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We examine the relation between intensity of competition in the loan market and risk of bank failure, in a model with adverse selection. As well established, the presence of the two opposite margin and risk-shifting effects creates conditions for nonmonotonicity: the conventional competition-fragility view may be challenged at high interest rates. These rates may however be too high to be compatible with oligopolistic equilibrium conditions. The challenging competition-stability view has been argued in terms of a representative borrower managing the profitability-safeness trade-off under moral hazard. However, the representative borrower assumption is not innocuous, playing down by construction the margin effect. The paper considers the adverse selection situation where that trade-off is managed by banks facing heterogeneous borrowers, and shows analytically, in the case of a trapezoidal distribution of idiosyncratic and systemic risk factors, that the conventional view is always valid.