We study comonotonicity of regulatory risk measures in terms of the primitives of the theory of risk measures: acceptance sets and eligible 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. These findings seem to call for a renewed discussion about the meaning and the role of comonotonicity within the theory of regulatory risk measures.
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