2015年-BIS国际清算银行_Mortgage_risk_and_the_yield_curve_53页_556kb

Summary of "Mortgage Risk and the Yield Curve"

Core Content

This paper investigates the feedback mechanism between the risk of mortgage-backed securities (MBS) and the yield curve. It proposes a dynamic equilibrium term structure model that incorporates the supply shocks from changes in MBS duration and convexity, and shows how these factors influence interest rate risk premia and yield volatility.

Main Points

1. MBS Duration and Bond Risk Premia

• MBS duration positively predicts nominal and real bond excess returns, especially for longer maturity bonds.
• The effect is weaker for real bonds due to their lower volatility and imperfect correlation with nominal rates.
• A one standard deviation change in MBS duration leads to:
  • A 381 basis point increase in the expected one-year excess return on a 10-year nominal bond.
  • A 199 basis point increase in the expected one-year excess return on a 10-year real bond.
• These effects imply a 38 basis point increase in 10-year nominal yields (assuming the effect occurs within a year).

2. Transient Nature of MBS Duration Shocks

• The predictive power of MBS duration on bond excess returns is transitory, with little additional effect beyond one year.
• The model accounts for fast mean reversion in MBS duration by linking it to interest rate mean reversion and mortgage refinancing.
• The Federal Reserve's increasing role in the MBS market has made the MBS duration channel weaker over time.

3. MBS Convexity and Yield Volatility

• MBS convexity increases interest rate volatility, with a hump-shaped term structure.
• The effect is most pronounced for maturities between two and three years.
• A one standard deviation change in MBS dollar convexity leads to a 37 basis point change in 2-year bond yield volatility.
• The model is calibrated to match these empirical findings and replicates them with similar economic magnitudes.

Key Information

• MBS are a significant part of the US fixed income market, comparable in size to Treasuries.
• MBS can be prepaid and refinanced, which causes large variations in duration.
• Duration is a measure of the sensitivity of MBS prices to changes in interest rates.
• The model assumes that financial institutions are the main absorbers of MBS risk, and their risk aversion and mean-variance preferences drive the equilibrium term structure.
• The market price of interest rate risk is proportional to the dollar duration of the total bond supply.
• The refinancing incentive is defined as the difference between the average MBS coupon and the reference long-term interest rate.
• The dollar convexity is the negative of the sensitivity of MBS duration to interest rate changes.
• The model is consistent with empirical evidence and is supported by data from 1997 to 2014.

Model Structure

• The model is a parsimonious dynamic equilibrium term structure model.
• It includes an affine factor for aggregate MBS dollar duration.
• The short rate follows a Vasicek (1977) process.
• The dynamics of MBS duration are given by:

$$
d D _ {t} = \kappa_ {D} (\theta_ {D} - D _ {t}) d t + \eta_ {y} d y _ {t} ^ {\bar {\tau}},
$$

where $ \kappa_D $ is the speed of mean reversion, $ \theta_D $ is the long-run mean, and $ \eta_y $ is the sensitivity of MBS duration to interest rate changes.

• The equilibrium term structure is given by:

$$
y _ {t} ^ {\tau} = \mathcal {A} (\tau) + \mathcal {B} (\tau) r _ {t} + \mathcal {C} (\tau) D _ {t},
$$

where $ \mathcal{A}(\tau) $, $ \mathcal{B}(\tau) $, and $ \mathcal{C}(\tau) $ are functions derived in the Online Appendix.

Empirical Support

• The statistical significance and magnitude of the estimates remain stable when controlling for standard predictors of bond risk premia and yield volatility, including yield factors, macroeconomic variables, and bond market liquidity measures.
• The predictive power of MBS duration and convexity is distinct from that of other factors, justifying the narrow focus of the paper on the MBS channel.
• The paper builds on previous studies, including Greenwood and Vayanos (2014), but differs in key aspects:
  • The net supply of bonds is endogenously driven by MBS duration.
  • The model jointly explains the effects of mortgage risk on both nominal and real bond risk premia and yield volatilities across different maturities.

Conclusion

The paper provides a theoretical and empirical framework that explains how MBS risk influences the yield curve and bond risk premia. It highlights the nonlinear and time-varying nature of this relationship, particularly the hump-shaped term structure of yield volatility. The model has practical implications for policy makers and market participants, as it shows that MBS duration and convexity play a significant role in shaping interest rate dynamics.