The Response of Interest Rates to U.S. and U.K. Quantitative Easing

Transcription

1 The Response of Interest Rates to U.S. and U.K. Quantitative Easing Jens H.E. Christensen & Glenn D. Rudebusch Federal Reserve Bank of San Francisco Term Structure Modeling and the Lower Bound Problem Lecture III.1 European University Institute Florence, September 9, 2015 The views expressed here are solely the responsibility of the authors and should not be interpreted as reflecting the views of the Federal Reserve Bank of San Francisco or the Board of Governors of the Federal Reserve System. 1 / 47

2 Motivation The financial crisis of brought the monetary policy target rate to its effective lower bound in the U.S. and the U.K. As a consequence, both the Fed and BoE were forced into the realm of unconventional monetary policy. In both countries, the primary tool has been so-called large-scale asset purchase (LSAP) programs, frequently referred to as quantitative easing (QE). The U.S. and U.K. programs appear similar relative to GDP and the size of their respective fixed-income markets. So should we expect similar yield responses? The purpose of this paper is to better understand the effect of the LSAP/QE programs on government bond yields and related interest rates. 2 / 47

3 Our Contribution 3 / 47 We analyze both the U.S. and the U.K. experience with bond purchases using an event study approach. We perform a real-time decomposition of yield changes into changes in policy expectations and term premiums. This can address the question of whether the so-called signaling or portfolio balance channel was at work in each country. We find significant differences in the yield response across the two countries. Differences in market functioning as well as central bank communication may explain this variation in response patterns.

4 Outline 4 / 47 1 Introduction 2 How Do Bond Purchase Programs Work? 3 Existing Literature and Event Study Approach 4 Model Framework 5 Results of U.S. Analysis 6 Results of U.K. Analysis 7 Cross-Country Analysis 8 Conclusion

5 How Do Bond Purchase Programs Work? Theoretically, bond purchases can lower yields through three main channels: 1 Signaling channel: Announcements of central bank bond purchases provide information to market participants about current or future economic conditions or monetary policy. 2 Portfolio balance channel: This channel operates when the central bank bond purchases, which change the relative supplies of assets held by the private sector, induce equilibrating changes in relative yields. The crucial departure from standard theory is that bonds of different maturities are imperfect substitutes. 3 Liquidity channel: It is also possible that purchases of longer-term securities affect yields by increasing market liquidity and reducing liquidity premiums, at least temporarily. Our study focuses on the first two channels. 5 / 47

6 Existing Literature on U.S. Experience with LSAPs The existing literature is dominated by papers that rely on event studies. A few notable examples include: Gagnon et al. (2011) use the Kim and Wright (2005) model. They mainly attribute yield declines following announcements regarding the Fed s first LSAP program to declines in term premiums, i.e., the portfolio channel is key. Krishnamurthy and Vissing-Jorgensen (2011) draw similar conclusions although without using any models. D Amico and King (2013) study the flow effects of the $300 billion Treasury purchases in the first LSAP program and find a significant, lasting effect. Bauer and Rudebusch (2014) account for estimation bias and emphasize the importance of the signaling channel. 6 / 47

7 U.S. LSAP Events Date Event Description 11/25/08 Initial LSAP Fed announces purchases of $100 billion in GSE announcement debt and up to $500 billion in MBS. 12/1/08 Bernanke speech Chairman Bernanke indicates that the Fed could purchase long-term Treasury securities. 12/16/08 FOMC statement The first FOMC statement that mentions possible purchases of long-term Treasuries. 1/28/09 FOMC statement FOMC states that it is ready to expand agency debt and MBS purchases and to purchase longterm Treasuries. 3/18/09 FOMC statement Fed will purchase an additional $750 billion in agency MBS and $100 billion in agency debt as well as $300 billion in long-term Treasuries. 8/12/09 FOMC statement Fed is set to slow the pace of the LSAP. The final purchases of Treasury securities will be in the end of October instead of mid-september. 9/23/09 FOMC statement Fed s purchases of agency debt and MBS will end in the first quarter of 2010, while its Treasury purchases will end as planned in October. 11/4/09 FOMC statement Amount of agency debt capped at $175 billion instead of the $200 billion previously announced. 7 / 47

8 The Event Study Approach To set the stage, we first look at the data. 8 / 47 Key assumption: Each announcement is a complete surprise and the entire reaction occurs on the announcement date. Potential biases include: Underestimation of effect as market participants may have anticipated some central bank action. Underestimation of effect as a one-day event window may be too short to capture all of the announcements effects. Overestimation of effect as a one-day window may capture an exaggerated initial market response that is unwound over time as investors expectations adjust. Final caveat: More than one thing happened on several event dates.

9 U.S. Treasury Yield Data 9 / 47 In the U.S. analysis, we use the following sample of daily U.S. Treasury yields: The data is from the Gürkaynak, Sack, and Wright (2007) database with eight maturities, {0.25, 0.5, 1, 2, 3, 5, 7, 10}, covering the period from December 1, 1987 to December 31, The data is updated daily and is publicly available at the website of the Board of Governors. This is the data analyzed in Gagnon et al. (2011). Also, it constitutes the core of the yield data used in the estimation of the Kim & Wright model. Finally, this data is also used in Christensen, Lopez, and Rudebusch (2010, 2012, 2014a,b, 2015a,b,c).

10 U.S. Treasury Yield Response 10 / 47 Event Maturity 6-month 1-year 2-year 5-year 10-year I Nov. 25, II Dec. 1, III Dec. 16, IV Jan. 28, V Mar. 18, VI Aug. 12, VII Sep. 23, VIII Nov. 4, Total net change

11 U.S. OIS Rate Response 11 / 47 Event Maturity 6-month 1-year 2-year 5-year 10-year I Nov. 25, II Dec. 1, III Dec. 16, IV Jan. 28, V Mar. 18, VI Aug. 12, VII Sep. 23, VIII Nov. 4, Total net change

12 Theoretical Foundation The key object of interest is the term premium of a bond maturing in τ years, which is defined as TP t (τ) = y t (τ) 1 τ t+τ t E P t [r s ]ds. That is, the term premium is the difference in expected return between a buy and hold strategy for a τ-year Treasury bond and an instantaneous rollover strategy at the risk-free rate r t. By having the above decomposition we can distinguish between changes in policy expectations and changes in term premiums. To make this operational, we rely on the arbitrage-free Nelson-Siegel (AFNS) models introduced in Christensen, Diebold, and Rudebusch (2011). 12 / 47

13 The AFNS Class of Models (1) Proposition: If the risk-free rate is defined by r t = L t + S t and the Q-dynamics of X t = (L t, S t, C t ) are given by dl t ds t = θ Q 1 0 λ λ θ Q 2 L t S t dt+σdw Q dc t 0 0 λ θ Q C 3 t where Σ is a constant matrix, then zero-coupon yields have the Nelson-Siegel factor structure: ( 1 e λτ) ( 1 e λτ ) y t (τ) = L t + S t + e λτ C t A(τ). λτ λτ τ This defines the AFNS model class. The constant yield-adjustment term, A(τ)/τ, ensures absence of arbitrage. t, 13 / 47

14 The AFNS Class of Models (2) Using the essentially affine risk premium specification of Duffee (2002), the P-dynamics are left unconstrained dl t ds t = κp 11 κ P 12 κ P 13 κ P 21 κ P 22 κ P θp 1 23 θ P dc t κ P 31 κ P 32 κ P 2 L t S t dt 33 θ3 P C t + σ σ 21 σ 22 0 σ 31 σ 32 σ 33 To reduce the number of parameters: dw L,P t dw S,P t dw C,P t. We follow CDR and restrict the Σ matrix to be diagonal. We employ a general-to-specific approach to obtain an appropriate specification of K P. 14 / 47

15 General-to-Specific Model Selection for the U.S. Alternative Goodness-of-fit statistics Specifications k p-value AIC BIC (1) Unrestricted K P 24 n.a. -561, ,172 (2) κ P 32 = , ,181 (3) κ P 32 = κp 31 = , ,189 (4) κ P 32 = κp 31 = κp 12 = , ,196 (5) κ P 32 =... = κp 13 = , ,205 (6) κ P 32 =... = κp 21 = , ,205 (7) κ P 32 =... = κp 23 = , ,174 The Akaike and Bayesian Information Criteria prefer the same specification of K P : KUS P κp κ P 21 κ P 22 κ P κ P 33 Finally, we try to account for the finite-sample bias discussed at length in Bauer et al. (2012). 15 / 47

16 The Preferred AFNS Model of U.S. Treasury Yields Our preferred specification of the AFNS model for U.S. Treasury yields has P-dynamics given by dl US t L US dst US = κ P dct US 21 κ P 22 κ P 23 θ P t 0 0 κ P 2 S US 33 θ3 P t dt Ct US σ dw L,P t + 0 σ 22 0 dw S,P t. 0 0 σ 33 dw C,P t Two things are worth noting regarding this specification: 1 The Nelson-Siegel level factor is restricted to be an independent unit-root process under both probability measures. 2 The four parameter restrictions in the mean-reversion matrix are statistically insignificant throughout our sample period. NB: This is the automated FRBSF term premium model. 16 / 47

17 Why Real-Time Analysis? Sigma L Sigma S Estimated value First LSAP announcement Nov. 25, Estimated value First LSAP announcement Nov. 25, We make a rolling real-time estimation of the preferred AFNS model for U.S. Treasury yields starting in January 2, This allows us to document the model s forecast performance and is consistent with the term premium definition. This contrasts with Bauer and Rudebusch (2014), who make a full sample estimation and look back in sample. 17 / 47

18 Model Performance (1) Rate in percent Kim & Wright model AFNS model First LSAP announcement Nov. 25, 2008 Correlation = 59.5% We compare our term premium to the Kim & Wright model. The two series have a relatively high correlation, but the KW term premium is notably smaller in periods when the target rate is near the bottom of the monetary policy cycle like the period since late 2008 that we are interested in analyzing. 18 / 47

19 Model Performance (2) 19 / 47 Forecasting method One-year forecast Two-year forecast Mean RMSE Mean RMSE Random walk Kim & Wright model AFNS model We compare the target rate forecasts from our model to those from the Kim & Wright model and the random walk assumption over the period from January 1998 to December The preferred AFNS model for the U.S. data is clearly competitive relative to the two benchmarks.

20 Model Performance (3) Rate in percent Kim & Wright model AFNS model Realized target rate First LSAP announcement Nov. 25, The chart shows the end-of-month two-year target rate forecasts as well as the subsequent target rate realization. Note the difficulty of the KW model in producing low target rate forecasts since This turns out to have implications for its ten-year Treasury yield decompositions. 20 / 47

21 Decomposition of U.S. Treasury Yield Response (1) 21 / 47 Date Model Avg. target rate Ten-year Treasury next ten years term premium Residual yield 11/25/08 KW AFNS /1/08 KW AFNS /16/08 KW AFNS /28/09 KW AFNS /18/09 KW AFNS /12/09 KW AFNS /23/09 KW AFNS /4/09 KW AFNS Net change KW AFNS

22 Decompositions from Shadow-Rate Model Date Model Avg. target rate Ten-year Treasury next ten years term premium Residual yield 11/25/08 CR B-CR /1/08 CR B-CR /16/08 CR B-CR /28/09 CR B-CR /18/09 CR B-CR /12/09 CR B-CR /23/09 CR B-CR /4/09 CR B-CR Net change CR B-CR The shadow-rate B-CR model leads to the same conclusion. 22 / 47

23 Decomposition of U.S. Treasury Yield Response (2) Net change in basis points Instantaneous forward rate Forecasted future spot rate Instantaneous forward term premium Time to maturity in years The chart shows the decomposition of the net response of the model-implied instantaneous forward rate curves. Policy expectations declined the most at the two- to three-year horizon consistent with a signaling effect. Term premiums declined most at long maturities. 23 / 47

24 Decomposition of U.S. Treasury Yield Response (3) 24 / 47 The yield decompositions from our preferred AFNS model indicate that 60 percent of the cumulative declines in the ten-year yield came from declines in policy expectations. This is consistent with the declines in OIS rates. Furthermore, if policy expectations actually declined as indicated by the AFNS model, it would be natural for term premiums to decline as well since the perceived policy uncertainty has declined. As a consequence, our estimated cumulative decline in the ten-year term premium of 29 basis points becomes an upper bound for the effect of the portfolio balance channel. Do the changes in the related markets for U.S. interest swap rates and industrial corporate bond yields support this interpretation?

25 U.S. LIBOR and Swap Rate Response 25 / 47 Event U.S. LIBOR and swap rates 3-month 2-year 5-year 10-year Nov. 25, Dec. 1, Dec. 16, Jan. 28, Mar. 18, Aug. 12, Sep. 23, Nov. 4, Total net change The reaction of U.S. LIBOR and swap rates is very similar to those of Treasury yields and OIS rates.

26 AA-rated corporate bond yields responded in a manner very similar to the Treasury bond yields. BBB-rated corporate bond yields (not shown) experienced slightly smaller declines. Thus, little evidence of market segmentation for close high-quality substitutes on these eight announcement dates. 26 / 47 U.S. Corporate Bond Yield Response (1) Event AA-rated U.S. industrial corporate bonds 6-month 1-year 2-year 5-year 10-year Nov. 25, Dec. 1, Dec. 16, Jan. 28, Mar. 18, Aug. 12, Sep. 23, Nov. 4, Total net change

27 Shorter-term speculative grade yields actually increased on the eight key LSAP announcement dates. The long-term speculative grade yields did decline, but much less than comparable Treasury yields. Concerns about credit risk and the severity of the crisis more than offset the positive effects of the policy actions. 27 / 47 U.S. Corporate Bond Yield Response (2) Event B-rated U.S. industrial corporate bonds 6-month 1-year 2-year 5-year 10-year Nov. 25, Dec. 1, Dec. 16, Jan. 28, Mar. 18, Aug. 12, Sep. 23, Nov. 4, Total net change

28 Does Signaling Affect Term Premiums? (1) Volatility in percent Twelve month options implied volatility First LSAP announcement Nov. 25, The chart shows the implied volatility of twelve-month options on eurodollar futures, a measure of policy uncertainty. This has declined from a pre-crisis average of about 255 basis points to average a mere 29 basis points since August If the risk of reversing policy is reduced by 89 percent, shouldn t the premium on this risk go down? 28 / 47

29 Does Signaling Affect Term Premiums? (2) Exp. Var. Ten-Year Term Premium CR Model Kim & Wright Model Constant (1.602) (1.901) (-1.840) (-2.932) (5.711) (-2.753) Implied volatility eurodollar options (4.500) (4.854) (12.421) (12.441) VIX (3.906) (4.302) (0.418) (0.956) R Table : Regressions of Term Premiums on Uncertainty Measures. Policy uncertainty clearly matter for term premiums! The average implied volatility declined 145 bps from the 11/25/08-7/29/11 period relative to the pre-crisis level Ten-year term premiums declined about 60 bps. Point: Even term premium declines might not reflect portfolio balance effects. 29 / 47

30 Summary of U.S. Analysis 30 / 47 Our results suggest the signaling channel was a dominating factor in driving down U.S. Treasury yields in response to the eight major LSAP announcements we analyze. In contrast, the portfolio balance channel appears to have played only a secondary role. Consistent with this there is little evidence of market segmentation in the U.S. even during this very stressed period. We speculate that the extended period language used by the FOMC might play a critical role for this outcome.

31 U.K. QE Events Date Event Description 2/11/09 February Press conference and Inflation Report indicated Inflation Report that asset purchases were likely. 3/5/09 MPC statement The MPC announced that it would purchase 75 billion of assets over three months. Gilt purchases would be restricted to the 5-25 year maturity range. 5/7/09 MPC statement The MPC announced that the amount of asset purchases would be extended by a further 50 billion to a total of 125 billion. 8/6/09 MPC statement The MPC announced that the amount of asset purchases would be extended to 175 billion and that the buying range would be extended to include gilts with residual maturity greater than three years. 11/5/09 MPC statement The MPC announced that the asset purchases would be extended to 200 billion. 2/4/10 MPC statement The MPC announced that the amount of asset purchases would be maintained at 200 billion. 10/6/11 MPC statement The MPC announced that the asset purchases would be extended to 275 billion. 31 / 47

32 Existing Literature on U.K. QE Experience 32 / 47 Joyce et al. (2011) is the most notable paper analyzing the U.K. QE experience. They focus on the first six events described on the previous slide. Their analysis of U.K. gilt yields and OIS rates suggest that term premiums in gilt yields declined a lot more than the policy expectations reflected in OIS rates. Hence, the portfolio channel appears to be the primary driver of the response of U.K. gilt yields. To set the stage, we again start by looking at the data.

33 U.K. Gilt Yield Data 33 / 47 In the U.K. analysis, we use the following sample of daily U.K. gilt yields: The data is from the website of the Bank of England with eight maturities, {0.25, 0.5, 1, 2, 3, 5, 7, 10}, covering the period from January 2, 1985 to December 31, The zero-coupon yields are constructed from underlying gilt prices using cubic-splines. The data is updated daily and is publicly available. This is the data analyzed in Joyce et al. (2011).

34 U.K. Gilt Yield Response 34 / 47 Event Maturity 6-month 1-year 2-year 5-year 10-year Feb. 11, Mar. 5, May 7, Aug. 6, Nov. 5, Feb. 4, Oct. 6, Total net change

35 U.K. OIS Rate Response Event Maturity 6-month 1-year 2-year 5-year 10-year Feb. 11, Mar. 5, May 7, Aug. 6, Nov. 5, Feb. 4, Oct. 6, Total net change U.K. OIS rates declined less than gilt yields. In particular, long-term OIS rates reacted less. 35 / 47

36 Interest swap rates also declined less than gilt yields. Thus, there is evidence of U.K. market segmentation. Hopefully, our models can shed light on this issue. 36 / 47 U.K. LIBOR and Swap Rate Response Event Maturity 3-month 2-year 5-year 10-year Feb. 11, Mar. 5, May 7, Aug. 6, Nov. 5, Feb. 4, Oct. 6, Total net change

37 General-to-Specific Model Selection for the U.K. Alternative Goodness-of-fit statistics Specifications k p-value AIC BIC (1) Unrestricted K P 24 n.a. -586, ,690 (2) κ P 13 = , ,699 (3) κ P 13 = κp 32 = , ,708 (4) κ P 13 = κp 32 = κp 12 = , ,716 (5) κ P 13 =... = κp 31 = , ,724 (6) κ P 13 =... = κp 21 = , ,731 (7) κ P 13 =... = κp 23 = , ,735 The Akaike Information Criterion prefers the following specification of K P : κ P KUK P κ P 22 κ P 23, 0 0 κ P 33 while the Bayesian Information Criterion calls for an even more parsimonious specification with diagonal K P. As before, we try to account for the finite-sample bias. 37 / 47

38 The Preferred AFNS Model of U.K. Gilt Yields 38 / 47 Our preferred specification of the AFNS model for U.K. gilt yields has P-dynamics given by dluk t dst UK = 0 κ P dct UK 22 κ P 23 θ P 0 0 κ P 2 LUK t S UK 33 θ3 P t dt Ct UK + σ σ σ 33 dw L,P t dw S,P t dw C,P t Thus, κ P 21 = 0 is the only difference relative to the U.S. model..

39 Model Performance 39 / 47 Model One-year forecast Two-year forecast Mean RMSE Mean RMSE Random walk Indep.-factor AFNS Preferred AFNS We are not aware of any established term structure model for U.K. gilt yields. For that reason we are limited to comparing our model to the random walk assumption. In the table above we focus on forecasting the future official Bank Rate one and two years ahead over the period from January 1995 to December The preferred AFNS model is on par with the random walk.

40 Decomposition of U.K. Gilt Yield Response (1) Event 2/11/09 3/5/09 5/7/09 8/6/09 11/5/09 2/4/10 10/6/11 Total Model Avg. target rate Ten-year Ten-year next ten years term premium Res. yield Indep Preferred Indep Preferred Indep Preferred Indep Preferred Indep Preferred Indep Preferred Indep Preferred Indep Preferred Gilt yield declines reflect declining term premiums. 40 / 47

41 Decomposition of U.K. Gilt Yield Response (2) Net change in basis points Instantaneous forward rate Forecasted future spot rate Instantaneous forward term premium Time to maturity in years The chart shows the decomposition of the net response of the model-implied instantaneous forward rate curve to the seven QE announcements. Policy expectations firmed at the two- to ten-year horizon. Term premiums declined at all horizons, but the most in the three- to ten-year maturity range. 41 / 47

42 Summary of U.K. Analysis 42 / 47 In contrast to the U.S. analysis, our results for the U.K. suggest that the portfolio balance channel and the resulting declines in bond yield term premiums are the key driver behind the declines in U.K. gilt yields. This is also consistent with the very moderate declines in long-term OIS and swap rates. Overall, this suggests that market segmentation might be an important issue in the U.K. fixed-income markets. Furthermore, we note that the key distinguishing feature between the U.S. and the U.K. monetary policy strategy since 2009 has been the absence of forward guidance from the U.K. MPC.

43 Cross-Country Analysis (1) 43 / 47 The response of U.S. interest rates to the U.K. QE announcements is, on net, tempered and can largely be explained by U.S. specific events. Thus, we focus on the U.K. interest rate response to the four U.S. LSAP announcements that occurred prior to the introduction of the U.K. QE program. Our previous results suggest that the signaling effect dominated in the U.S. yield response. The question is whether we can detect similar effects in the U.K. data.

44 Cross-Country Analysis (2) Event Gilt yields 6-month 1-year 2-year 5-year 10-year Nov. 25, Dec. 1, Dec. 16, Jan. 28, Total net change Event U.K. OIS rates 6-month 1-year 2-year 5-year 10-year Nov. 25, Dec. 1, Dec. 16, Jan. 28, Total net change / 47

45 Cross-Country Analysis: Decomposition of U.K. Gilt Yield Response to U.S. LSAP Announcements Event Model Avg. target rate Ten-year Res. Ten-year next ten years term prem. yield 11/25/08 Indep Preferred /1/08 Indep Preferred /16/08 Indep Preferred /28/09 Indep Preferred Total Indep Preferred Our model decompositions of the response of the ten-year gilt yield also suggest that about two-thirds of the reaction reflected declines in policy expectations. 45 / 47

46 Cross-Country Analysis (3) 46 / 47 The data suggests a strong signaling effect in the U.K. data from the early U.S. LSAP announcements, very similar to what we found in the U.S. data. Importantly, there is no evidence of market segmentation in the U.K. on these four dates. Thus, there is no apparent reason why the U.K. QE announcements could not have generated a similar yield response across markets in particular in light of the fact that market stress was likely less severe during that later period. This further supports the view that the U.K. QE program only operated through the portfolio balance channel.

47 Conclusion We analyze the effects on government bond yields of the Fed s first LSAP program and the BoE s QE program. Using dynamic term structure models, our results suggest that the main effect of the Fed s LSAP program was to lower policy expectations, while the portfolio balance channel appears to be less important. For the U. K., our analysis suggests the opposite result; namely, yield declines following QE announcements appear to have been entirely driven by reductions in term premiums. Given the similar bond purchase amounts and rationales in the two countries, the differences are notable. We speculate that the differences can be traced back to differences in policy communication and financial market structure. 47 / 47