Overcoming Dimensional Dependence of Worst Case Scenarios and Maximum Loss

Maximum Loss over admissibility domains with a specified probability mass shows a peculiar kind of dimensional dependence: for a fixed portfolio and fixed probability of the admissibility domain, the inclusion of additional irrelevant risk factors increases Maximum Loss. For elliptical distributions we propose a definition of Maximum Loss which we show to be free of this undesirable property. If we characterise the admissibility domain by its Mahalanobis radius instead of its probability mass, the inclusion of irrelevant risk factors, or of risk factors which are highly correlated to other risk factors does not affect Maximum Loss