Enhanced indexation via chance constraints

Abstract

The enhanced index tracking (EIT) represents a popular investment strategy designed to create a portfolio of assets that outperforms a benchmark, while bearing a limited additional risk. This paper analyzes the EIT problem by the chance constraints (CC) paradigm and proposes a formulation where the return of the tracking portfolio is imposed to overcome the benchmark with a high probability value. Besides the CC-based formulation, where the eventual shortage is controlled in probabilistic terms, the paper introduces a model based on the Integrated version of the CC. Here the negative deviation of the portfolio performance from the benchmark is measured and the corresponding expected value is limited to be lower than a given threshold. Extensive computational experiments are carried out on different set of benchmark instances. Both the proposed formulations suggest investment strategies that track very closely the benchmark over the out-of-sample horizon and often achieve better performance. When compared with other existing strategies, the empirical analysis reveals that no optimization model clearly dominates the others, even though the formulation based on the traditional form of the CC seems to be very competitive.