This paper provides a critical analysis of the subadditivity axiom, which is the key condition for
coherent risk measures as introduced by Artzner et al. (1999). Contrary to the subadditivity
assumption, bank mergers can create extra risk. We begin with an analysis how a merger affects
depositors, junior or senior bank creditors, and bank owners. Next it is shown that bank mergers can
result in higher payouts having to be made by the deposit insurance scheme. Finally, we
demonstrate that if banks are interconnected via interbank loans, a bank merger could lead to
additional contagion risks. We conclude that the subadditivity assumption should be rejected, since a
subadditive risk measure, by definition, cannot account for such increased risks.