Enhanced indexation via chance constraints
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Enhanced indexation via chance constraints Patrizia Beraldi1 · Maria Elena Bruni1 Received: 27 May 2019 / Revised: 10 June 2020 / Accepted: 1 August 2020 © The Author(s) 2020
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. Keywords Enhanced indexation · Chance constraints · Stochastic programming
1 Introduction Over the last decades, index tracking (IT) has become an increasingly popular investment strategy all over the world. The aim is to create a portfolio of assets that replicates (tracks) the movements of a given financial index taken as benchmark. The difference between the performance of the replicating portfolio and the benchmark is generally referred to as tracking error and the problem entails the definition of a portfolio that minimizes this gap. On the basis of the specific * Patrizia Beraldi [email protected] 1
Department of Mechanical, Energy and Management Engineering, Università della Calabria, Via P. Bucci, Cubo 41 C, Rende, Italy
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tracking-error function used, different formulations have been proposed [see, for example, Mutunge and Haugland (2018) and the references therein]. The IT is traditionally referred to as a passive management strategy. In contrast, an active strategy aims at defining portfolios that achieve higher returns than the benchmark, generating an “excess of return”. Sometimes the term indexplus-𝛼 portfolio is used to indicate a portfolio that outperforms the benchmark by a given, typically small, value 𝛼 . Since, in general, there is no guarantee of achieving a positive excess of return under every circumstance, the risk of underperforming the benchmark should be limited. Enhanced index tracking (EIT), or simply enhanced indexation, can be seen as an evolution of the IT relying on the idea of properly combining the strengths of both the p
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