Abstract
This paper estimates the impact of the Federal Reserve’s 2008–2011 quantitative easing (QE) program on the US term structure of interest rates. We estimate an arbitrage-free term structure model that explicitly includes the quantity impact of the Fed’s trades on Treasury market prices. As such, we are able to estimate both the magnitude and duration of the QE price effects. We show that the Fed’s QE program affected forward rates without introducing arbitrage opportunities into the Treasury security markets. Short- to medium- term forward rates were reduced (\(<\)12 years), but the QE had little if any impact on long-term forward rates. This is in contrast to the Fed’s stated intentions for the QE program. The persistence of the rate impacts increased with maturity up to 6 years then declined, with half-lives lasting approximately 4, 6, 12, 8 and 4 months for the 1, 2, 5, 10 and 12 years forwards, respectively. Since bond yields are averages of forward rates over a bond’s maturity, QE affected long-term bond yields. The average impacts on bond yields were 327, 26, 50, 70, and 76 basis points for 1, 2, 5, 10 and 30 years, respectively.
Similar content being viewed by others
Notes
See Bernanke and Reinhart (2004) for a discussion of monetary policies around the zero lower bound for short-term interest rates.
This is because the spot rate is defined by the limit condition: \(R(t)=\underset{\Delta \rightarrow 0}{\lim }\left( \frac{1-P(t,t+\Delta )}{P(t,t+\Delta )}\cdot \frac{1}{\Delta }\right) \).
For example, for each \(T, \Psi (t,T)\) needs to be a semimartingale.
Bolder (2001) provides a good technical guide on implementing a Kalman filter.
This is sometimes called a Vasicek (1977) model.
We also explored the estimation using forward rates based on a polynomial spline smoothing procedure yielding similar results. For brevity these results are not reported in the subsequent text.
Data source: http://www.federalreserve.gov/econresdata/.
Instead, one could obtain estimated spot rates using the intercept of the smoothed GSW forward rate curve with the y-axis. We choose not to use these estimates because the intercept with the y-axis explicitly depends on the functional form of the smoothing function, which in turn, is greatly influenced by the prices of the long-term Treasuries. In reality, short-term Treasury rates (\(<\)1 year) are influenced more by the impact of the Fed’s short-term interest rate policies than the assumed shape of a smoothing function. Our estimation methodology avoids this potential bias.
See WSJ Blog, Market Beat, November 20, 2009, “Some Treasury Bill Rates Negative Again Friday;” Bloomberg, November 19, 2009, “US 3-month Bills Turn Negative on Concern Risk Rally Overdone;” Bloomberg, June 27, 2011, “Treasury 4-week Bill Rates Negative for First Time since 2010;” WSJ Blog, Market Beat, August 4, 2011, “From One Crisis to Another: One Month T-Bill Yields go Negative Again.”
See Bloomberg.com/news, August 5, 2011, “BNY Mellon Makes Clients Pay for Deposits as Investors Seek Safety in Cash;” Online WSJ, August 5, 2011, “New Fee to Bank Cash.”
These adjusted probabilities are called the forward price martingale probability measures, see Jarrow (2009).
A par bond yield is that coupon payment that makes a bond’s current price equal its face value ($100). We compute the true coupon bond’s par-bond yield using the true zero-coupon bond prices.
The large difference between the 1 and 2 years yields is due to the fact that the 2-year Treasury note has coupons. If the 1 and 2 years Treasuries were both zero-coupon bonds, then the yields would be just a simple average of forward rates, and the 2 year’s yield would be \(>\)200 basis points.
References
Adrian T., Crump, R., & Moench, E. (2012). Pricing the term structure with linear regression. Working paper, Federal Reserve Bank of New York.
Babbs, S., & Nowman, K. B. (1999). Kalman filtering of generalized vasicek term structure models. Journal of Financial and Quantitative Analysis, 34(1), 115–130.
Bank, P., & Baum, D. (2004). Hedging and portfolio optimization in financial markets with a large trader. Mathematical Finance, 14, 1–18.
Baxter, M., & Rennie, A. (1996). Financial calculus: An introduction to derivative pricing. Cambridge: Cambridge Univ. Press.
Bernanke, B., & Reinhart, V. (2004). Conducting monetary policy at very low short-term interest rates. American Economic Review, 94(2), 85–90.
Bernanke, B., Reinhart, V., & Sack, B. (2004). Monetary policy alternatives at the zero bound: An empirical assessment. Brookings Papers on Economic Activity, 2, 1–78.
Bolder, D. (2001). Affine term-structure models: Theory and implementation. Bank of Canada Working Paper.
Brigo, D., & Mercurio, F. (2006). Interest rate models: Theory and practice—with smile, inflation and credit (2nd ed.). Berlin: Springer.
D’Amico, S., & King, T. (2012). Flow and stock effects of large-scale treasury purchases: Evidence on the importance of local supply. Finance and Economics Discussion Series 2012–2044. Washington: Board of Governors of the Federal Reserve System.
Fuster, A., & Willen, P. (2010). $1.25 Trillion is still real money: Some facts about the effects of the Federal Reserve’s Mortgage Market Investments. Working paper, Federal Reserve Bank of Boston.
Gagnon, J., Raskin, M., Remache, J., & Sack, B. (2010). Large-scale asset purchases by the federal reserve: Did they work? Federal Reserve Bank of New York Staff Report no. 441.
Gürkaynak, R., Sack, B., & Wright, J. (2007). The U.S. Treasury yield curve: 1961 to the present. Journal of Monetary Economics, 54, 2291–2304.
Hamilton, J., & Wu, J. (2012). The effectiveness of alternative monetary policy tools in a zero lower bound environment. Journal of Money, Credit, and Banking, 44, 3–46.
Heath, D., Jarrow, R., & Morton, A. (1992). Bond pricing and the term structure of interest rates: A new methodology for contingent claims valuation. Econometrica, 60, 77–105.
Jarrow, R. (1992). Market manipulation, bubbles, corners, and short-squeezes. Journal of Financial and Quantitative Analysis, 27, 311–336.
Jarrow, R. (2009). The term structure of interest rates. Annual Review of Financial Economics, 1, 69–96.
Jarrow, R., Protter, P., & Roch, A. (2012). A liquidity based model for asset price bubbles. Quantitative Finance, 12(9), 1339–1349.
Jeanblanc, M., Yor, M., & Chesney, M. (2009). Mathematical methods for financial markets. Berlin: Springer.
Joyce, M., Lasaosa, A., Stevens, I., & Tong, M. (2010). The financial market impact of quantitative easing. Bank of England Working Paper 393.
Krishnamurthy, A., & Vissing-Jorgensen, A. (2011). The effects of quantitative easing on interest rates: channels and implications for policy. Working Paper.
Li, C., & Wei, M. (2012). Term structure modelling with supply factors and the Federal Reserve’s Large Scale Asset Purchase Programs. Working paper, Federal Reserve Board of Governors, Division of Monetary Affairs, Washington, D.C.
Meaning, J., & Zhu, F. (2011). The impact of recent central bank asset purchase programmes. BIS Quarterly Review, December, 73–83.
Oda, N., & Ueda, K. (2005). The effects of the Bank of Japan’s zero interest rate commitment and quantitative monetary easing on the yield curve: A macro-finance approach. Bank of Japan Working Paper No. 05-E-6.
Svensson, L. (1994). Estimating and interpreting forward rates: Sweden 1992–4, NBER Working Paper.
Swanson, E. (2011). Let’s twist again: A high-frequency event-study analysis of operation twist and its implications for QE2. Brookings Papers on Economic Activity.
Vasicek, O. (1977). An equilibrium characterization of the term structure. Journal of Financial Economics, 5, 177–188.
Wright, J. (2012). What does monetary policy do to long-term interest rates at the zero lower bound? Working paper, Johns Hopkins University.
Author information
Authors and Affiliations
Corresponding author
Additional information
Helpful comments from workshops at the Federal Reserve Bank of New York and the Federal Reserve Board in Washington D.C. are gratefully acknowledged.
Appendix
Appendix
Proof of Theorem 1
From expression (11), for \(t\le \tau \), we have
The HJM condition on \(f(t,T)\) implies that
The HJM condition on \(F(t,T)\) implies that
where \(\Phi _{i}(t)\) (\(\phi _{i}(t)\)) is the price of risk for factor i with (without) the Fed’s price impact.
From expression. (27) and (28), we obtain the difference in risk premium:
From expression (11), for \(t>\tau \), we have
The HJM condition on \(F(t,T)\) implies that
From expressions (27) and (29), we obtain the difference in risk premium:
To sum up, the Fed’s impact on the risk premium is
In the special case of a one-factor model, we have
\(\square \)
Rights and permissions
About this article
Cite this article
Jarrow, R., Li, H. The impact of quantitative easing on the US term structure of interest rates. Rev Deriv Res 17, 287–321 (2014). https://doi.org/10.1007/s11147-014-9099-7
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11147-014-9099-7
Keywords
- Quantitative easing
- The term structure of interest rates
- Arbitrage-free models
- Large trader
- Quantity impact on price