标题： 最大收益-损失比率是一种糟糕的绩效衡量标准 显示英文标题

标题： The best gain-loss ratio is a poor performance measure

摘要： 从规范的角度来看，增减比率被认为具有非常好的性质。 作为确认，我们证明了在存在随机禀赋的情况下，最佳市场增减比率是一个可接受性指数，并为其在一般概率空间上的对偶表示提供了依据。 然而，增减比率的设计初衷是为了有限的$\Omega$，在这种情况下表现最佳。 对于一般的$\Omega$和大多数连续时间模型，最佳增减比率要么是无限大，要么无法达到。 此外，由于其尺度不变性属性，它表现出一种奇怪的行为，在此背景下似乎并不理想。 这些缺陷充分证明了（最佳）增减比率是一种糟糕的绩效衡量标准。 显示英文摘要

摘要： 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 $\Omega$, 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.