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arXiv · 1401.3133

Capital adequacy tests and limited liability of financial institutions

Pablo Koch-Medina·Santiago Moreno-Bromberg·Cosimo Munari
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Abstract

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.

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Pablo Koch-Medina, Santiago Moreno-Bromberg, Cosimo Munari. 2014-01-14. Capital adequacy tests and limited liability of financial institutions. https://arxiv.org/abs/1401.3133

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