Which eligible assets are compatible with comonotonic capital requirements?

TL;DR

This paper investigates how the choice of eligible assets influences the compatibility of comonotonic risk measures with capital adequacy, revealing limitations with risky assets and emphasizing the importance of asset selection.

Contribution

It demonstrates that comonotonicity depends heavily on the eligible asset choice and is generally only compatible with risk-free assets in capital adequacy frameworks.

Findings

Comonotonicity is incompatible with risky eligible assets under VaR and Expected Shortfall.

Compatibility with comonotonicity is primarily achieved with risk-free assets.

The study challenges the traditional role of comonotonicity in capital adequacy.

Abstract

Within the context of capital adequacy, we study comonotonicity of risk measures in terms of the primitives of the theory: acceptance sets and eligible, or reference, assets. We show that comonotonicity cannot be characterized by the properties of the acceptance set alone and heavily depends on the choice of the eligible asset. In fact, in many important cases, comonotonicity is only compatible with risk-free eligible assets. The incompatibility with risky eligible assets is systematic whenever the acceptability criterion is based on Value at Risk or any convex distortion risk measure such as Expected Shortfall. These findings qualify and arguably call for a critical appraisal of the meaning and the role of comonotonicity within a capital adequacy context.