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

G Guastaroba , Renata Mansini , Włodzimierz Ogryczak , M Grazia Speranza


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.
Author G Guastaroba
G Guastaroba,,
, Renata Mansini
Renata Mansini,,
, Włodzimierz Ogryczak IAiIS
Włodzimierz Ogryczak,,
- The Institute of Control and Computation Engineering
, M Grazia Speranza
M Grazia Speranza,,
Journal seriesEuropean Journal of Operational Research, ISSN 0377-2217
Issue year2016
Publication size in sheets0.9
Keywords in EnglishEnhanced index tracking; Omega ratio; Portfolio optimization; Linear programming; Mixed integer linear programming
projectConstruction of robust investment portfolios by means of the generalized ordered weighted averages. Project leader: Ogryczak Włodzimierz, , Phone: 6190, start date 01-07-2013, end date 30-06-2016, 505D/1031/0047 , Completed
WEiTI Projects financed by NSC [Projekty finansowane przez NCN]
Development of methodology of control, decision support and production management. Project leader: Zieliński Cezary, , Phone: 5102, start date 19-05-2015, end date 31-12-2016, 504/02233/1031, Completed
WEiTI Działalność statutowa
Languageen angielski
Guastaroba Ogryczakw i in EJOR 2016.pdf 2.78 MB
Score (nominal)40
ScoreMinisterial score = 40.0, 27-03-2017, ArticleFromJournal
Ministerial score (2013-2016) = 40.0, 27-03-2017, ArticleFromJournal
Publication indicators WoS Impact Factor: 2016 = 3.297 (2) - 2016=3.582 (5)
Citation count*27 (2018-07-16)
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* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.