The best gain-loss ratio is a poor performance measure
AbstractThe 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 $\Omega$, and works best in that case. For general $\Omega$ and in most continuous time models, the best gain-loss is either infinite or fails to be attained. In addition, it displays an odd behaviour 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.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1209.6439.
Date of creation: Sep 2012
Date of revision: Dec 2012
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-10-06 (All new papers)
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