We exploit the exogenous shock to the Brazilian banking system caused by the international turmoil of 2008 and find evidence that the run to systemically important banks is better explained by the perception of a too-big-to-fail policy than by bank fundamentals. We infer that the extra inflow of deposits received by systemically important banks during crises gives them an important competitive advantage. Our analysis also indicates that a bank’s share of funding from institutional investors affects the nonfinancial firms’ and institutional investors’ decision to run.