Mortgage Convexity

Mortgage Convexity The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Hanson, Samuel Gregory. "Mortgage Convexity." Journal of Financial Economics (forthcoming). (Internet Appendix at http:// www.people.hbs.edu/shanson/MBS_IA_20140104.pdf) Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:12175237 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#OAP Mortgage Convexity Samuel G. Hanson Harvard Business School [email protected] This draft: January 2014 First draft: July 2012 Abstract Most home mortgages in the United States 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 US government bond returns. I thank seminar participants at the Boston University, Federal Reserve Board, the Copenhagen Business School FRIC’13Conference, as well as John Campbell, Anna Cieslak, Robin Greenwood, Arvind Krishnamurthy, Lasse Pedersen, Erik Stafford, Jeremy Stein, Larry Summers, Adi Sunderam, and Dimitri Vayanos for helpful comments. I am grateful to an anonymous referee for many helpful suggestions. I gratefully acknowledge funding from the Harvard Business School Division of Research. 1 Introduction A distinguishing feature of bond markets in the United States is the prominent role of fixed-rated home mortgages. Most fixed-rate mortgages issued in the US grant the borrower the right to prepay the loan at any time without penalty. When long-term interest rates decline, the option to prepay the mortgage and refinance at the current interest rate moves towards the money. Because lenders expect to be repaid sooner, the effective duration of outstanding mortgage- backed securities (MBS) falls– i.e., the sensitivity of MBS prices to changes in long-term yields declines. Conversely, as long-term interest rates rise, the prepayment option moves out of the money and the effective duration of MBS rises. To quote a Wall Street adage, this means that a mortgage-backed security “goes up like a 2 year bond”when rates fall and “goes down like a 6 year”when rates rise. More formally, the negative relationship between price and yield is convex for a noncallable bond. By contrast, the price-yield relation for callable bonds such as MBS is typically concave– a feature that bond investors call “negative convexity.” Aggregate mortgage refinancing activity varies significantly over time. Because refinancing entails large financial and nonfinancial costs, households typically follow a trigger rule, refinancing only when their option is suffi ciently far in the money. Thus, depending on the past path of mortgage rates, there are times when many households move from being far from refinancing to being close to refinancing and vice versa. I argue that the resulting changes in aggregate MBS duration act as massive supply shocks to the total quantity of interest rate risk that must be borne by investors in the broader bond market. Because these shifts in bond market duration are large relative to bond investors’risk tolerance, they have a significant impact on equilibrium term premium– i.e., on the expected return on long-term default-free bonds over short-term default- free bonds. In summary, time-variation in aggregate mortgage refinancing has a significant effect on the pricing of interest rate risk throughout the US fixed income market and, in particular, has a large impact on US Treasury yields. Why do shifts in expected household mortgage refinancing affect the aggregate amount of interest rate risk that bond market investors must bear? First, household borrowers only gradu- ally exercise their prepayment options following a decline in prevailing mortgage rates. Second, household borrowers do not alter their bond holdings to hedge their time-varying interest rate ex- posure. That is, households do not adjust their asset portfolios to offset the time-varying interest rate risk they are bearing on the liability side. The gradual response of mortgage prepayments to changes in mortgage rates and the lack of household hedging means that there are times when households are bearing more or less interest rate risk. Conversely, there are times when bond investors are bearing less or more risk. Thus, shifting refinancing expectations generate a form of aggregate market congestion: there are times when most households are effectively borrowing long term and other times when most are borrowing short term. If the risk-bearing capacity of professional bond investors is limited in the short run, then the term premium must adjust to induce investors to bear these risks. The sheer size of the MBS market within the US bond market plays a crucial role in this story. Bond markets have witnessed several MBS duration supply shocks that are larger than 1 the shift in duration induced by the Federal Reserve’sQuantitative Easing policies from 2008 to 2012. For instance, there have been several occasions when the quarterly change in MBS duration was equivalent to a $1 trillion increase (in 2012 dollars) in the supply of 10-year Treasury notes, with a corresponding reduction in the supply of short-term T-bills. By way of comparison, the quarterly new-issue supply of 10-year Treasury notes in 2012 was roughly $65 billion. Thus, past shifts in MBS duration have arguably been very large relative to the risk tolerance of bond market arbitrageurs. I develop a simple model of this mortgage convexity mechanism. The model has the following key ingredients. First, expectations of future household mortgage refinancing vary over time, which induces shifts in the effective duration of household mortgage borrowing. Second, aggregate bond risks are priced by risk-averse, specialized bond investors as in Vayanos and Vila (2009). This ensures that demand curves for aggregate bond risks slope downward, so the term premium must adjust to induce investors to absorb the aggregate supply of bond duration. Specifically, the model predicts that measures of aggregate bond market duration, which derive most of their power from variation in MBS duration, should positively predict bond excess returns. Furthermore, since shocks to MBS duration are fairly transient, one would expect fluctuations in MBS duration to lead to high frequency variation in bond risk premia. The model shows how negative MBS convexity may contribute to the excess sensitivity of long-term yields to movements in short rates (Gurkaynak, Sack, and Swanson (2005)) and, more generally, to the excess volatility of long-term yields (Shiller (1979)). Excess sensitivity reflects what might be called a “MBS duration spiral.” An initial shock to the short rate directly raises long yields due to the expectations hypothesis. The rise in long yields raises the duration of MBS. The term premium must rise in order to induce risk-averse bond investors to bear the larger aggregate quantity of interest rate risk. The resulting rise in yields further raises MBS duration, which further raises the term premium, and so on. Thus, the fact that MBS duration is increasing in long yields gives rise to a positive-feedback channel that generates excess sensitivity and excess volatility. The model also suggests that this positive-feedback mechanism is strongest when the mortgage market is on a “refinancing cliff”–i.e., when a small movement in long rates will significantly impact refinancing behavior and, hence, MBS duration. The model therefore predicts that excess sensitivity and volatility should be most pronounced when the MBS market is more negatively convex. I also show that an MBS duration shock should have a larger effect on the expected excess returns of long-term bonds than on those of intermediate-term bonds. This is a natural conse- quence of the fact that an MBS duration shock raises the current duration risk premium in bond markets. However, since these shocks are transient, shocks to MBS duration have a humped- shaped effect on the yield curve and the forward rate curve. The effects of a supply shock on yields– which equals the effect on the bond’s average returns over its lifetime– will be greater for intermediate term bonds than for long-term bonds when the supply shock is expected to be short-lived. That is, a shock to MBS duration increases the curvature of the yield curve. This suggests that transient shocks to MBS duration may account for some of the predictive power of the Cochrane and Piazzesi (2005) factor which picks up time-variation in the curvature of the 2 yield curve and is useful for forecasting transitory variation in bond returns. I find strong support for these predictions in US interest rate data between 1989 and 2011. Measures of MBS duration are strong predictors of excess government bond returns. And they appear to contain information that is not reflected in traditional forecasting variables based on the current shape of the yield curve.

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