Index Tracking Portfolio Construction with Sector Weight and Turnover Constraints

This study examines the index tracking problem using constrained optimization with sector weight and turnover constraints. We implement a mixed-integer quadratic programming (MIQP) model using the Gurobi framework. Our goal is to construct concentrated portfolios that replicate the Standard & Poor’s (S&P) 100 performance. The approach employs a rolling window methodology with in-sample optimization and out-of-sample validation periods to assess performance across varying market conditions. The analysis evaluates constraint combination effects on tracking accuracy, portfolio stability, and computational requirements for 10- and 20-stock portfolios. Results demonstrate that constraints improve index alignment and portfolio stability, while enabling substantial computational efficiency gains primarily through solution space reduction.