The Value of the Bank under Endogenous Liquidity Risk: The Modigliani-Miller Theorem Revisited

Abstract

This paper demonstrates that the Modigliani Miller Theorem on capital structure does in general not apply to banks when faced with endogenous liquidity risk in form of bank runs and asset illiquidity. The Modigliani Miller Theorem states that under certain assumptions, firms with different capital structure must have same values if they have identical return distributions (risk class). This paper shows, under endogenous liquidity risk the bank's risk class changes in debt ratio and coupons demanded by depositors such that the Modigliani Miller Theorem can in general not apply when repricing of risk in form of higher coupons is taken into account. In equilibrium, bank value is non-monotone in capital structure. In particular, only the all equity financed bank achieves the highest risk class. This paper offers a new perspective on Modigliani Miller from the view point of a game theoretic setting in which a bank sets capital structure and coupons to maximize equity value where the bank internalizes the effect her choice has on depositors' coordination behaviour and thus bank stability.