Systematic risk, bank moral hazard, and bailouts

We show that the impact of government bailouts (liquidity injections) on a representative bank's risk taking depends on the level of systematic risk of its loans portfolio. In a model where bank's output follows a geometric Brownian motion and the government guarantees bank's liabilities, we show first that more generous bailouts may or may not induce banks to take on more risk depending on the level of systematic risk; if systematic risk is high (low), a more generous bailout decreases (increases) bank's risk taking. Second, the optimal liquidity policy itself depends on systematic risk. Third, the relationship between bailouts and bank's risk taking is not monotonic. When systematic risk is low, the optimal liquidity policy is loose and more generous bailouts induce banks to take on more risk. If systematic risk is high and the optimal liquidity policy is tight, less generous bailouts induce banks to take on less risk. However, when high systematic risk makes a very tight liquidity policy optimal, a less generous bailout could increase bank's risk taking. While in this model there is only one representative bank, in an economy with many banks, a higher level of systematic risk could also be a source of systemic risk if a tighter liquidity policy induces correlated risk taking choices by banks.