index tracking under realistic market frictions.
Abstract
This study extends an existing single-period mixed-integer linear programming (MILP) formulation to a multi-period index-tracking problem. The proposed model allows the tracking portfolio to be rebalanced at predetermined times while limiting the associated transaction costs. Two benchmark strategies are considered: a fixed portfolio with no rebalancing and a portfolio reselected under a large transaction-cost limit intended to approximate unrestricted rebalancing. The models are evaluated using constituent data for the SSE 50 and CSI 100 indices. Tracking performance is measured in-sample and out-of-sample for different portfolio cardinalities, sample lengths, and transaction-cost limits. Among the parameter values examined, at least one multi-period specification produces a lower out-of-sample root-mean-square error (RMSE) than both benchmarks in seven of the eight reported configurations. However, the optimal transaction-cost limit varies across configurations, indicating that tracking performance is sensitive to the permitted degree of rebalancing.