The aim of this paper is twofold. First, I study how the proportion of …xed and variable-rate mortgages in an economy can a¤ect the way shocks are propagated. Second, I analyze optimal implementable simple monetary policy rules and the welfare implications of this proportion. I develop and solve a New Keynesian dynamic stochastic general equilibrium model that features a housing market and a group of constrained individuals who need housing collateral to obtain loans. A given proportion of constrained households borrows at a variable rate, while the rest borrows at a …xed rate.The model predicts that in an economy with mostly variable-rate mortgages, an exogenous interest rate shock has larger e¤ects on borrowers than in a …xed-rate economy. Aggregate e¤ects are also larger for the variable-rate economy. For plausible parametrizations, di¤erences are muted by wealth e¤ects on labor supply and by the presence of savers. More persistent shocks, such as in ‡ation target and technology shocks, cause larger aggregate di¤erences. From a normative perspective I …nd that, in the presence of collateral constraints, the optimal Taylor rule is less aggressive against in ‡ation than in the standard sticky-price model. Furthermore, for given monetary policy, a high proportion of …xed-rate mortgages is welfare enhancing.