We provide a model with endogenous portfolios of secured and unsecured household debt. Secured debt is collateralized by owner-occupied housing whereas unsecured debt can be discharged according to bankruptcy regulations. We show that the calibrated model matches important quantitative characteristics of observed wealth and debt portfolios for prime-age consumers in the U.S. We then establish the quantitative result that home equity does not serve as informal collateral for unsecured debt since, as in the data, unsecured debtors hold small amounts of home equity in equilibrium. Thus, observed variations in homestead exemptions, which are an important part of U.S. bankruptcy regulation, have a small effect on the quantity and price of unsecured debt.