Weakening the Gain-Loss-Ratio measure to make it stronger

The Gain-Loss-Ratio, proposed by Bernardo and Ledoit (2000), can either be used as a performance measure on a market with known prices or to derive price intervals in incomplete markets. For both applications, there is a considerable theoretical drawback: it reaches infinity for nontrivial cases in many standard models with continuous probability space. In this paper, a more general ratio is proposed, which includes the original Gain-Loss-Ratio as a limit case. This “Substantial Gain-Loss-Ratio” is applicable in case of continuous probabilities. Additionally, in its function as a performance measure it helps illuminate the source of out-performance that a portfolio reveals.