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      The Best Gain-Loss Ratio is a Poor Performance Measure

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      Author(s)
      Biagini, S.
      Pinar, M. Ç.
      Date
      2013-03-06
      Source Title
      SIAM Journal on Financial Mathematics
      Print ISSN
      1052-6234
      Electronic ISSN
      1945-497X
      Publisher
      Society for Industrial and Applied Mathematics
      Volume
      4
      Issue
      1
      Pages
      228 - 242
      Language
      English
      Type
      Article
      Item Usage Stats
      170
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      163
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      Abstract
      The gain-loss ratio is known to enjoy very good properties from a normative point of view. As a confirmation, we show that the best market gain-loss ratio in the presence of a random endowment is an acceptability index, and we provide its dual representation for general probability spaces. However, the gain-loss ratio was designed for finite Ω and works best in that case. For general Ω and in most continuous time models, the best gain-loss is either infinite or fails to be attained. In addition, it displays an odd behavior due to the scale invariance property, which does not seem desirable in this context. Such weaknesses definitely prove that the (best) gain-loss is a poor performance measure.
      Keywords
      Gain-loss Ratio
      Acceptability Indexes
      Incomplete Markets
      Martingales
      Quasi-concave Optimization
      Duality Methods
      Market Modified Risk Measures
      Permalink
      http://hdl.handle.net/11693/13066
      Published Version (Please cite this version)
      http://dx.doi.org/10.1137/120866774
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      • Department of Industrial Engineering 758
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