Banque Nationale De Belgique Sa · EURONEXT:BNB
Banque Nationale De Belgique Sa — Investor Presentation (February 2025)
48 slides from Banque Nationale De Belgique Sa's investor presentation, Feb 5, 2025
Slide 1: The Natural Rate of Interest in the Euro Area: Evidence from Inflation-Indexed Bonds
The Natural Rate of Interest in the Euro Area: Evidence from Inflation-Indexed Bonds Jens Henrik Eggert Christensen & Sarah Mouabbi Seminar Presentation National Bank of Belgium Brussels, February 5, 2025 The views in this paper are solely the responsibility of the authors and should not be interpre
Slide 2: Motivation
Motivation Before the global pandemic, interest rates around the world had fallen in the previous decades leading to a consensus about a lower new normal for interest rates. However, the post-pandemic sharp rise in global interest rates has raised questions about that consensus. We revisit this issu
Slide 3: Contribution
Contribution We use a novel term structure model of real yields that accounts for bond-specific risk premia taken from Christensen and Rudebusch (2019). Advantages of this approach: – No requirement of stable, correct macro specification; – No adjustment for bounds on nominal interest rates; – Execu
Slide 4: Long-Term Yields and Our Estimate of r*
Long-Term Yields and Our Estimate of rt∗ 5 Ten−year nominal yield Ten−year real yield r*(t) 4 3 Rate in percent 2 1 0 −1 −2 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020 2022 2024 Shown are French ten-year nominal and real yields. Also shown is our estimate of rt∗ . Most of the net decline in lo
Slide 5: Outline
Outline 1 Identifying rt∗ with real bond prices 2 The inflation-indexed bond data 3 An arbitrage-free model with bond-specific risk 4 Bond-specific risk premia 5 rt∗ analysis 6 Stance of monetary policy 7 Conclusion 5 / 48
Slide 6: Real Bond Prices in a Frictionless World
Real Bond Prices in a Frictionless World We begin our analysis assuming a world with no frictions to the trading of financial claims. For simplicity, we focus on decomposing P t (τ ), the price of a zero-coupon real bond at time t that has a single payoff, namely one consumption unit, at maturity t
Slide 7: An Affine Model of Real Yields
An Affine Model of Real Yields We follow the usual empirical finance approach that models bond prices with latent factors, denoted X t , and the assumption of no residual arbitrage opportunities. We assume that Xt follows an affine Gaussian process dXt = K P (θ P − Xt )dt + ΣdWtP . Also, the instant
Slide 8: Our Definition of r*
Our Definition of rt∗ Our definition of the equilibrium rate of interest r t∗ is t+10 1 rt∗ = EtP [rs ]ds, 5 t+5 that is, the average expected real short rate over a five-year period starting five years ahead. This 5yr5yr forward average expected real short rate should be little affected by short-te
Slide 9: Outline
Outline 1 Identifying rt∗ with real bond prices 2 The inflation-indexed bond data 3 An arbitrage-free model with bond-specific risk 4 Bond-specific risk premia 5 rt∗ analysis 6 Stance of monetary policy 7 Conclusion 9 / 48
Slide 10: Maturity Distribution of French OATe Bonds
Maturity Distribution of French OATe Bonds 35 30 Time to maturity in years 25 20 15 10 5 0 2002 2006 2010 2014 2018 2022 Shown is the universe of French OATe bonds. Note the diverse set of bonds issued with maturities of up to 33 years. We use daily bond prices from 10/31/02 to 12/30/22. 10 / 48
Slide 11: French OATe Bond Yields
French OATe Bond Yields 4 2 Rate in percent 0 −2 −4 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020 2022 2024 Shown are the yield to maturity series for all 19 bonds. Some business cycle variation around general slow-moving trend. Note the sharp reversal since late 2021. Are there convenience prem
Slide 12: Index Ratios of French OATe Bonds
Index Ratios of French OATe Bonds 1.5 1.4 1.3 Rate 1.2 1.1 1.0 0.9 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020 2022 2024 Thanks to general positive inflation in the euro area, no single French OATe bond has experienced net deflation. Hence, the value of their deflation protection is likely neg
Slide 13: Measure of the Credit Risk of French OATe Bonds
Measure of the Credit Risk of French OATe Bonds 300 Five−year French CDS rate 5yr5yr Franco−German real yield spread Avg. French credit spread 250 Avg. French credit spread, 4−week m.a. Rate in basis points 200 150 100 50 0 2003 2005 2007 2009 2011 2013 2015 2017 2019 2021 2023 We use the French 5yr
Slide 14: Outline
Outline 1 Identifying rt∗ with real bond prices 2 The inflation-indexed bond data 3 An arbitrage-free model with bond-specific risk 4 Bond-specific risk premia 5 rt∗ analysis 6 Stance of monetary policy 7 Conclusion 14 / 48
Slide 15: The Inflation-Indexed Bond Discount Function
The Inflation-Indexed Bond Discount Function We follow Andreasen, Christensen, and Riddell (RF, 2021) and discount the cash flow of a given inflation-indexed bond i with a bond-specific function: r it = rt + β i (1 − e−λ R,i (t−t i ) 0 )XtR . Time since issuance, t-t0i , is a proxy for the notion th
Slide 16: Frictionless Dynamics – AFNS Model
Frictionless Dynamics – AFNS Model Proposition: If the risk-free real rate is defined by rt = Lt + St and the Q-dynamics of the factors Xt = (Lt , St , Ct ) are ⎛ ⎞ ⎛ ⎞ ⎡⎛ Q ⎞ ⎛ ⎞⎤ dLt 0 0 0 θ1 Lt ⎝ dSt ⎠ = ⎝ 0 λ −λ ⎠ ⎣⎝ θQ ⎠ − ⎝ St ⎠⎦ dt+ΣdWtQ , 2 dCt 0 0 λ θ3Q Ct where Σ is a constant matrix, then
Slide 17: The Augmented AFNS-R Model
The Augmented AFNS-R Model We refer to the AFNS model augmented with the bond-specific risk factor XtR as the AFNS-R model. Its four state variables, Xt = (Lt , St , Ct , XtR ), have risk-neutral Q-dynamics given by ⎛ ⎞ ⎛ ⎞ ⎡⎛ ⎞ ⎛ ⎞⎤ ⎛ ⎞ dLt 0 0 0 0 0 Lt dWtL,Q ⎜ dSt ⎟ ⎜ 0 λ −λ 0 ⎟ ⎢⎜ ⎟ ⎜ ⎟⎥ ⎜ S,Q ⎟
Slide 18: Inflation-Indexed Bond Pricing
Inflation-Indexed Bond Pricing Now, consider the value of the inflation-indexed bond issued at time t0 with maturity at t + τ that pays an annual coupon C. Its clean price is t1 N tj P t (t0 , τ ) = C(t1 − t)E Q e− t r (s,t0 )ds + CE Q e− t r (s,t0 )ds j=2 t+τ +E e− t r (s,t0 )ds . Q Note only two m
Slide 19: Market Prices of Risk
Market Prices of Risk To facilitate empirical implementation, we use the essentially affine risk premium specification introduced in Duffee (2002). This implies that the risk premia Γt are state-dependent Γt = γ 0 + γ 1 Xt , where γ 0 ∈ R4 and γ 1 ∈ R4×4 are unrestricted. Thus, the unrestricted AFNS
Slide 20: Measurement Equation and Model Estimation
Measurement Equation and Model Estimation To make the fitted bond pricing errors comparable across maturities and time, we scale each bond price by its duration P t (t0 , τ ) t (t0 , τ ) P = + εt , Dt (t0 , τ ) Dt (t0 , τ ) where P t (t0 , τ ) is the model-implied bond price and Dt (t0 , τ ) is its
Slide 21: Outline
Outline 1 Identifying rt∗ with real bond prices 2 The inflation-indexed bond data 3 An arbitrage-free model with bond-specific risk 4 Bond-specific risk premia 5 rt∗ analysis 6 Stance of monetary policy 7 Conclusion 21 / 48
Slide 22: Calculation of Bond-Specific Risk Premia
Calculation of Bond-Specific Risk Premia First, we use the estimated parameters and the filtered states to calculate the fitted bond prices P̂t . Second, we calculate the matching frictionless price P̃t by switching off the bond-specific risk factor. These bond prices are then converted into yields
Slide 23: Average OATe Bond-Specific Risk Premium
Average OATe Bond-Specific Risk Premium 60 Third OAT−euro bond issued 40 1/22−2004 Rate in basis points 20 0 −20 −40 −60 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020 2022 2024 Shown is the avg. estimated bond-specific risk premium for the AFNS-R model with diagonal K P and Σ. It averages close
Slide 24: Bond-Specific Premium – Factor Dynamics Sensitivity
Bond-Specific Premium – Factor Dynamics Sensitivity 60 Unconstrained dynamics Independent dynamics 40 Rate in basis points 20 0 −20 −40 −60 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020 2022 2024 We consider the AFNS-R with maximally flexible unconstrained dynamics. The estimated bond-specific r
Slide 25: Bond-Specific Premium – Data Frequency Sensitivity
Bond-Specific Premium – Data Frequency Sensitivity 60 40 Rate in basis points 20 0 −20 −40 Quarterly Monthly Weekly Daily −60 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020 2022 2024 We alter data frequency: daily, weekly, monthly, quarterly. Overall, the bond-specific risk premia have modest sen
Slide 26: Outline
Outline 1 Identifying rt∗ with real bond prices 2 The inflation-indexed bond data 3 An arbitrage-free model with bond-specific risk 4 Bond-specific risk premia 5 rt∗ analysis 6 Stance of monetary policy 7 Conclusion 26 / 48
Slide 27: Term Premium Calculation
Term Premium Calculation We define real term premiums in the standard way: 1 t+τ P TPt (τ ) = yt (τ ) − Et [rs ]ds, τ t where yt (τ ) refers to the adjusted frictionless zero-coupon yield; EtP [rs ] is the expected future frictionless short rate. Note: P-dynamics are important. 27 / 48
Slide 28: Model Selection in the AFNS-R Model
Model Selection in the AFNS-R Model For yield decompositions, the P-dynamics of the state variables are crucial. To find the appropriate P-dynamics, we use a general-to-specific strategy starting from an unrestricted K P : ⎛ P ⎞ κ11 κP12 κP13 κP14 ⎜ κP κP κP κP ⎟ KP = ⎜ 21 22 23 24 ⎟ ⎝ κP31 κP32 κP3
Slide 29: Preferred AFNS-R Model Specification
Preferred AFNS-R Model Specification KP Lt St Ct XtR θP Σ Lt 0.0422 0 0 0 0.0391 0.0054 (0.0815) (0.0282) (0.0000) St 0 0.9795 0.8147 0 -0.0258 0.0117 (0.3201) (0.2722) (0.0111) (0.0002) Ct 0 0 0.4896 0 -0.0203 0.0184 (0.2715) (0.0130) (0.0003) XtR 0 0 0 0.0782 -0.0251 0.0158 (0.1396) (0.0385) (0.00
Slide 30: 5yr5yr Real Yield Decomposition
5yr5yr Real Yield Decomposition 4 3 2 Rate in percent 1 0 −1 5yr5yr frictionless real yield 5yr5yr real term premium r*(t) −2 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020 2022 2024 Shown is the decomposition of the 5yr5yr real yield from the preferred AFNS-R model. The real term premium has pro
Slide 31: r* Estimate – Sensitivity to Factor Dynamics
rt∗ Estimate – Sensitivity to Factor Dynamics 2 0 Rate in percent −2 −4 r*(t), unrestricted KP r*(t), diagonal KP r*(t), preferred KP −6 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020 2022 2024 To assess the effect of the assumed factor dynamics, we compare our preferred r t∗ estimate to those fr
Slide 32: r* Estimate – Sensitivity to Bond-Specific Risk
rt∗ Estimate – Sensitivity to Bond-Specific Risk 2 1 Rate in percent 0 −1 r*(t), AFNS model r*(t), AFNS−R model −2 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020 2022 2024 To assess the effect of adjusting for the bond-specific risk premia, we compare our preferred r t∗ estimate to that from a pr
Slide 33: r* Estimate – Sensitivity to Data Frequency
rt∗ Estimate – Sensitivity to Data Frequency 2 1 Rate in percent 0 −1 Quarterly Monthly Weekly Daily −2 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020 2022 2024 To assess the effect of changing the data frequency, we estimate the preferred AFNS-R model using daily, weekly, monthly, and quarterly
Slide 34: r* Estimate – Sensitivity to Real-Time Analysis
rt∗ Estimate – Sensitivity to Real-Time Analysis 2 1 Rate in percent 0 −1 −2 r*(t), full sample r*(t), real time −3 2015 2016 2017 2018 2019 2020 2021 2022 2023 Given the robustness across data frequencies, we examine the real-time performance using monthly data. To do so, we estimate the preferred
Slide 35: Comparison with Foreign Market-Based r* Estimate
Comparison with Foreign Market-Based rt∗ Estimate 3 2 Rate in percent 1 0 −1 Euro r*(t), AFNS−R model US r*(t), CR −2 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020 2022 2024 Shown is the market-based rt∗ estimate from the U.S. taken from Christensen and Rudebusch (CR) (2019). Our euro-
Slide 36: Comparison with Macro-Based Estimates of r*
Comparison with Macro-Based Estimates of rt∗ 6 r*(t), AFNS−R model r*(t), HLW r*(t), DGGT r*(t), FS r*(t), DFHMT r*(t), BLM 4 Rate in percent 2 0 −2 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 2020 2025 Shown are macro-based rt∗ estimates from Holston et al. (HLW) (2017), Del Negro e
Slide 37: Ten-Year Projections of r*
Ten-Year Projections of rt∗ 3 2 1 Rate in percent 0 −1 r*(t), AFNS−R model −2 r*(t), median projection r*(t), 90% confidence band r*(t), realizations −3 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020 2022 2024 2026 2028 2030 2032 2034 Following Christensen et al. (JME, 2015), we use simulations t
Slide 38: Outline
Outline 1 Identifying rt∗ with real bond prices 2 The inflation-indexed bond data 3 An arbitrage-free model with bond-specific risk 4 Bond-specific risk premia 5 rt∗ analysis 6 Stance of monetary policy 7 Conclusion 38 / 48
Slide 39: Stance of Monetary Policy
Stance of Monetary Policy We consider the following definition of the stance of monetary policy ζt = rt − rt∗ , where rt is the instantaneous real short rate, while rt∗ is the natural rate. To empirically implement this definition, we use: Our market-based rt∗ estimate; Fitted one-year real yields a
Slide 40: Market-Based Measures of Monetary Policy Stance
Market-Based Measures of Monetary Policy Stance 8 6 4 Rate in percent 2 0 −2 −4 −6 Stance of monetary policy, one−year fitted real yield, no cutoff Stance of monetary policy, one−year fitted real yield, 12−month cutoff Stance of monetary policy, one−year frictionless real yield −8 2002 2004 2006 200
Slide 41: Comparison with Text-Based Policy Stance Measure
Comparison with Text-Based Policy Stance Measure 1.0 4 Stance of monetary policy, AFNS−R model (lhs) ECB stance, HP (rhs) 0.5 2 Rate in percent Unit 0.0 0 −0.5 −2 −1.0 −4 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020 2022 2024 Hubert and Poitier (HP) (2024) construct a text-based measure of ECB’
Slide 42: Stance Estimate – Sensitivity to Real-Time Analysis
ζt Estimate – Sensitivity to Real-Time Analysis 3 2 1 Rate in percent 0 −1 −2 −3 Stance of monetary policy, full sample Stance of monetary policy, real time −4 2015 2016 2017 2018 2019 2020 2021 2022 2023 For robustness, we examine the real-time performance of our market-based ζt measure of the mone
Slide 43: Regression Analysis: r* & Growth Forecasts
Regression Analysis: rt∗ & Growth Forecasts Our rt∗ estimate and Consensus Forecasts calendar year ahead growth forecasts, monthly frequency, NW estimated coefficient standard deviations with 12 lags: |Δrt∗ | = 0.1086 + 0.0697|Δg 1yr (Euro)t | + εt , (11.77) (3.02) |Δrt∗ | = 0.1121 + 0.0442|Δg 1yr (
Slide 44: Regression Analysis: Governing Council Dates
Regression Analysis: Governing Council Dates We regress our rt∗ estimate and measures of the policy stance, ζt , on a dummy for the ECB governing council dates, daily frequency, NW estimated coefficient standard deviations with 5 lags: |Δrt∗ | = 0.0175 + 0.0015DtGC dates + εt , (51.38) (1.11) |ΔζtFi
Slide 45: Outline
Outline 1 Identifying rt∗ with real bond prices 2 The inflation-indexed bond data 3 An arbitrage-free model with bond-specific risk 4 Bond-specific risk premia 5 rt∗ analysis 6 Stance of monetary policy 7 Conclusion 45 / 48
Slide 46: Conclusion
Conclusion To complement earlier empirical work based on macroeconomic models and data, we estimate the natural rate using only prices of inflation-indexed bonds. By adjusting for both bond-specific risk and real term premia, we uncover investors’ expectations for the underlying frictionless real sh
Slide 47: Updated Avg. OATe Bond-Specific Risk Premium
Updated Avg. OATe Bond-Specific Risk Premium 60 40 Rate in basis points 20 0 −20 −40 −60 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020 2022 2024 2026 Shown is the avg. estimated OATe bond-specific risk premium from our preferred AFNS-R model through January 2025 at monthly frequency. Currently,
Slide 48: Updated Stance of Monetary Policy
Updated Stance of Monetary Policy 2 1 0 Rate in percent −1 −2 −3 −4 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020 2022 2024 2026 By deducting our rt∗ estimate from the fitted one-year OATe real yield, we get a market-based proxy measure of the stance of monetary policy. Note that monetary policy
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