Fuzzy portfolio allocation models through a new risk measure and fuzzy Sharpe ratio

Thanh Thi Nguyen, Lee Nigel Gordon-Brown, Abbas Khosravi, Douglas Creighton, Saeid Nahavandi

Research output: Contribution to journalArticleResearchpeer-review

45 Citations (Scopus)


A new portfolio risk measure that is the uncertainty of portfolio fuzzy return is introduced in this paper. Beyond the wellknown 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 achievemore optimal solutions than using GA, although GA can offer a series of well-diversified portfolio solutions diagrammed in a Pareto frontier.
Original languageEnglish
Pages (from-to)656 - 676
Number of pages21
JournalIEEE Transactions on Fuzzy Systems
Issue number3
Publication statusPublished - 2015

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