(Society for Industrial and Applied Mathematics, 2013-03-06) Biagini, S.; Pinar, M. Ç.
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.
