Absolute return portfolios

Valle, Cristiano Arbex; Meade, Nigel; Beasley, John E.

doi:10.1016/j.omega.2013.12.003

Cited by 28 publications

(8 citation statements)

References 33 publications

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“…The resulting formulation is a MILP model. Valle et al [36] study the problem of determining an absolute return portfolio and propose a three-stage solution approach. The authors discuss how their approach can be extended to solve the EITP.…”

Section: Recent Literature On the Enhanced Index Tracking Problemmentioning

confidence: 99%

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Linear programming models based on Omega ratio for the Enhanced Index Tracking Problem

Guastaroba

Mansini

Ogryczak

et al. 2016

European Journal of Operational Research

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Modern performance measures differ from the classical ones since they assess the performance against a benchmark and usually account for asymmetry in return distributions. The Omega ratio is one of these measures. Until recently, limited research has addressed the optimization of the Omega ratio since it has been thought to be computationally intractable. The Enhanced Index Tracking Problem (EITP) is the problem of selecting a portfolio of securities able to outperform a market index while bearing a limited additional risk. In this paper, we propose two novel mathematical formulations for the EITP based on the Omega ratio. The first formulation applies a standard definition of the Omega ratio where it is computed with respect to a given value, whereas the second formulation considers the Omega ratio with respect to a random target. We show how each formulation, nonlinear in nature, can be transformed into a Linear Programming model. We further extend the models to include real features, such as a cardinality constraint and buy-in thresholds on the investments, obtaining Mixed Integer Linear Programming problems. Computational results conducted on a large set of benchmark instances show that the portfolios selected by the model assuming a standard definition of the Omega ratio are consistently outperformed, in terms of out-of-sample performance, by those obtained solving the model that considers a random target. Furthermore, in most of the instances the portfolios optimized with the latter model mimic very closely the behavior of the benchmark over the out-of-sample period, while yielding, sometimes, significantly larger returns.

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Section: Recent Literature On the Enhanced Index Tracking Problemmentioning

confidence: 99%

“…Note that when µ α − y t > 0, d t takes exactly such a value by forcing u t = 0, whereas when µ α − y t < 0 inequality (35) forces u t = 1 to guarantee a positive right-hand side, and d t takes value zero thanks to inequality (36).…”

Section: Additional Modeling Issuesmentioning

confidence: 99%

Linear programming models based on Omega ratio for the Enhanced Index Tracking Problem

Guastaroba

Mansini

Ogryczak

et al. 2016

European Journal of Operational Research

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“…The resulting formulation is a MILP model. Valle et al [55] present a three-stage solution approach for the problem of selecting an absolute return portfolio, and show how it can be extended to the enhanced index tracking problem.…”

Section: Enhanced Index Tracking and Multi-objective Portfolio Optimimentioning

confidence: 99%

A heuristic framework for the bi-objective enhanced index tracking problem

Filippi

Guastaroba

Speranza

2016

Omega

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The index tracking problem is the problem of determining a portfolio of assets whose performance replicates, as closely as possible, that of a financial market index chosen as benchmark. In the enhanced index tracking problem the portfolio is expected to outperform the benchmark with minimal additional risk. In this paper, we study the bi-objective enhanced index tracking problem where two competing objectives, i.e., the expected excess return of the portfolio over the benchmark and the tracking error, are taken into consideration. A bi-objective Mixed Integer Linear Programming formulation for the problem is proposed. Computational results on a set of benchmark instances are given, along with a detailed out-of-sample analysis of the performance of the optimal portfolios selected by the proposed model. Then, a heuristic procedure is designed to build an approximation of the set of Pareto optimal solutions. We test the proposed procedure on a reference set of Pareto optimal solutions. Computational results show that the procedure is significantly faster than the exact computation and provides an extremely accurate approximation.

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“…They can be a fixed cost applied to each selected security in the portfolio; or a variable cost to be paid which depends on the amount invested in each security included in the portfolio (see e.g. [3,4,11,23,25,34,35] and the references therein). This dependence can be proportional to the investment or given by a fixed cost that is only charged if the amount invested exceeds a given threshold, or by some other functional form (see e.g.…”

Section: Introductionmentioning

confidence: 99%