We examine the portfolio choice of banks in a micro-funded model of runs. To insure riskaverse investors against liquidity risk, competitive banks offer demand deposits. We use global games to link the probability of a bank run to the portfolio choice. Based upon interim information about risky investment, banks liquidate investments to hold a safe asset. This partial hedge against investment risk reduces the withdrawal incentives of investors for a given deposit rate. As a result of the portfolio choice, (i) banks provide more liquidity ex ante (so banks offer a higher deposit rate), and (ii) the welfare of investors increases.