Bond Market Exposures to Macroeconomic and Monetary Policy Risks

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1 Carnegie Mellon University Research CMU Society for Economic Measurement Annual Conference 15 Paris Jul 4th, 9:3 AM - 11:3 AM Bond Market Exposures to Macroeconomic and Monetary Policy Risks Boston College, dongho.song@bc.edu Follow this and additional works at: Part of the Economics Commons, "" ( July 4, 15). Society for Economic Measurement Annual Conference. Paper This Event is brought to you for free and open access by the Conferences and Events at Research CMU. It has been accepted for inclusion in Society for Economic Measurement Annual Conference by an authorized administrator of Research CMU. For more information, please contact research-showcase@andrew.cmu.edu.

2 Bond Market Exposures to Macroeconomic and Monetary Policy Risks Boston College July 4, 15 SEM Conference 15

3 Establishing Key Stylized Facts: corr(stock,bond) return on the five-year Treasury bond. stock market return (CRSP value-weighted portfolio of stocks). See Baele, Bekaert, and Inghelbrecht (1); Campbell, Pflueger, and Viceira (13); Campbell, Sunderam, and Viceira (13); David and Veronesi (13); Burkhardt and Hasseltoft (1)

4 Establishing Key Stylized Facts: corr( c, π) [ ] [ ] [ ] [ ] ct+1 µc xc,t ηc,t+1 + measurement errors = + + π t+1 µ π x π,t η π,t+1 [ ] xc,t+1 x π,t+1 = [ ] [ ] ρc xc,t + ρ π x π,t use monthly c and π = cpi. [ ] ec,t+1, e e t+1 N(, Σ t ) π,t+1

5 Establishing Key Stylized Facts: 197s - 199s corr( c, π) corr(stock,bond) yield curve slope Data, Model + + See Wachter (6), Piazzesi and Schneider (6), Bansal and Shaliastovich (13)

6 Establishing Key Stylized Facts: 196s and s corr( c, π) corr(stock,bond) yield curve slope Data + + Model Model +

7 Why is it important? The evidence poses a significant challenge to existing approaches (e.g., Wachter (6), Piazzesi and Schneider (6), Bansal and Shaliastovich (13)) π is perceived as a carrier of bad good news for future c yet, π risks seem to be there: upward sloping yield curve Need a new model to study the main drivers of π, bond, stock risks E(π), σ(π), ρ(π) dropped significantly the risks properties of stock and bond changed significantly flattening of the yield curve less violation of the Expectations Hypothesis sign change in the stock-bond correlation

8 Why is it important? The evidence poses a significant challenge to existing approaches (e.g., Wachter (6), Piazzesi and Schneider (6), Bansal and Shaliastovich (13)) π is perceived as a carrier of bad good news for future c yet, π risks seem to be there Need a new model to study the main drivers of π, bond, stock risks E(π), σ(π), ρ(π) dropped significantly the risks properties of stock and bond changed significantly flattening of the yield curve less violation of the Expectations Hypothesis sign change in the stock-bond correlation the slope of the yield curve remains positive

9 Objective Build a regime-switching general equilibrium model that characterizes the monetary and macroeconomic determinants of inflation, asset prices, and bond-stock return correlation reconciles both old and new stylized facts Key model features an endowment economy with long-run risks in c, EZ preferences endogenous π dynamics implied by the Taylor rule exogenous regime-switching as potential source of risk variations 1 in the Taylor rule coefficients in the covariance of c with π

10 Intuition: Inflation Risks in Simplest Form Setting Taylor Rule = Fisher equation yields φπ t = r t + E t [π t+1 ] r t is the real rate from Euler equation π t = { f (φ,...)r t, if φ > 1 nonstationary, if φ 1 Inflation risks depend on the joint determination of monetary policy aggressiveness: φ { φ > 1, φ 1} macroeconomic shocks: corr(π t, r t ) corr(π t, c t ) {+, }

11 Inflation Risk Characterization Active φ > 1 Countercyclical corr(π t, c t ) < Passive φ 1 Procyclical corr(π t, c t ) > Key risks in the economy can be characterized by Monetary Policy Active Passive Countercyclical CA CP Procyclical PA PP Agents in the model know the probability of moving across regimes Regime uncertainties reflected in today s bond market prices

12 Inflation Findings Estimate the model using asset prices and macroeconomic data Quantify the risks: the darker the riskier Monetary Policy Active Passive Countercyclical CA CP Procyclical PA PP Upward sloping yield curve in all regimes Negative stock-bond correlation in procyclical inflation regime

13 Findings Account for several 196 other 197 features 198 of the bond 199 market 1 time varying risk premiums Procyclical Inflation bond return predictability Active Monetary violation Policy of the expectations hypothesis Provide the timeline of the regimes (the darker the riskier) Countercyclical Inf. Procyclical Inf. Active MP Passive MP PP PA CP CA CP PA PP PA CP PP

14 Model Details Real consumption dynamics c t = µ c + x c,t + η c,t x c,t = ρ c x c,t 1 + e c,t + β(s t )e π,t, e j,t N(, σj,t 1) σ j,t independent AR(1) Taylor Rule i t = µ i (S t) + φ c (S t)( c t µ c ) + φ π(s t)(π t µ π x π,t) + x π,t + x m,t }{{}}{{}}{{}}{{} c gap π fluctuation π target mp shock x π,t, x m,t AR(1) Stochastic discount factor from EZ preferences, c t m t = m(θ, x j,t, σ j,t, β(s t),...) Taylor rule Inflation from it = it Fisher (m t, c t, E t [π t+1 ],...) π t = π(θ, φ c (S t ), φ π (S t ), β(s t ), x j,t, σ j,t, P...)

15 Intuition: Term Structure Nominal bond yields (ignoring monetary policy shock) y n,t $ = 1 ( B n, $ + B n,1,c $ x c,t + B n,1,π $ x π,t + B n,,c $ σc,t + B n,,π $ n }{{}}{{}}{{}}{{}}{{} bond price state x c,t x π,t σ c,t σ π,t σ π,t ) If nominal vol dominates, then risk increases with maturity upward sloping yield curve Their relative magnitudes determined by 1 stochastic volatilities monetary policy regimes 3 macroeconomic shock regimes

16 Intuition: Term Structure Nominal bond yields (ignoring monetary policy shock) y n,t $ = 1 ( B n, $ + B n,1,c $ x c,t + B n,1,π $ x π,t + B n,,c $ σc,t + B n,,π $ n }{{}}{{}}{{}}{{}}{{} bond price state x c,t x π,t σ c,t σ π,t σ π,t ) If real vol dominates, then long-term yields fall in bad times downward sloping yield curve Their relative magnitudes determined by 1 stochastic volatilities monetary policy regimes 3 macroeconomic shock regimes

17 Intuition: Stock-Bond Correlation Log price-dividend ratio pd t = D + D 1,c x c,t + D 1,π x π,t + D,c σc,t + D,π }{{}}{{}}{{}}{{} + σ π,t Correlation between stock and bond returns: corr t [r m t+1, r $ n,t+1 ] =... B n,1,c $ D 1,c }{{}}{{} + + price σc,t B n,1,π $ }{{} + D 1,π σπ,t }{{} state stock x c,t x π,t σc,t σπ,t bond stock-bond correlation is (+) if nominal vol dominates

18 Intuition: Stock-Bond Correlation Log price-dividend ratio pd t = D + D 1,c x c,t + D 1,π x π,t + D,c σc,t + D,π }{{}}{{}}{{}}{{} + mildly /+ Correlation between stock and bond returns: corr t [r m t+1, r $ n,t+1 ] σ π,t =... B n,1,c $ D 1,c σc,t B n,1,π $ D 1,π }{{}}{{}}{{}}{{} mildly /+ price state σ π,t stock x c,t x π,t σc,t σπ,t bond stock-bond correlation is ( ) if real vol dominates

19 Identification and Estimation Apply nonlinear Bayesian method Particle filter + MCMC Estimation sample: Quarterly SPF, monthly macroeconomic data monthly stock price, Treasury bond yields data Use mixed-frequency data to pin down the key state variables and identify macroeconomic/monetary policy regime shifts regime-switching coefficients: φ c(s t), φ π(s t), β(s t) stochastic volatilities: σ c,t, σ π,t latent long-run growth, inflation target, monetary policy shock: x c,t, x π,t, x m,t

20 Estimated Regime Transition Probabilities Continuation Half-life P Countercyclical Inflation 99. % 7.5 years P Procyclical Inflation 94.1 % 1 years P Active Monetary Policy 99. % 6 years P Passive Monetary Policy 97.5 %.5 years Most of the time, π shock is large and countercyclical 1 inflation risk premium is positive stock and bond return correlation is positive The long-run Taylor principle holds (by construction) 1 the regime in which passive policy is realized is short-lived ensures stationary inflation dynamics

21 Model-Implied Correlation between c and π Data Model corr( c t, π t ) corr( c t, π t ) Regime Estimate Median 5% 95% CA : Countercyclical Inf, Active MP [-.75, -.8] CP : Countercyclical Inf, Passive MP [-.49,.35] PA : Procyclical Inf, Active MP.1. [-.9,.11] PP : Procyclical Inf, Passive MP.14. [-.1,.16] When inflation shock is procyclical π, c positively comove Monetary policy alone cannot change the sign Passive monetary policy creates more dispersion

22 Model-Implied Yield Spread y n y 3m, n {1y 5y, 1y} corr(π, c) <, Active MP corr(π, c) <, Passive MP y y 3y 4y 5y 1y corr(π, c) >, Active MP 1y y 3y 4y 5y 1y corr(π, c) >, Passive MP y y 3y 4y 5y 1y 4 1y y 3y 4y 5y 1y regime-switching NOT allowed counter-/procyclicality amplified in passive monetary policy regime

23 Model-Implied Yield Spread y n y 3m, n {1y 5y, 1y} corr(π, c) <, Active MP corr(π, c) <, Passive MP y y 3y 4y 5y 1y corr(π, c) >, Active MP y y 3y 4y 5y 1y corr(π, c) >, Passive MP y y 3y 4y 5y 1y 1 1y y 3y 4y 5y 1y upward sloping yield curve due to regime uncertainties shifts in monetary policy affect the variance of the yield curve

24 Model-Implied Stock-Bond Return Correlation corr(π, c) <, Active MP corr(π, c) <, Passive MP y 3y 4y 5y corr(π, c) >, Active MP. y 3y 4y 5y corr(π, c) >, Passive MP y 3y 4y 5y y 3y 4y 5y procyclical π shock generates negative stock-bond return correlation monetary policy alone cannot change the sign

25 Conclusion I estimate an equilibrium asset pricing model that allows for shifts in 1 the aggressiveness of the central bank to inflation fluctuations the covariance between the long-run growth and inflation target My Bayesian estimation provides strong evidence of regime changes passive monetary policy: 197s countercyclical inflation shocks: 197s - mid199s Main findings upward sloping yield curve due to regime uncertainties positive bond-stock return correlation when π shock is procyclical policy shifts affect the nd moment of π and yield curve Future research: extension to the production economy

26 Appendix: Piazzesi and Schneider (6) Revisited Return Structural shift for all coefficients z t = µ + s t 1 + ε t, z t = [π t, c t ] s t = φs t 1 + φkε t, ε t N(, Ω) s: [ S t =.6 [.1,.].5 ] [ S t 1 + ε t, var(φkε t) =.14 [.6,.5].3 ] s: [.41.6 S t =.7 [.3,.18].83 ] [.78.9 S t 1 + ε t, var(φkε t) =.9 [.1,.8].55 ] Drop in E(π), σ(π), ρ(π) and sign switch in covariance

27 Appendix: Shifts in the Slope of the Phillips Curve FIGURE 5: TIME VARIATION IN THE SLOPE OF THE PHILLIPS CURVE Panel A: Sample Split in mid-198s, Backward-Looking PC Panel B: Sample Split in mid-198s, Forward-Looking PC t-e t BACK Q1-1984Q4 1985Q1-7Q3 7Q3-13Q1 7Q4 8Q 8Q1 8Q3 11Q1 11Q 1Q4 1Q3 13Q1 11Q3 1Q1 1Q 11Q4 9Q1 9Q4 9Q3 9Q 1Q4 1Q3 1Q1 1Q SPF t-e t, GDP deflator - 4 8Q1 8Q 7Q4 8Q3 1Q3 1Q1 1Q 13Q1 1Q4 11Q4 196Q1-1984Q4 1985Q1-7Q3 7Q3-13Q1 11Q3 11Q 11Q1 1Q3 1Q4 1Q 1Q1 9Q1 9Q4 9Q3 9Q Unemployment gap Unemployment gap Panel C: Counterfactual Inflation Paths from Time-Varying Slopes inflation (CPI) Coibon and Gorodnichenko (13): Is The Phillips Curve Alive and Well After All?

28 Appendix: Term Premium t,n = y t,n 1 n n 1 i= E t(y t+i,1 ) corr(π, c) <, Active MP corr(π, c) <, Passive MP y y 3y 4y 5y 1y corr(π, c) >, Active MP.5 1y y 3y 4y 5y 1y corr(π, c) >, Passive MP y y 3y 4y 5y 1y.5 1y y 3y 4y 5y 1y term premium more important in the Active MP regime

29 Appendix: CP Excess Return Predictive Regression 8 corr(π, c) <, Active MP y 3y 4y 5y corr(π, c) >, Active MP 8 corr(π, c) <, Passive MP y 3y 4y 5y corr(π, c) >, Passive MP y 3y 4y 5y y 3y 4y 5y higher R when Active MP and corr(π, c) <

30 Appendix: Expectations Hypothesis (EH) Slope Coefficient corr(π, c) <, Active MP corr(π, c) <, Passive MP y 3y 4y 5y corr(π, c) >, Active MP 3 y 3y 4y 5y corr(π, c) >, Passive MP y 3y 4y 5y 3 y 3y 4y 5y Passive MP decreases the degree of violation of EH

31 Appendix: (EH) Slope Coefficient ( ) (yt,n ) 1 y t+1,n 1 y t,n = α n + β n y t,1 + ɛ t+1 n 1 Slope coefficient β n = 1 cov(e trx t+1,n, y t,n y t,1 ) var(y t,n y t,1 ) 1 1 cov(e trx t+1,n, y t,n y t,1) term spread contains less information about expected excess bond returns var(y t,n y t,1) variance of the term spread increases Passive MP raises var(y t,n y t,1 )

32 Appendix: Equilibrium Bond Yield Loadings Level Factors Volatility Factors x c,t x π,t σc,t σπ,t Expected Expected Growth Expected Growth Growth Expected Inflation Inflation CA CA CA CA CA CA CP CP CP CP CP CP PA PA PA PA PA PA PP PP PP PP PP PP Growth Growth Uncertainty Uncertainty Inflation Inflation Uncertainty Inflation Uncertainty Uncertainty CA CA CA CA CP CP CP CP CA CA CP CP CA CP PA PA PA PA PP PP PP PP PA PP PA PP PA PP Active MP: loadings on level factors are nearly flat across maturities Passive MP: loadings on level factors decrease over maturities

33 Appendix: U.K. Real Bond Yields, c, π Real Consumption Per Capita and CPI Inflation Δc π y 1y 15y Real Yields

34 Appendix: U.K. Real Bond Yields, c, π Return.5 Rolling Window Years: corr(π, Δc) Real Yield Spread: y t,n y t,5y, n {6y,..., 15y}

35 Consumption Reaction to 1 % Point Inflation Surprises Horizon Horizon

36 Inflation Reaction to 1 % Point Inflation Surprises Horizon Horizon

37 Bond Market 7s, 8s, 9s s Full Sample Correlation between Stock and Bond Return Corr(r m, r y ) Correlation between Spread and Growth Corr(y 5y -y 3m, c) Excess Bond Return Predictability, R rx y,t+1y onto forward t Term Spread Regression, Slope Coefficient r y,t+1y onto y y,t -y 1y,t

38 Calibration I: Neutral Inflation [ ct+1 ] π t+1 [ ] xc,t+1 x π,t+1 [ ] σ c,t+1 σ π,t+1 = = = [ µc ] [ ] [ ] xc,t σc η + + c,t+1 µ π x π,t σ π η π,t+1 [ ] [ ] [ ] [ ] ρc xc,t 1 χc,π σc,t e + c,t+1 ρ π x π,t 1 σ π,t e π,t+1 [ ] [ ] [ ] (.1)σ c.99σ (.1)σπ + c,t σw,c w.99σπ,t + c,t+1 σ w,π w π,t+1 regime 1: ρ c =.99, ρ π =.998 and χ c,π = regime : ρ c =.99, ρ π =.6 and χ c,π = P = [ ]

39 Yield Curve, Stock-Bond Correlation: Calibration I 4.9 yield curve stock-bond correlation regime 1 regime

40 Calibration II: Non-Neutral Inflation [ ct+1 ] π t+1 [ ] xc,t+1 x π,t+1 [ ] σ c,t+1 σ π,t+1 = = = [ µc ] [ ] [ ] xc,t σc η + + c,t+1 µ π x π,t σ π η π,t+1 [ ] [ ] [ ] [ ] ρc xc,t 1 χc,π σc,t e + c,t+1 ρ π x π,t 1 σ π,t e π,t+1 [ ] [ ] [ ] (.1)σ c.99σ (.1)σπ + c,t σw,c w.99σπ,t + c,t+1 σ w,π w π,t+1 regime 1: ρ c =.99, ρ π =.998 and χ c,π =.3 regime : ρ c =.99, ρ π =.6 and χ c,π =.5 P = [ ]

41 Yield Curve, Stock-Bond Correlation: Calibration II yield curve stock-bond correlation regime 1 regime

42 Calibration III: Non-Neutral Inflation [ ct+1 ] π t+1 [ ] xc,t+1 x π,t+1 [ ] σ c,t+1 σ π,t+1 = = = [ µc ] [ ] [ ] xc,t σc η + + c,t+1 µ π x π,t σ π η π,t+1 [ ] [ ] [ ] [ ] ρc xc,t 1 χc,π σc,t e + c,t+1 ρ π x π,t 1 σ π,t e π,t+1 [ ] [ ] [ ] (.1)σ c.99σ (.1)σπ + c,t σw,c w.99σπ,t + c,t+1 σ w,π w π,t+1 regime 1: ρ c =.99, ρ π =.998 and χ c,π =.3 regime : ρ c =.99, ρ π =.6 and χ c,π =.1 P = [ ]

43 Yield Curve, Stock-Bond Correlation: Calibration III yield curve stock-bond correlation regime 1 regime

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