In this paper, I analyze the ability of monetary policy to stabilize both the macroeconomy and financial markets under two different scenarios: fixed- and variable-rate mortgages. I develop and solve a new Keynesian dynamic stochastic general equilibrium model (DSGE) that features a housing market and a group of constrained individuals who need housing collateral to obtain loans. A given share of constrained households borrows at a variable rate, whereas the rest borrow at a fixed rate. I consider two alternative ways of introducing a macroprudential approach to enhancing financial stability: one in which monetary policy, using the interest rate as an instrument, responds to credit growth; and a second one in which the macroprudential instrument is instead the loan-to-value ratio (LTV). The results show that when rates are variable, a countercyclical LTV rule performs better in stabilizing financial markets than monetary policy. However, when rates are fixed, even though monetary policy is less effective in stabilizing the macroeconomy, it does a good job in promoting financial stability.