The Best Gain-Loss Ratio is a Poor Performance Measure
Date
2013-03-06Source 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
ArticleItem Usage Stats
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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 RatioAcceptability Indexes
Incomplete Markets
Martingales
Quasi-concave Optimization
Duality Methods
Market Modified Risk Measures