We document that overcollateralisation of banks’ secured liabilities is positively associated with the risk premium on their unsecured funding. We rationalize this finding in a theoretical model in which costs of asset encumbrance increase collateral haircuts and the endogenous risk of a liquidity-driven bank run. We then test the model’s predictions using a novel dataset on asset encumbrance of the European banks. Our empirical analysis demonstrates that banks with more costly asset encumbrance have higher rates of overcollateralisation and rely less on secured debt. Consistent with theory, the effects are stronger for banks that are likely to face higher fire-sales discounts. This evidence acts in favour of the hypothesis that asset encumbrance increases bank risk, although this relationship is rather heterogeneous.