This paper studies how the proportion of fixed- and variable-rate mortgages affects business cycles and welfare. I develop and solve a New Keynesian dynamic stochastic general equilibrium model with a housing market and a group of constrained individuals who need housing collateral to obtain loans. The model predicts that with mostly variable-rate mortgages, an exogenous interest rate shock has larger effects on borrowers than in a fixed-rate economy. For plausible parameterizations, aggregate differences are muted by wealth effects on labor supply and by the presence of savers. For given monetary policy, a high proportion of fixed-rate mortgages is welfare enhancing.