Optimal bailouts, bank's incentive and risk

We show how the impact of a government bailout in the form of liquidity assistance on the ex ante effort of a representative bank depends on the volatility of its investment. The bank's investment delivers a cashflow that follows a geometric Brownian motion and the government guarantees the bank's liabilities. To counter the bank's expectations of a bailout, the government may choose a tighter liquidity policy when the bank's effort is not observable. This tighter liquidity induces more prudent ex ante behavior by the bank, but it may have the opposite effect when investment volatility is high. This novel effect arises because the bank could be discouraged to be prudent precisely because the chances of receiving liquidity assistance are low.