Macro factors and sovereign bond spreads: aquadraticno-arbitragemodel Peter Hˆrdahl a, Oreste Tristani b a Bank for International Settlements, b European Central Bank 17 December 1 All opinions are personal and should not be attributed to the BIS or the ECB. P. Hˆrdahl (BIS) Euro sovereign bond spreads 17 December 1 1 / 3
Motivation 1-year yield spreads vs Germany 16 14 1 Greece Portugal Spain France Italy 1 8 6 4 1998 4 6 8 1 1 P. Hˆrdahl (BIS) Euro sovereign bond spreads 17 December 1 / 3
Motivation Peripheral euro area sovereign bond yields have risen sharply above comparable yields on German government bonds. These spread increases have coincided with rapidly deteriorating Öscal conditions and eroding market conödence. Can country-speciöc fundamentals explain the rise in spreads? Or do factors unrelated to fundamentals play an important role (e.g. self-fulölling dynamics)? Attempts to model the dynamics of sovereign yields/spreads as functions of observable fundamentals have been challenging. P. Hˆrdahl (BIS) Euro sovereign bond spreads 17 December 1 3 / 3
Motivation (cont.) We examine the drivers of euro area sovereign bond spreads, including observable macro fundamentals key features: (i) allow sovereign spreads to depend on observable fundamentals (debt/gdp, economic growth) (ii) allow for non-linear e ects of Öscal fundamentals on spreads (iii) include a common credit factor (iv) let all factors a ect debt/gdp to allow us to capture feedback of higher spreads on debt (to a Örst approximation) P. Hˆrdahl (BIS) Euro sovereign bond spreads 17 December 1 4 / 3
Outline Methodology / Literature / Model Data and estimation method Results: model Öt, estimated common factor, quantiöcation of nonlinear e ects, risk premia estimates, spread decompositions Conclusions P. Hˆrdahl (BIS) Euro sovereign bond spreads 17 December 1 5 / 3
Methodology & literature Starting point: reduced-form credit models (Lando (1994), Du e & Singleton (1998), Du ee (1999),...), in which assumptions are made about the process for default intensity. Default is doubly stochastic: default arrives randomly, and the arrival intensity process L t varies randomly over time. Advantage: tractable bond pricing; for zero recovery & discrete time: "!# P t (n) = E Q t exp n  j=1 (r t+j 1 + L t+j ) The intensity L t may be a function of a set of factors. P. Hˆrdahl (BIS) Euro sovereign bond spreads 17 December 1 6 / 3
Methodology & literature (cont.) We apply this framework to euro sovereign bonds. Much of the available literature on sovereign credit has focused on emerging markets (Du e, Pedersen & Singleton (3), Pan & Singleton (8), Longsta et al. (11)); Dai and Philippon (6) focused on US, but assumed no credit risk. More recent interest in advanced economies, in particular the euro area: Laubach (11), Monfort & Renne (11) Borgy et al. (11), Ang & Longsta (11),... These studies typically model default intensities and sovereign spreads as a ne functions of some unobservable factors (Borgy et al. use observable macro factors) P. Hˆrdahl (BIS) Euro sovereign bond spreads 17 December 1 7 / 3
Methodology We want to allow macro fundamentals to play an important role for spreads; in particular (expected) debt/gdp. A linear relationship may not be optimal: theoretical results suggest a non-linear relationship (e.g. Bi, 11, Juessen et al., 11, Corsetti et al., 1) As economies approach the Öscal limit the point where a government no longer has the ability to Önance its debt by raising taxes bond yields become steeply non-linear. There is also empirical evidence of a non-linear relationship between bond yields and Öscal fundamentals (Alesina et al., 199; Ardagna et al. 7; Bernoth et al., 4). P. Hˆrdahl (BIS) Euro sovereign bond spreads 17 December 1 8 / 3
Methodology (cont.) Looking at recent euro area developments: challenging to assume a linear relationship between spreads and Öscal fundamentals a quadratic speciöcation seems more promising: 1 1 8 1-year spread, Portugal observed linear fit (on debt/gdp) linear-quadratic fit 6 4 1998 4 6 8 1 1 P. Hˆrdahl (BIS) Euro sovereign bond spreads 17 December 1 9 / 3
Model We start with the result of Du e and Singleton (1999): under RMV, credit risky bonds can be priced as default-free bonds using a default-adjusted discount rate r t = r t + L t, L t is a ìrecovery-adjusted default intensityî We assume that L t depends on: country-speciöc expected GDP growth: g t country-speciöc expected debt/gdp: d t debt-to-gdp squared: d t a common latent factor: C t We assume VAR factor dynamics for g, d and C. P. Hˆrdahl (BIS) Euro sovereign bond spreads 17 December 1 1 / 3
Model (cont.) Default intensities and state variables Default intensity: L i t = l i + l i Xt i + Xt i X i Xt i State vector, country j: X t = h i C t, gt j, dt j State dynamics: X t = FX t 1 + # t with restrictions: C t : AR(1); independent of macro fundamentals g t : AR(1) [interactions not signiöcant] d t : allowed to depend on all factors P. Hˆrdahl (BIS) Euro sovereign bond spreads 17 December 1 11 / 3
Model (cont.) Bond prices Assuming a standard SDF, and a ne market prices of risk (Du ee, ), y t = y + y 1 X t, we can price risky bonds using exponential quadratic bond prices of Ahn, Dittmar & Gallant () and Leippold & Wu () (Realdon (6) in discrete time): Pt n = exp A n + B n X t + Xt C n X t A n = A n 1 +... B n = B n 1 F +... C n = F C n 1 F +... P. Hˆrdahl (BIS) Euro sovereign bond spreads 17 December 1 1 / 3
Data Monthly data, January 1999 November 11., 3, 4, 5, 7, 1-year zero-coupon yields on Greek, Portuguese, Spanish, Italian and French government bonds (NS estimates), minus corresponding German yields. g j t : one-year ahead expected GDP growth; constructed from semi-annual European Commission forecasts; monthly data obtained using the Kalman Ölter (VAR) d j t : one-year ahead expected debt-to-gdp ratio (constructed in the same way). g and d are in deviation from sample mean (pre-crisis mean for d) P. Hˆrdahl (BIS) Euro sovereign bond spreads 17 December 1 13 / 3
Estimation Joint ML estimation assuming Gaussian shocks. Allow all spreads and macro factors to be imperfectly observed: Gaussian measurement errors Spreads are not linear in the factors: we canít use a regular Kalman Ölter We use the unscented Kalman Ölter (Julier & Uhlmann (1997, 4)): deterministic sampling of ësigma pointsí around the mean of the state variables propagate points through the non-linear function recover Örst two moments of the non-linear system use this to update the Ölter P. Hˆrdahl (BIS) Euro sovereign bond spreads 17 December 1 14 / 3
Parameter estimates: default intensities L t = l + lx t + (X t ) XX t ; l = (l C, l g, l d ) Parameter Greece Portugal Spain France Italy l 1.36.1.39.3 (.3) (.7) (.) (.1) l C 1. (1.739) l g 1.31 (.3) l d 1. (.59) X d,d.116 (.19).74 (.).1 (.).19 (.7).41 (.).17 (.5).15 (.).441 (.117).1 (.4).8 (.13).4 (.).19 (.6).3 (.).6 (.).4 (.).3 (.3).41 (.45).94 (.9) P. Hˆrdahl (BIS) Euro sovereign bond spreads 17 December 1 15 / 3
Results: model validation Estimated and observed spreads 8 Greece Portugal 6 15 4 1 5 4 6 8 1 1 Spain 5 4 3 1 4 6 8 1 1 4 6 8 1 1 y fitted y actual 5y fitted 5y actual 1y fitted 1y actual P. Hˆrdahl (BIS) Euro sovereign bond spreads 17 December 1 16 / 3
Results: model validation Estimated and observed spreads (cont.) 1.5 France 8 Italy 1 6.5 4 6 8 1 1 4 4 6 8 1 1 y fitted y actual 5y fitted 5y actual 1y fitted 1y actual P. Hˆrdahl (BIS) Euro sovereign bond spreads 17 December 1 17 / 3
Results: model validation One-year ahead forecasts of 1-year spreads 6 Spain 3 France 4 1-9 1 11 1 13-1 9 1 11 1 13 6 Italy 4 realized model Consensus forecast - 9 1 11 1 13 P. Hˆrdahl (BIS) Euro sovereign bond spreads 17 December 1 18 / 3
Results: model validation Conditional spread volatilities Greece spread vols 3 Greece, 5y vol 1.5 1 1.5 5 1 4 6 8 1 1.8 Portugal spread vols 3 Portugal, 5y vol.6.4 1. 5 1 model-implied 4 6 8 1 1 GARCH P. Hˆrdahl (BIS) Euro sovereign bond spreads 17 December 1 19 / 3
Results Estimated common factor 1 5-5 -1-15 4 5 6 7 8 9 1 11 1 P. Hˆrdahl (BIS) Euro sovereign bond spreads 17 December 1 / 3
Results Is allowing for nonlinearities important? Greece 1.5 France 15 1 5 4 6 8 1 1 1.5 4 6 8 1 1 6 Italy 4 linearized model full non-linear model observed 4 6 8 1 1 P. Hˆrdahl (BIS) Euro sovereign bond spreads 17 December 1 1 / 3
Results The role of the distress risk premium: 1-year spreads Greece 1.5 France 15 1 1 5 4 6 8 1 1.5 4 6 8 1 1 6 Italy 4 total spread spread net of risk premium 4 6 8 1 1 P. Hˆrdahl (BIS) Euro sovereign bond spreads 17 December 1 / 3
Results One-year (risk-neutral) default probabilities (5% loss assumed) P. Hˆrdahl (BIS) Euro sovereign bond spreads 17 December 1 3 / 3
Results Decomposition of default risk component (1y spread less premium) 6 Greece.3 France 4..1-4 6 8 1 1 -.1 4 6 8 1 1 1 Italy.5 common growth debt constant -.5 4 6 8 1 1 P. Hˆrdahl (BIS) Euro sovereign bond spreads 17 December 1 4 / 3
Results Decomposition of distress risk premium (1y) 6 Greece.6 France 4.4. - 4 6 8 1 1 -. 4 6 8 1 1 3 Italy 1-1 common growth debt constant - 4 6 8 1 1 P. Hˆrdahl (BIS) Euro sovereign bond spreads 17 December 1 5 / 3
Results 1-year spread responses to adverse shocks common shock, 1.4.3..1 4 common shock, 11.4.3..1 growth shock, 1 3 1 4 growth shock, 11 3 1 debt/gdp shock, 1.4.3..1.3..1 4 debt/gdp shock, 11.4 4 4 4 Greece Portugal Spain France Italy P. Hˆrdahl (BIS) Euro sovereign bond spreads 17 December 1 6 / 3
Conclusions We estimate a non-linear reduced-form credit model for sovereign spreads of Öve euro area countries. Using country-speciöc debt-to-gdp and GDP growth along with a common factor, our model can capture well features of sovereign spreads along several dimension. Macro factors are important drivers of sovereign spreads, mainly through the default risk component. In particular, spreads depend non-linearly on debt-to-gdp. For all countries, except Greece, the surge in spreads has mainly been due to rising distress risk premia. For this component, the common factor plays a central role. P. Hˆrdahl (BIS) Euro sovereign bond spreads 17 December 1 7 / 3
Extra slides German zero-coupon yields vs. OIS zero rates 5 4.5 4 3.5 3.5 y Germany 1.5 y OIS 5y Germany 1 5y OIS.5 1y Germany 1y OIS 7 8 9 1 11 1 P. Hˆrdahl (BIS) Euro sovereign bond spreads 17 December 1 8 / 3
Extra slides Macroeconomic data: observed and Öltered (KF) expected GDP growth, Greece 5 1 5 expected debt/gdp, Greece -5 5 1 expected GDP growth, Portugal 5-5 5 1 expected GDP growth, Spain 5-5 5 1 5 1 expected debt/gdp, Portugal 1 5 5 1 expected debt/gdp, Spain 1 5 5 1 P. Hˆrdahl (BIS) Euro sovereign bond spreads 17 December 1 9 / 3
Extra slides Macroeconomic data: observed and Öltered (KF) expected GDP growth, France 4 - -4-6 5 1 expected GDP growth, Italy 4 - -4-6 5 1 expected debt/gdp, France 1 8 6 4-5 1 expected debt/gdp, Italy 1 8 6 4-5 1 P. Hˆrdahl (BIS) Euro sovereign bond spreads 17 December 1 3 / 3
Extra slides Filtered macro variables (UKF) and data expected GDP growth, Greece 5 1 5 expected debt/gdp, Greece -5 5 1 expected GDP growth, Portugal 5-5 5 1 expected GDP growth, Spain 5 5 1 expected debt/gdp, Portugal 1 5 5 1 expected debt/gdp, Spain 1 5-5 5 1 filtered 5 1 data P. Hˆrdahl (BIS) Euro sovereign bond spreads 17 December 1 31 / 3
Extra slides Filtered macro variables (UKF) and data expected GDP growth, France - -4 3 1 expected debt/gdp, France -6 5 1-1 5 1 expected GDP growth, Italy 3 expected debt/gdp, Italy - 1-4 -6 5 1-1 5 1 filtered data P. Hˆrdahl (BIS) Euro sovereign bond spreads 17 December 1 3 / 3