Mortgage Convexity

Abstract

Most home mortgages in the U.S. are fixed-rate loans with an embedded prepayment option. When long-term rates decline, the effective duration of mortgage-backed securities (MBS) falls due to heightened refinancing expectations. I show that these changes in MBS duration function as large-scale shocks to the quantity of interest rate risk that must be borne by professional bond investors. I develop a simple model in which the risk tolerance of bond investors is limited in the short run, so these fluctuations in MBS duration generate significant variation in bond risk premia. Specifically, bond risk premia are high when aggregate MBS duration is high. The model offers an explanation for why long-term rates may appear to be "excessively sensitive" to movements in short rates and explains how changes in MBS duration act as a positive-feedback mechanism that amplifies interest rate volatility. I find strong support for these predictions in the time series of U.S. government bond returns.