What risks could stablecoins pose to the financial system? We argue that the stabilization mechanisms of stablecoins give rise to the risk of confidence runs, which can propagate to broader cryptoasset markets and the traditional financial sector. We also argue that stablecoins can contribute to financial stability risks by facilitating the buildup of leverage and liquidity mismatch in decentralized finance. Such risks cannot be addressed by ensuring the price stability of stablecoins alone. Finally, we explore the potential implications of stablecoins for the current system of bank-intermediated credit and for monetary policy.