The theory of acceptance sets and their associated risk measures plays a key
role in the design of capital adequacy tests. The objective of this paper is to
investigate, in the context of bounded financial positions, the class of
surplus-invariant acceptance sets. These are characterized by the fact that
acceptability does not depend on the positive part, or surplus, of a capital
position. We argue that surplus invariance is a reasonable requirement from a
regulatory perspective, because it focuses on the interests of liability
holders of a financial institution. We provide a dual characterization of
surplus-invariant, convex acceptance sets, and show that the combination of
surplus invariance and coherence leads to a narrow range of capital adequacy
tests, essentially limited to scenario-based tests. Finally, we emphasize the
advantages of dealing with surplus-invariant acceptance sets as the primary
object rather than directly with risk measures, such as loss-based and
excess-invariant risk measures, which have been recently studied by Cont,
Deguest, and He (2013) and by Staum (2013), respectively
