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Fuzzy portfolio allocation models through a new risk measure and fuzzy sharpe ratio
journal contribution
posted on 2015-06-01, 00:00 authored by Thanh Thi NguyenThanh Thi Nguyen, L Gordon-Brown, Abbas KhosraviAbbas Khosravi, Douglas CreightonDouglas Creighton, Saeid NahavandiA new portfolio risk measure that is the uncertainty of portfolio fuzzy return is introduced in this paper. Beyond the well-known Sharpe ratio (i.e., the reward-to-variability ratio) in modern portfolio theory, we initiate the so-called fuzzy Sharpe ratio in the fuzzy modeling context. In addition to the introduction of the new risk measure, we also put forward the reward-to-uncertainty ratio to assess the portfolio performance in fuzzy modeling. Corresponding to two approaches based on TM and TW fuzzy arithmetic, two portfolio optimization models are formulated in which the uncertainty of portfolio fuzzy returns is minimized, while the fuzzy Sharpe ratio is maximized. These models are solved by the fuzzy approach or by the genetic algorithm (GA). Solutions of the two proposed models are shown to be dominant in terms of portfolio return uncertainty compared with those of the conventional mean-variance optimization (MVO) model used prevalently in the financial literature. In terms of portfolio performance evaluated by the fuzzy Sharpe ratio and the reward-to-uncertainty ratio, the model using TW fuzzy arithmetic results in higher performance portfolios than those obtained by both the MVO and the fuzzy model, which employs TM fuzzy arithmetic. We also find that using the fuzzy approach for solving multiobjective problems appears to achieve more optimal solutions than using GA, although GA can offer a series of well-diversified portfolio solutions diagrammed in a Pareto frontier.
History
Journal
IEEE transactions on fuzzy systemsVolume
23Issue
3Pagination
656 - 676Publisher
IEEELocation
Piscataway, N.J.Publisher DOI
ISSN
1063-6706eISSN
1941-0034Language
engPublication classification
C Journal article; C1 Refereed article in a scholarly journalCopyright notice
2015, IEEEUsage metrics
Keywords
Science & TechnologyTechnologyComputer Science, Artificial IntelligenceEngineering, Electrical & ElectronicComputer ScienceEngineeringFuzzy returnfuzzy Sharpe ratiogenetic algorithm (GA)portfolio optimizationreturn uncertaintyVALUE-AT-RISKRANDOM-VARIABLESCORRELATION-COEFFICIENTSELECTIONNUMBERSVARIANCERETURNSOPTIMIZATIONOPERATIONSMOMENTSArtificial Intelligence and Image Processing
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