Gaustaroba, Gianfranco and Mansini, Renata and Ogryczak, Wlodzimierz and Speranza, M. Grazia (2014): Linear Programming Models based on Omega Ratio for the Enhanced Index Tracking Problem.

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Abstract
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 buyin 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 outofsample 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 outofsample period, while yielding, sometimes, significantly larger returns.
Item Type:  MPRA Paper 

Original Title:  Linear Programming Models based on Omega Ratio for the Enhanced Index Tracking Problem 
Language:  English 
Keywords:  Enhanced Index Tracking, Omega Ratio, Portfolio Optimization, Linear Program ming, Mixed Integer Linear Programming. 
Subjects:  C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61  Optimization Techniques ; Programming Models ; Dynamic Analysis C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63  Computational Techniques ; Simulation Modeling G  Financial Economics > G1  General Financial Markets G  Financial Economics > G1  General Financial Markets > G11  Portfolio Choice ; Investment Decisions 
Item ID:  67097 
Depositing User:  prof. Wlodzimierz Ogryczak 
Date Deposited:  07. Oct 2015 13:21 
Last Modified:  07. Oct 2015 13:43 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/67097 