The best gain-loss ratio is a poor performance measure
Please cite this item using this persistent URLhttp://hdl.handle.net/11693/20706
SIAM Journal on Financial Mathematics
- Research Paper 
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 O and works best in that case. For general O 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. © 2013 Society for Industrial and Applied Mathematics.