Portfolio Optimisation: Models and Solution Approaches

Beasley, John E.

doi:10.1287/educ.2013.0114

Cited by 12 publications

(9 citation statements)

References 39 publications

(49 reference statements)

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“…In this context it is natural to express these performance measures with respect to a market index as a given target. Meade and Beasley [25] (see also Beasley [1]) introduce a nonlinear optimization model that maximizes the following modified Sortino ratio:…”

Section: Some Basic Conceptsmentioning

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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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: Some Basic Conceptsmentioning

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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“…A disadvantage of the POSP is that -while it is parsimonious and algebraically simple-it underrepresents real-world scenarios. As discussed in Beasley [2013], the problem becomes NP-hard when some realistic constraints are also considered, among others: including bounds on the number of assets allowed in the portfolio, including bounds on the level of investment allowed for each individual asset, and forcing some assets to be mandatory in any portfolio due to the investor preferences. However, the computational intractability can be alleviated by metaheuristic algorithms that provide the decision maker with near-optimal solutions within reasonable computational times.…”

Section: Portfolio Optimization and Selection Problemmentioning

confidence: 99%

A Survey on Financial Applications of Metaheuristics

2017

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Modern heuristics or metaheuristics are optimization algorithms that have been increasingly used during the last decades to support complex decision making in a number of fields, such as logistics and transportation, telecommunication networks, bioinformatics, finance, etc. The continuous increase in computing power, together with advancements in metaheuristics frameworks and parallelization strategies, are empowering these types of algorithms as one of the best alternatives to solve rich and reallife combinatorial optimization problems that arise in a number of financial and banking activities. This paper reviews some of the works related to the use of metaheuristics in solving both classical and emergent problems in the finance arena. A non-exhaustive list of examples includes rich portfolio optimization, index tracking, enhanced indexation, credit risk, stock investments, financial project scheduling, option pricing, feature selection, bankruptcy and financial distress prediction, and credit risk assessment. The paper also discusses some open opportunities for researchers in the field, and forecast the evolution of metaheuristics to include real-life uncertainty conditions into the optimization problems being considered.• Applied computing➝Operational research➝Decision analysis • Applied computing➝Law, social and behavioral sciences➝Economics.

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“…Both models select a portfolio whose return distribution dominates the distribution of the benchmark with respect to the second-order stochastic dominance paradigm. A tutorial on the portfolio optimization problem, with a more general perspective, but including the index tracking and the enhanced indexation problems, has been recently provided by Beasley [7].…”

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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Portfolio Optimisation: Models and Solution Approaches

Cited by 12 publications

References 39 publications

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

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

A Survey on Financial Applications of Metaheuristics

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

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