Multi-Period Portfolio Optimization for Index Tracking in Finance

Index tracking, a classical passive investment strategy in finance, attempts to reproduce the performance of a specific market index by holding only a subset of the constituent assets in the index. To realize this, various portfolio optimization methods have been developed. In the literature, all the existing works focus on single-period optimization (SPO) for index tracking portfolio design. However, in the financial markets, such SPO methods may lead to frequent portfolio rebalances, resulting in high transaction costs. In this paper, a novel multi-period optimization (MPO) approach to index tracking portfolio design is proposed, which is able to account for transaction costs and holding costs. The MPO for index tracking is formulated as a nonconvex optimization problem and solved successively by dealing with a second-order cone programming subproblem based on the successive convex optimization procedure. Numerical simulations showcase that the proposed MPO method is able to achieve comparative tracking performance with lower costs compared to the classical SPO method.