We define a financial system to be fragile if small shocks have disproportionately large effects. In a model of financial intermediation, we show that small shocks to the demand for liquidity cause either high asset-price volatility or bank defaults or both. Furthermore, as the liquidity shocks become vanishingly small, the asset-price volatility is bounded away from zero. In the limit economy, with no shocks, there are many equilibria. However, if banks face idiosyncratic liquidity shocks, then the only equilibria that are robust to the introduction of small aggregate risk involve stochastic consumption as well as volatile asset, prices. (JEL: D5, D8, G2)