Shocks to a bank's ability to raise liquidity at short notice can trigger depositor panics. Why don't banks take a more active role in managing these risks? We study contingent risk management (hedging) in a standard global-games model of a bank run. Banks fail to hedge precisely when the exposure to a shock is most severe, just when risk management would have the biggest impact. Higher bank capital and broader deposit-insurance coverage crowd out hedging by banks that already manage risk, yet encourage more banks to establish risk management desks in the first place. The model also yields testable implications for hedging incentives and policy design.