WORKING PAPER 217. Sovereign Bond Risk Premiums. Engelbert J. Dockner, Manuel Mayer, Josef Zechner

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1 WORKING PAPER 217 Sovereign Bond Risk Premiums Engelber J. Dockner, Manuel Mayer, Josef Zechner

2 The Working Paper series of he Oeserreichische Naionalbank is designed o disseminae and o provide a plaform for discussion of eiher work of he saff of he OeNB economiss or ouside conribuors on opics which are of special ineres o he OeNB. To ensure he high qualiy of heir conen, he conribuions are subjeced o an inernaional refereeing process. The opinions are sricly hose of he auhors and do in no way commi he OeNB. The Working Papers are also available on our websie (hp:// and hey are indexed in RePEc (hp://repec.org/). Publisher and edior Ediorial Board of he Working Papers Coordinaing edior Oeserreichische Naionalbank Oo-Wagner-Plaz 3, 1090 Vienna, Ausria PO Box 61, 1011 Vienna, Ausria oenb.info@oenb.a Phone (+43-1) Fax (+43-1) Doris Rizberger-Grünwald, Ernes Gnan, Marin Summer Marin Summer Design Communicaions and Publicaions Division DVR ISSN (Prin) ISSN X (Online) Oeserreichische Naionalbank, All righs reserved.

3 Sovereign Bond Risk Premiums Engelber J. Dockner, Manuel Mayer, and Josef Zechner Absrac Sovereign credi risk has become an imporan facor driving governmen bond reurns. We herefore inroduce an empirical asse pricing model which explois informaion conained in boh forward ineres raes and forward CDS spreads. Our analysis covers euro-zone counries wih German governmen bonds as credi risk-free asses. We consruc a marke facor from he firs hree principal componens of he German forward curve as well as credi risk facors from he principal componens of forward CDS curves. Our resuls show ha predicabiliy of risk premiums of sovereign euro-zone bonds improves subsanially if he marke risk facor is augmened by a common euro zone and an orhogonal counry-specific credi risk facor, measured by an increase in he average R 2 over euro-zone sovereigns from 0.21 o Furhermore, we find ha mos of he variaion of sovereign bond risk premiums is aribuable o he common euro-zone credi risk facor while counry-specific credi risk facors play a subordinae role. Keywords: Sovereign bond risk premiums, marke and credi risk facors, euro-zone deb crisis. Deceased on April 16, Conac: Manuel Mayer: OeNB Oeserreichische Naionalbank and VGSF Vienna Graduae School of Finance, Josef Zechner: WU Vienna Universiy of Economics and Business (CEPR and ECGI).

4 1 Inroducion Risk premiums of sovereign bonds vary subsanially over ime. This has been documened in several seminal sudies such as Fama & Bliss (1987) and Campbell & Shiller (1991) or, more recenly, by Cochrane & Piazzesi (2005) and Duffee (2011). 1 Cochrane & Piazzesi (2005), for example, find ha risk premiums for U.S. governmen bonds can be prediced by a linear combinaion of one-year forward raes wih an R 2 as high as 44%. These findings confirm ha forward ineres raes conain imporan informaion abou ime-varying sovereign risk premiums. A cenral feaure of Cochrane & Piazzesi (2005) is ha governmen bond risk premiums are explained exclusively via he cross secion of essenially defaul-free yields. While his is an approach consisen wih he majoriy of exising erm srucure models, recen sovereign deb crises have demonsraed forcefully ha governmen bond yields can no longer be considered o be wihou credi risk. In pas years even mos developed counries erm srucures of governmen bond yields have been driven by wo facors: he erm srucure of defaul-free spo raes and he erm srucure of sovereign credi spreads. In his paper we make use of daa for sovereign credi defaul swap (CDS) conracs of eigh euro-zone counries and of ineres raes exraced from he German erm srucure o consruc separae yield and credi facors. On a monhly basis we calculae one-year forward ineres raes saring in one, hree, five, and seven years implici in he German erm srucure. As hese forward raes are highly correlaed, we exrac he firs hree principal componens (PCs) and use hese o consruc a linear riskless erm-srucure facor. For simpliciy, we refer o his facor as he marke facor which is idenical for all euro-zone counries. In addiion, we calculae one-year forward CDS spreads saring in one, hree, five, and seven years o consruc credi facors for each counry, excep for Germany. These credi facors are calculaed in a hree-sep approach. Firs, we exrac he firs principal componen from each counry s CDS forward curve. We find ha for each counry he firs PC explains more han 90% of he variaion in CDS forward spreads. In a second sep, we calculae he firs principal componen from he counry-specific firs principal componens. This provides us wih a credi facor ha capures common euro-zone credi risk which we call he euro-zone credi facor. In a hird sep, we regress he counry-specific PCs on he euro-zone credi facor o isolae he orhogonal componen, i.e. he error erm of he regression. This error erm represens our counry-specific credi facor. 1 Addiional references sudying he ime variaion of bond risk premiums include Ferson & Harvey (1991), Ilmanen (1995) and Dahlquis & Hasselof (2013). 1

5 Using his approach o consruc marke and credi risk facors, we find ha he use of credi risk facors subsanially improves predicabiliy of excess bond reurns. We find ha predicing governmen bond excess reurns exclusively by he marke risk facor, as in Cochrane & Piazzesi (2005), yields an average R 2 over our sample of euro-zone sovereigns of However, including credi risk facors increases he average R 2 o 0.61, ranging from 0.51 for France o 0.73 for Ireland. Moreover, he decomposiion of credi risk of euro-zone sovereigns ino a common euro-zone componen and an orhogonal counry-specific componen reveals ha mos of he variaion of sovereign bond risk premiums is aribuable o he common euro-zone facor while he counry-specific facors play a subordinae role. In line wih Longsaff e al. (2011) who documen ha CDS spreads are driven by a common credi facor ha is highly correlaed o he US sock and high-yield markes we find ha he common euro-zone credi risk facor is relaed o he European sock marke. Finally, checking he robusness of our sovereign bond pricing model we find ha neiher a change in he decomposiion of he credi facors nor using swap raes as riskless ineres raes changes our overall conclusions. The analysis of risk premiums of sovereign bonds has become an acive area of research and our paper relaes o several exising empirical sudies. Cochrane & Piazzesi (2005) analyze he ime variaion of expeced excess bond reurns and find ha a en-shaped lagged linear facor of one-year forward ineres raes conains informaion abou fuure excess bond reurns. According o heir findings, his facor predics excess bond reurns wih differing mauriies remarkably well. I is shown o be couner-cyclical and o have predicive power also for sock reurns. Duffee (2011) challenges his approach and argues ha yields as facors for risk premiums are neiher heoreically necessary nor empirically suppored. He shows ha almos half of he variaion of bond risk premiums canno be deeced using he cross-secion of yields as in Cochrane & Piazzesi (2005). Insead, he idenifies a facor ha goes beyond he cross secion of yields and refers o his as he hidden facor. He finds ha flucuaions in his hidden componen have srong forecasing power for boh fuure shor-erm ineres raes and excess bond reurns. Our paper is consisen wih hese findings. In our framework he credi facors ake he role of he hidden facor used in Duffee (2011). Dahlquis & Hasselof (2013) sudy inernaional bond risk premiums and idenify local and global facors ha have srong forecasing power and are no spanned by he cross secion of yields. I urns ou ha heir global facor is closely relaed o he inernaional business cycle and US bond risk premiums. Similarly, Ludvigson & Ng (2009) do no rely 2

6 on he cross secion of yields when forecasing governmen bond risk premiums bu idenify macroeconomic facors, insead. They find ha real and inflaion facors have imporan forecasing power for fuure excess reurns on US governmen bonds, above and beyond he predicive power conained in forward raes and yield spreads. As a consequence, risk premiums in heir model have a marked couner-cyclical componen, which is consisen wih exising heories ha invesors ge compensaed for he risk associaed wih macro-economic flucuaions. Cieslak & Povala (2011) decompose yields ino long-horizon expeced inflaion and mauriy-relaed cycles and sudy he predicabiliy of bond excess reurns. The mauriy-relaed cycles are used o consruc a forecasing facor ha explains up o and above 50% of he in-sample and 30% of he ou-of-sample variaion of yearly excess bond reurns. In conras o our paper, none of he papers discussed above uilizes credi facors o explain governmen bond risk premiums. Longsaff e al. (2011) sudy sovereign credi risk using CDS daa. They find ha a large fracion of sovereign credi risk can be aribued o global facors. During he period from 2000 o 2010 up o 64% of he variaion of sovereign credi spreads is accouned for by he firs principal componen of CDS spreads. This value increases o 75% during he period of he financial crisis ranging from 2007 o The firs principal componen of CDS spreads has a negaive correlaion of wih he US sock marke and a correlaion of 0.61 wih changes in he VIX index. As credi spreads are driven by a global facor, Longsaff e al. (2011) analyze wheher his facor is priced and find ha a hird of he oal CDS spread can be aribued o a global CDS risk premium. Our paper differs from Longsaff e al. (2011) by focusing on governmen bond risk premiums as a funcion of he riskless erm srucure of ineres raes, a common euro-zone, and a counry-specific credi facor. Caceres e al. (2010) also sudy sovereign credi spreads and explore how much of heir movemens are due o a shif in global risk aversion or due o counryspecific risks, arising from worsening fundamenals or from spillovers originaing in oher sovereigns. They find ha, while a he beginning of he crisis shifs in risk aversion conribued a major share o increased credi spreads, laer in he crisis, counry-specific facors have sared o play a more imporan role. Bernoh e al. (2012) sudy bond yield differenials among EU governmen bonds. They show ha governmen spreads conain a risk premium ha increases wih fiscal imbalances and depends negaively on he size of he issuer s bond marke. Finally, Haugh e al. (2009) analyze large recenly observed movemens in yield spreads for sovereign bonds in he euro zone. While he increase in average risk aversion is an imporan facor ha explains he levels of CDS spreads, i is found ha fiscal performance 3

7 plays an imporan role, oo. They presen evidence ha incremenal deerioraions in fiscal performance lead o larger increases in he spread, wih he consequence ha financial marke reacions could become an increasingly imporan consrain on fiscal policy for some counries. Overall, our resuls inegrae well wih he exising empirical lieraure discussed above. As in Cochrane & Piazzesi (2005), we consruc a facor ha is based on he cross secion of risk-free yields ha we idenify wih he German erm srucure. We hen augmen his facor wih a common and a counry-specific credi facor, which we derive from he forward curve of sovereign CDS spreads. As he CDS marke is driven by credi fundamenals of a counry, i is clear ha hese facors cover fundamenals ha canno be capured by he cross secion of he riskless German erm srucure. Hence, in his way our analysis complemens he resuls found in Duffee (2011), Ludvigson & Ng (2009), and on an inernaional level, in Dahlquis & Hasselof (2013). Our paper is organized as follows. In he nex secion we presen a descripion of our empirical model. In secion 3 we presen he daase, summarize our regression resuls, quanify he esimaed risk premiums, and repor he main findings of he paper. In secion 4 we perform a number of robusness checks. Firs, we esimae an alernaive model in which we omi he decomposiion of credi risk ino a common euro-zone and a counry-specific componen. Second, we use euro-zone swap raes insead of German yields as our riskless ineres raes. Third, we esimae our model for a shorer sample period ha excludes negaive yields. Finally, we perform an ou-of-sample analysis of our resuls. Secion 5 concludes. 2 Model Specificaion This secion inroduces he empirical model of sovereign bond excess reurns. Our approach builds on he exising findings discussed in he inroducion ha forward prices conain valuable informaion o explain and predic risk premiums. As our focus is on decomposing sovereign bond risk premiums ino marke and credi risk facors, we sar wih he German erm srucure of spo raes, which we idenify as riskless ineres raes, as well as counry-specific erm srucures of CDS spreads for each counry in he sample. To consruc he marke facor we derive one-year forward raes from he German erm srucure of spo raes. We denoe he one-year forward ineres rae beween daes + n 1 and + n by: 4

8 f (n) = P (DE,n 1) P (DE,n) P (DE,n), (1) where P (DE,n) denoes he German zero-coupon bond price a ime wih mauriy n years. The consrucion of he marke facor is no done by employing he forward raes direcly bu by making use of heir firs hree principal componens, insead. To be consisen wih he consrucion of our credi facors, we uilize one-year forward raes saring in one, hree, five, and seven years, i.e. f (2), f (4), f (6), and, o calculae he firs hree principal componens denoed by: f (8) MF = ( MF (1), MF (2), MF (3) ). (2) A linear combinaion of hese PCs defines he marke facor which is idenical for each counry in he euro zone. The credi facors are obained in he following way. Firs, we use he mos liquid spo CDS mauriies of one, hree, five, seven, and en years o derive he spreads of forward CDS conracs saring in one, hree, five, and seven years wih a mauriy of one year, respecively. The forward CDS raes are denoed by cf (i,n), where n {2, 4, 6, 8} and i capures he counry. Hence, cf (i,4) denoes he forward CDS rae a ime of a conrac saring in hree years wih a mauriy of one year for counry i. From he ime series of hese forward CDS raes he firs PCs are calculaed for each counry i, denoed by P C (i). Using hese PCs we perform a second principal componen analysis o exrac he euro-zone credi facor, CF (Euro). Hence, he common euro-zone credi facor is he firs PC of he individual counries firs PCs. Finally, we regress each counry s firs PC on he euro-zone credi facor, P C (i) = β (i) CF (Euro) + ɛ (i), (3) and define he orhogonal error erm, i.e. he residual of his regression, as he counry-specific credi facor CF (Counry,i) ɛ (i). This procedure resuls in a common euro-zone credi facor as well as orhogonal counry-specific credi facors for all counries excep Germany. Following he approach of Cochrane & Piazzesi (2005), we hen regress excess bond reurns on marke and credi risk facors. We use P (i,n) o denoe he n-year zero-coupon bond price of counry i and define one-year holding period reurns as: 5

9 +1 = P (i,n 1) +1 P (i,n). (4) r (i,n) P (i,n) Excess holding period reurns for mauriy n are calculaed as: rx (i,n) +1 = r (i,n) +1 r (DE,n) +1, (5) wih r (DE,n) +1 being he one-year holding period reurn of a German zero-coupon bond wih mauriy n years. Having specified he excess reurns for differen mauriies we nex define he average excess reurn as he mean over mauriies of 1 o 8 years: rx (i) +1 = 1 ( (i,1) rx +1 + rx (i,2) +1 + rx (i,3) +1 + rx (i,4) +1 + rx (i,5) +1 + rx (i,6) +1 + rx (i,7) +1 + rx (i,8) ) (6) In our baseline model, we regress average excess holding period reurns on marke and credi risk facors: rx (i) +1 = δ (i) 0 + γ (i) MF + δ (i) 1 CF (Euro) + δ (i) 2 CF (Counry,i) + ε (i) +1, (7) where ε (i) +1 represens he error erm for counry i and γ (i) = ( γ (i) 1, γ (i) 2, γ (i) ) 3 is a vecor of exposures of average excess bond reurns o he marke facor. Noe ha he marke facor MF is idenical among all counries, implying ha here is a single marke risk facor in he euro zone. Equaion (7) addiionally documens our modeling of a common euro-zone and counry-specific credi facors. In addiion o he baseline model we esimae individual-mauriy regressions of he form: rx (i,n) +1 = δ (i) 0 + γ (i) MF + δ (i) 1 CF (Euro) + δ (i) 2 CF (Counry,i) + ε (i) +1. (8) Taking expecaions on boh sides of equaions (7) or (8) we find ha he oal risk premium is he sum of he esimaed marke risk premium (MRP), he euro-zone credi risk premium (ECRP), and he counry-specific credi risk premium (CCRP). The euro-zone and counry-specific credi risk premiums can be added o yield he oal credi risk premium (TCRP) for counry i. Denoing he esimaed coefficiens of equaions (7) and (8) by γ (i), δ (i) 1, and δ (i) 2 we have: 6

10 MRP γ (i) MF, (9) ECRP δ 1 (i) CF (Euro), CCRP δ 2 (i) CF (Counry,i), T CRP δ 1 (i) CF (Euro) + δ 2 (i) CF (Counry,i). 3 Bond Risk Premiums 3.1 Daase We use monhly CDS spreads of USD-denominaed conracs for eigh euro-zone counries: Ausria, Belgium, France, Ireland, Ialy, Neherlands, Porugal, and Spain. The ninh counry is Germany wih is erm srucure being assumed o represen he risk-free curve. Ou of hese eigh euro-zone counries we have peripheral saes as well as core counries such as Ausria, Belgium, France, and he Neherlands. Our daa sources are Bloomberg and Daasream, wih he sample period ranging from Ocober, 2006 o March, We do no include Greece since is CDS daa is available only unil February The sample period covers roughly wo years of pre-crisis daa as well as he financial and European deb crisis period. We include CDS mauriies of 1, 3, 5, 7, and 10 years since hese represen he mos frequenly raded enors. The resricion o euro-zone counries comes wih he advanage ha we need no deal wih exchange-rae risk and can idenify he erm srucure of a single counry, Germany, as he risk-free erm srucure. For he same sample period, we collec monhly zero-coupon yields from Bloomberg. We obain hese daa for mauriies of 1, 2, 3, 4, 5, 6, 7, and 8 years for all counries. Tables (10) and (11) summarize he descripive saisics of he excess holding period reurns which are compued from he zero-coupon yield daa as oulined in secion (2) as well as he descripive saisics of he forward CDS spreads which are compued from he CDS daa as oulined in he appendix. 3.2 Principal Componens as Risk Facors The German erm srucure as well as he counry-specific CDS curves are he basis for he consrucion of our marke and credi risk facors. As oulined in 7

11 secion 2, we do no use forward raes direcly o measure he marke risk facor bu exrac principal componens, insead. In secion 4.1 we ake an alernaive approach and use forward ineres raes and forward CDS spreads direcly o consruc he marke and credi risk facors. The firs hree PCs for he German spo raes are repored in able (1) Panel A. The resuls confirm previous findings ha he firs hree PCs explain almos all variaion conained in he spo raes, wih he firs facor being a level, he second a slope, and he hird a curvaure facor (see Lierman & Scheinkman (1991)). Nex we exrac PCs from he erm srucure of forward CDS spreads for each counry separaely. Tables (1) o (3) presen he corresponding resuls. We find ha he firs PC explains a leas 90% of each individual counry s variaion in forward CDS spreads and in he analysis below we represen he informaion in he enire CDS forward curve exclusively by is firs PC. For compleeness we also repor he second and hird PCs in ables (1) o (3). Analogous o he case of he German erm srucure, he firs PC of he forward CDS spreads represens a level facor, wih loadings across counries and across mauriies being close o 0.5. Also, for mos counries, he second PC represens a slope and he hird a curvaure facor. The PC analysis reveals ha he loadings across counries are quaniaively very similar and ha hey share idenical paerns. We herefore invesigae wheher he counry-specific PCs are driven by a common underlying facor. To exrac his common euro-zone facor we apply a principal componens analysis o he firs PC of each counry. The resuls of his approach are presened in able (4). The common credi facor explains 89% of he variaion of counry componens. Given ha he loadings of he common facor are quaniaively very similar and range from 0.33 for Ausria o 0.37 for France, he common euro-zone credi facor can be inerpreed as a level facor. 3.3 Esimaion Resuls We firs esimae he baseline model as given by equaion (7). As discussed above, he esimaion is done under he assumpion ha he marke facor, capuring variaions in he risk-free erm srucure, is idenical for each euro-zone counry. As in Cochrane & Piazzesi (2005) we use yearly holding period reurns and esimae he model based on a monhly frequency. Hence, we face an overlapping daa problem and use Newey-Wes (HAC) covariance esimaors in all esimaions. As argued by Cochrane & Piazzesi (2005) we use 18 lags for he Newey-Wes correcion o increase he chance ha i correcs for he MA(12) srucure induced by he overlapping daa. 8

12 Table (5) summarizes he main resuls for he baseline model. We firs urn o he resuls on he credi risk facors. They reveal a highly significan and posiive effec of he common euro-zone credi facor on fuure excess reurns. The p-values of he coefficiens δ (i) 1 do no exceed 0.01 wih he excepion of Spain wih a p-value of Thus, increased euro-zone wide sovereign risk levels are significanly and posiively associaed wih risk premiums in governmen bond markes of all counries covered. We nex urn o he effecs of he counry-specific credi facors, capured by he coefficiens δ (i) 2. Table (5) reveals ha for Ausria, Ialy, and Neherlands counryspecific credi facors have a highly significan and posiive effec on fuure risk premiums, while for Belgium, France, Porugal, Ireland, and Spain he esimaes are insignifican. The laer resul may reflec he fac ha hese counries are imporan sources of sysemic risk wihin he euro zone, so ha here are no significan orhogonal counry-specific facors in heir bond markes. Regarding he coefficiens of he marke facors, denoed by γ (i) 1, γ (i) 2, and γ (i) 3, we find ha for each counry excep France, and marginally Ialy and Spain, a leas one of he marke risk facors is significan. While he coefficiens of he level and curvaure facor exhibi opposie signs for differen counries, we find ha he slope of he German erm srucure is negaively relaed o fuure excess reurns for all counries. While also previous sudies, such as Harvey (1988), Esrella & Hardouvelis (1991), Esrella & Mishkin (1997), Fama & French (1989), Siegel (1991), Fama & Bliss (1987), or Nyberg (2013), have highlighed ha he slope of he erm srucure is relaed o risk premiums, our findings differ in ha i is he negaive of he slope ha predics risk premiums. We aribue his finding o he fac ha a significan par of our daase represens he period of he financial and European deb crisis. Overall, he model seems o exhibi subsanial explanaory power. The average R 2 of he baseline model amouns o 0.61 ranging from 0.51 for France o 0.73 for Ireland. By conras, esimaing he baseline model wihou he common euro-zone and he counry-specific credi facors yields an average R 2 of only Hence, including credi risk facors subsanially increases he explanaory power of he model. The sandard deviaion of he excess reurns in comparison o he sandard deviaions of he esimaed marke risk premiums (M RP ), he common euro-zone credi risk premiums (ECRP ), and he counry-specific risk premiums (CCRP ) reveal he relaive conribuions of risk facors and corresponding risk premiums o he oal 9

13 variaion of expeced excess reurns of sovereigns. A comparison of hese sandard deviaions is given in able (12). Focusing on he boom line of his able which displays average values, we find ha he esimaed euro-zone credi risk premium exhibis he highes volailiy wih a sandard deviaion of almos 0.05, followed by he marke and counry-specific credi risk premiums wih sandard deviaions of 0.03 and 0.02, respecively. Hence, i appears ha over he sample period mos of he variaion of expeced excess bond reurns of euro-zone counries is aribuable o he common euro-zone credi risk facor, whereas counry-specific credi risk premiums seem o play a subordinae role. The dominance of he common euro-zone facor suggess ha invesors canno eliminae hese risks hrough diversificaion. Hence, governmen bonds exposed o common euro-zone credi risk will only be aracive for invesors if hey offer a posiive risk premium. Table (6) repors he R 2 of he individual-mauriy regressions as given by equaion (8). For he one-year mauriy he average R 2 amouns o I slighly increases o 0.65 for he wo-year mauriy and hen monoonically decreases o 0.55 for he eigh-year mauriy. Finally comparing our resuls o Longsaff e al. (2011) who find ha CDS spreads are driven by a common credi facor ha is highly correlaed wih he US sock and high-yield markes we look a he correlaion beween he common euro-zone credi facor and he STOXX Europe 50 index and find a correlaion of Robusness In his secion we perform a number of robusness checks for our findings. Firs, we specify an alernaive model in which we do no use principal componens o consruc marke and credi facors, bu insead, direcly use forward ineres raes and forward CDS spreads in our regressions. Second, we use euro-zone swap raes insead of he German erm srucure as our riskless benchmark as one migh argue ha even Germany is exposed o some sovereign risk. We hen proceed o re-esimae he model for a shorer period, excluding subperiods in which yields of euro-zone sovereigns urn negaive. Finally, we conduc an ou-of-sample analysis and check he robusness of our resuls over a number of subperiods. 10

14 4.1 Forward Raes as Risk Facors The approach inroduced in he preceding secion makes use of informaion conained in forward raes exraced hrough principal componens. While principal componens allow us o consruc a common euro-zone and orhogonal counryspecific credi facors, hese are laen facors and, hence, do no direcly represen economic variables. In his secion we choose an alernaive roue and consruc marke and credi risk facors, using forward raes direcly. Hence, wih his approach i is no possible o differeniae beween a common euro-zone and counry-specific credi facors. We denoe he alernaive marke and credi risk facors by: MF (A) = ( f (2), f (4), f (6), f (8) ), CF (i,a) = ( cf (i,2), cf (i,4), cf (i,6), cf (i,8) ). These facors are ranslaed ino an esimaed marke and credi risk premium by esimaing he alernaive model: rx (i) +1 = δ (i) 0 + γ (i) MF (A) + δ (i) CF (i,a) + ε (i) +1, (10) where he parameer vecors are given by: γ (i) = ( γ (i) 1, γ (i) 2, γ (i) 3, γ (i) ) 4, δ (i) = ( δ (i) 1, δ (i) 2, δ (i) 3, δ (i) 4 ). In line wih secion 2 we define he esimaed marke and credi risk premium as: MRP (A) γ (i) MF (A), (11) T CRP (A) δ (i) CF (i,a). Table (7) repors he resuls for he model given by equaion (10). Comparing hese resuls wih hose from he sandard model repored in able (5) reveals wo imporan findings. Firs, using forward raes direcly insead of PCs increases he average R 2 from 0.61 o This increase in he R 2 reflecs he fac ha he 11

15 represenaion of he marke risk facor by he firs hree principal componens of he German forward ineres raes, he represenaion of he common euro-zone risk facor by he firs PC of he individual counry s firs PCs, and he represenaion of he counry-specific risk facors by he orhogonal par o he common euro-zone risk facor are associaed wih a loss of informaion ha resuls in a lower R 2. Second, we find ha while he majoriy of forward CDS spreads is significan for mos counries, forward ineres raes are significan in noably fewer cases and ypically a he shor mauriies. Finally, we compare he relaive conribuions of risk facors and corresponding risk premiums o he oal variaion of excess reurns. Table (13) repors he sandard deviaions of excess holding period reurns, marke risk premiums, and credi risk premiums. The average sandard deviaion amouns o 0.04 for he esimaed credi risk premium and o 0.03 for he esimaed marke risk premium. Hence, in line wih he baseline model he resuls sugges ha for our sample period he majoriy of he variaion of excess bond reurns can be aribued o variaions in he credi risk facors. 4.2 Swap Raes as Riskless Ineres Raes In secion 2 we used he German erm srucure of ineres raes o calculae he marke risk facor and he excess holding period reurns. One migh argue, however, ha even Germany is exposed o some sovereign risk. Hence, using he German erm srucure may no be appropriae when modeling defaul free ineres raes. In his secion we herefore follow an alernaive approach and use euro-zone swap raes obained from Daasream as riskless ineres raes. Comparing swap raes wih German zero-coupon yields shows ha over he sample period he average swap raes are higher han he German zero-coupon yields. The differences range from 52 basis poins for a hree-year mauriy o 34 basis poins for an eigh-year mauriy. In line wih secion 2 we use he erm srucure of swap raes o compue one-year forward raes saring in one, hree, five, and seven years, denoed by f (2,s), f (4,s), f (6,s), and f (8,s). Again we exrac he firs hree principal componens from hese forward raes which ogeher consiue he marke risk facor: MF (s) = ( MF (1,s), MF (2,s), MF (3,s) ). (12) We hen redefine excess holding period reurns on he basis of swap raes. Hence, 12

16 we replace equaion (5) by: rx (i,n,s) +1 = r (i,n) +1 r (n,s) +1, (13) where r (n,s) +1 denoes he swap rae wih mauriy n. Finally, we define average excess holding period reurns: rx (i,s) +1 = 1 ( (i,1,s) rx +1 + rx (i,2,s) +1 + rx (i,3,s) +1 + rx (i,4,s) +1 (14) 8 + rx (i,5,s) +1 + rx (i,6,s) +1 + rx (i,7,s) +1 + rx (i,8,s) ) +1. Wih hese definiions we can specify he model using swap raes as: rx (i,s) +1 = δ (i) 0 + γ (i) MF (s) + δ (i) 1 CF (Euro) + δ (i) 2 CF (Counry,i) + ε +1. (i) (15) Table (8) repors he esimaion resuls for equaion (15). Overall, he resuls from his specificaion are similar bu weaker han hose obained for he baseline specificaion using he German erm srucure. None of he coefficiens of he forward swap raes is consisen in sign across all counries and several coefficiens are insignifican. The common euro-zone facor is no significan for Ausria and France, while he counry-specific credi risk facor is no significan for Belgium, Ireland, and Porugal. A comparison of ables (5) and (8) shows ha he average R 2 drops from 0.61 o 0.48 when using swap raes o proxy for he riskless erm srucure. Hence, in our analysis swap raes seem o be a less suiable proxy for risk-free ineres raes han German zero-coupon yields. One possible explanaion for his resul is ha swap raes are exposed o couner pary risk. 2 Especially during he financial crisis such a credi risk componen implici in he swap raes migh have been subsanial and also correlaed wih sovereign risk. 4.3 Excluding Negaive Yields One imporan feaure of he euro-zone zero-coupon yield daa used in his paper is ha beginning in he second half of 2014, yields, especially wih shorer mauriies, become negaive. In order o check wheher and how negaive yields affec our 2 See, for example, Feldhüer & Lando (2008). 13

17 esimaion resuls, we re-esimae he model for a shorer sample period ending in March 2014, hereby excluding negaive yields in our sample. The resuls of esimaing equaion (7) for his shorer sample period are repored in able (9). I urns ou ha while he average R 2 increases only slighly from 0.61 o 0.63, he average R 2 M, i.e. he R 2 of a model including only marke facors, increases from 0.21 o This value is close o he value of 0.35 ha Cochrane & Piazzesi (2005) find in heir specificaion. Hence, he marke risk facor explains fuure excess reurns much beer during he shorened period han over he full sample including negaive yields. Table (9) also shows ha while he coefficiens of he level and curvaure facor, γ (i) 1 and γ (i) 3, are largely insignifican, he slope of he German erm srucure, γ (i) 2, is significanly and negaively relaed o fuure excess reurns for mos counries in he sample. We hus conclude ha when excluding negaive yields i is, among he marke facors, mainly he slope componen ha drives fuure excess reurns. 4.4 Ou-of-sample Analysis In his secion we perform an ou-of-sample analysis in which we randomly (by drawing wihou replacemen) spli our sample ino a raining se consising of 75% of he daa and a es se consising of he remaining 25%. We hen esimae he model for he raining se and compue he prediced values and he pseudo R 2 for he es se. We repea his procedure imes and repor he median as well as he 5% and 95% quaniles of he pseudo R 2 for he es se for each counry. We perform his ou-of-sample analysis for he alernaive model specificaion discussed in secion 4.1 and hence we do no rely on a principal componens analysis of our forward ineres raes and forward CDS spreads. The resuls are presened in able (14) in he appendix and show ha he average of he median R 2 over he differen counries amouns o 0.60, close o he average R 2 of 0.65 of he alernaive model presened in able (7). The averages of he 5% and 95% quaniles of he R 2 over he differen counries amoun o 0.36 and 0.75, respecively. The average of he median RM 2 amouns o 0.28, again close o he average RM 2 of 0.30 of he alernaive model. The corresponding average 5% and 95% quaniles of he RM 2 equal 0.11 and 0.48, respecively. 14

18 5 Conclusion This paper explores risk premiums in euro-zone governmen bond markes. In he spiri of Fama & Bliss (1987) and Cochrane & Piazzesi (2005) we use he erm srucure of forward ineres raes as explanaory variables for subsequen risk premiums. Since Germany was considered a safe haven by invesors hroughou recen episodes of European sovereign risk, we use he yield curve of German zero-coupon governmen bonds as a proxy for he erm srucure of riskless ineres raes in he euro zone. In he baseline specificaion of our economeric model we exrac he firs hree principal componens, represening a level, slope, and curvaure facor, from he erm srucure of German forward ineres raes and use hese facors o consruc a marke risk facor. The main conribuion of he paper is o augmen his marke risk facor by facors accouning for sovereign credi risk in he euro zone. To his end we collec CDS spreads for a se of eigh euro-zone counries and calculae for each counry he corresponding one-year forward CDS spreads one year, hree years, five years, and seven years ou. For each of he eigh counries we find ha he firs principal componen of he erm srucure of forward CDS spreads explains a leas 90% of heir variaion. In our baseline model we herefore focus exclusively on he firs principal componen of he erm srucure of forward CDS spreads for each counry. In a second principal componen analysis we exrac he firs principal componen from hese eigh counries firs principal componens and define i as our common euro-zone credi facor. Finally, counry-specific credi risk facors are defined by he error erm of a simple linear regression of each counry s firs principal componen on he common euro-zone credi facor. We demonsrae ha he marke risk facor, he common euro-zone credi risk facor, and he counry-specific credi facors provide a robus model of risk premiums in euro-zone governmen bond markes. Specifically, we find ha he common eurozone credi facor urns ou o be a significan predicor of bond risk premiums for all counries while he counry-specific credi facors are significan for only a subse of he counries in our sample. Furhermore, we find ha augmening he marke risk facor wih our common eurozone and counry-specific credi facors increases he average R 2 across counries from 0.21 o 0.61, ranging from 0.51 for France o 0.73 for Ireland. The imporance of he common euro-zone credi facor is suppored by he volailiy of he componen of risk premiums which is due o his facor. This volailiy amouns o 0.05 on 15

19 average across counries whereas he average volailiy of he componen of risk premiums ha is due o he marke and counry-specific credi facors amouns o 0.03 and 0.02, respecively. This suggess ha over our sample period mos of he variaion of risk premiums of euro-zone counries is aribuable o he common euro-zone credi facor, whereas counry-specific credi risk premiums seem o play a subordinae role. We perform four main robusness ess. Firs, we use forward ineres raes and forward CDS spreads direcly as explanaory variables, raher han heir principal componens. For his alernaive model specificaion we confirm he main resuls of our baseline model. Second, we re-esimae he model using swap raes as a proxy for riskless ineres raes, raher han German zero-coupon yields. We find ha over our sample period swap raes were subsanially higher han German zero-coupon yields, indicaing ha he laer represen a beer proxy for riskless ineres raes. Consisen wih his observaion we find ha he resuls based on swap raes are weaker han hose for he baseline model. Third, we re-esimae he model for a shorer sample period, excluding he ime period in which negaive yields occur. We confirm our main resuls and find ha when excluding negaive yields, he average predicive power of he marke risk facor rises from 0.21 o 0.36 and ha among he individual marke risk facors, he slope of he erm srucure of German forward ineres raes represens he mos significan facor. Fourh, we conduc an ou-ofsample analysis in which we repeaedly and randomly spli our daase ino raining and es ses, esimae our model for he raining ses, and compue he prediced values and he pseudo R 2 for he es ses. Comparing he quaniles of hese R 2 wih hose from our baseline model, we confirm our main resuls. Overall we find ha he erm-srucures of forward ineres raes and forward CDS spreads conain imporan informaion abou fuure risk premiums for euro-zone governmen bonds. Furhermore, risk premiums ha are due o a credi risk componen can be decomposed ino a common euro-zone as well as counry-specific componens, where he former conribues he larges share of he ime-variaion of oal euro-zone bond risk premiums. 16

20 6 Appendix 6.1 CDS Valuaion & Forward CDS Spreads This secion summarizes he exracion of forward CDS spreads from he erm srucure of spo CDS spreads. The mehodology applied follows sandard CDS valuaion echniques as presened for example in O Kane (2008). The fair spread of a CDS conrac denoed by c T equaes he premium and proecion leg of he conrac. The premium leg V prem represens he expeced presen value of premium paymens made by he proecion buyer o he proecion seller unil he conrac maures or a credi even occurs: V prem = c T RP V T, (16) RP V T = + N δ( n 1, n )Z(, n )Q(, n ) (17) n=1 N n δ( n 1, u)z(, u)( dq(, u)), n=1 n 1 where n for n = 1,..., N denoe he premium paymen daes, 0 =, T = N denoes he mauriy dae of he conrac, and δ( n 1, n ) refers o he day coun fracion beween wo consecuive premium paymen daes n 1 and n. The variable Z(, u) denoes he price of a risk-free zero-coupon bond a ime mauring a ime u and Q(, u) refers o he risk-neural survival probabiliy unil ime u. Hence, he firs erm on he righ-hand side of equaion (17) is he expeced presen value of premium paymens made by he proecion buyer o he proecion seller assuming ha a credi even can occur only a paymen daes while he second erm capures he effec of premium accrued if a credi even occurs beween paymen daes. The proecion leg V pro is he expeced presen value of he proecion paymen made by he proecion seller o he proecion buyer if a credi even occurs: T V pro = (1 R) Z(, u)( dq(, u)), (18) 17

21 where R denoes he recovery rae. Equaing he premium and proecion leg yields: c T = (1 R) T Z(, u)( dq(, u)). (19) RP V T Given observed CDS spreads we boosrap he survival curve Q(, i ) for various mauriies i, seing he recovery rae R o he marke convenion of 40% and compuing risk-free zero-coupon bond prices Z(, u) based on he German zerocoupon yield curve. A forward CDS conrac is a conrac ha provides proecion agains defaul of a reference obligaion for a fuure ime period saring a a forward dae τ, τ > 0, unil a mauriy dae T. The premium o be paid over his fuure proecion period is deermined oday a conrac incepion. For such a forward CDS conrac, marke paricipans should be indifferen beween rading a spo CDS conrac wih mauriy dae T or a combinaion of spo and forward conracs covering he same period of ime: c T RP V T = c τ RP V τ + cf τ,t RP V τ,t, (20) where RP V τ,t = RP V T RP V τ and cf τ,t is he spread of a forward CDS conrac wih forward dae τ and mauriy dae T. Hence, forward CDS spreads can be compued by: cf τ,t = ct RP V T RP V T c τ RP V τ RP V τ. (21) Noe ha in secion 2 we denoe one-year forward CDS spreads saring in one, hree, five, and seven years by cf (i,n), where n {2, 4, 6, 8}, for simpliciy. Hence, he noaion cf (i,n) above. in secion 2 corresponds o cf +n 1,+n as used in equaion (21) 18

22 Table 1: Principal Componens Analysis (1) Panel A Forward Ineres Raes Principal -Percen -Toal Componen -explained - Firs Second Third Loadings -Firs -Second -Third f (2) f (4) f (6) f (8) Panel B Forward CDS Ausria Principal -Percen -Toal Componen -explained - Firs Second Third Loadings -Firs -Second -Third cf (2) cf (4) cf (6) cf (8) Panel C Forward CDS Belgium Principal -Percen -Toal Componen -explained - Firs Second Third Loadings -Firs -Second -Third cf (2) cf (4) cf (6) cf (8)

23 Table 2: Principal Componens Analysis (2) Panel A Forward CDS France Principal -Percen -Toal Componen -explained - Firs Second Third Loadings -Firs -Second -Third cf (2) cf (4) cf (6) cf (8) Panel B Forward CDS Ireland Principal -Percen -Toal Componen -explained - Firs Second Third Loadings -Firs -Second -Third cf (2) cf (4) cf (6) cf (8) Panel C Forward CDS Ialy Principal -Percen -Toal Componen -explained - Firs Second Third Loadings -Firs -Second -Third cf (2) cf (4) cf (6) cf (8)

24 Table 3: Principal Componens Analysis (3) Panel A Forward CDS Neherlands Principal -Percen -Toal Componen -explained - Firs Second Third Loadings -Firs -Second -Third cf (2) cf (4) cf (6) cf (8) Panel B Forward CDS Porugal Principal -Percen -Toal Componen -explained - Firs Second Third Loadings -Firs -Second -Third cf (2) cf (4) cf (6) cf (8) Panel C Forward CDS Spain Principal -Percen -Toal Componen -explained - Firs Second Third Loadings -Firs -Second -Third cf (2) cf (4) cf (6) cf (8)

25 Table 4: Principal Componens Analysis (4) Counry Componens Principal -Percen -Toal Componen -explained - Firs Second Third Loadings -Firs -Second -Third Ausria Belgium France Ireland Ialy Neherlands Porugal Spain Table (1) Panel A shows he resuls of a principal componens analysis of German one-year forward ineres raes saring in one, hree, five, and seven years (denoed by f (2), f (4), f (6), and f (8) ) as oulined in secion 2. The upper par shows he proporion of oal variance explained by each of he firs hree principal componens as well as he cumulaive proporion. The lower panel presens he loadings of he firs hree principal componens. Table (1) Panels B and C as well as ables (2) and (3) show he resuls of a principal componens analysis of one-year forward CDS spreads saring in one, hree, five, and seven years (denoed by cf (i,2), cf (i,4), cf (i,6), and cf (i,8) ) for Ausria, Belgium, France, Ireland, Ialy, he Neherlands, Porugal, and Spain as oulined in secion 2. Table (4) presens he resuls of a principal componens analysis of he individual counries firs principal componens. 22

26 Table 5: Baseline Regression 23 Model: rx (i) +1 = δ(i) 0 + γ (i) MF + δ (i) 1 (Euro) CF + δ (i) (Counry,i) 2 CF + ε (i) +1 -Ausria -Belgium -France -Ireland -Ialy -Neherl. -Porugal -Spain δ (i) (0.07) -(0.2) -(0.49) -(0.03) -(0.08) -(0) -(0.11) -(0.18) γ (i) e e-04-8e (0.05) -(0.47) -(0.34) -(0.93) -(0.07) -(0.01) -(0.96) -(0.17) γ (i) e (0.16) -(0.04) -(0.87) -(0.02) -(0.19) -(0.32) -(0) -(0.13) γ (i) (0.03) -(0.49) -(0.38) -(0.06) -(0.91) -(0.71) -(0) -(0.06) δ (i) (0) -(0) -(0.01) -(0) -(0) -(0) -(0) -(0.06) δ (i) (0) -(0.77) -(0.13) -(0.15) -(0) -(0) -(0.2) -(0.13) R R 2 M This able repors he resuls of esimaing equaion (7). The sample period ranges from Ocober 2006 o March 2017 and he esimaion is based on monhly daa covering 114 observaions. Numbers in parenheses represen p-values based on Newey-Wes (HAC) covariance esimaors. R 2 M denoes he R 2 of a regression wihou credi risk facors.

27 Table 6: Individual-Mauriy Regressions -Ausria -Belgium -France -Ireland -Ialy -Neherl. -Porugal -Spain -Mean R 2 1Y R 2 M 1Y R 2 2Y R 2 M 2Y R 2 3Y R 2 M 3Y R 2 4Y R 2 M 4Y R 2 5Y R 2 M 5Y R 2 6Y R 2 M 6Y R 2 7Y R 2 M 7Y R 2 8Y R 2 M 8Y This able repors he R 2 of esimaing equaion (8) for mauriies 1Y o 8Y. The sample period ranges from Ocober 2006 o March 2017 and he esimaion is based on monhly daa covering 114 observaions. RM 2 denoes he R2 of a regression wihou credi risk facors.

28 Table 7: Baseline Regression Alernaive Model 25 Model: rx (i) +1 = δ(i) 0 + γ (i) MF (A) + δ (i) CF (i,a) + ε (i) +1 -Ausria -Belgium -France -Ireland -Ialy -Neherl. -Porugal -Spain δ (i) (0.05) -(0.43) -(0.44) -(0.26) -(0.8) -(0.27) -(0.96) -(0.1) γ (i) (0.12) -(0.1) -(0.22) -(0) -(0.01) -(0.82) -(0) -(0) γ (i) (0.2) -(0.77) -(0.21) -(0) -(0.13) -(0.79) -(0) -(0) γ (i) (0.46) -(0.97) -(0.33) -(0.37) -(0.89) -(0.33) -(0.65) -(0.11) γ (i) (0.77) -(0.1) -(0.16) -(0.34) -(0.96) -(0.31) -(0.1) -(0.55) δ (i) 1-3e-04-5e-04-5e-04-2e-04-3e-04-4e-04-7e-04-7e-04 -(0.09) -(0.02) -(0.01) -(0.34) -(0.25) -(0) -(0) -(0) δ (i) 2-3e-04-5e-04-3e e-04-4e e-04 -(0.22) -(0.01) -(0.09) -(0.06) -(0.23) -(0) -(0.9) -(0.01) δ (i) 3-6e e (0.39) -(0.04) -(0.06) -(0.14) -(0.07) -(0.03) -(0) -(0) δ (i) 4-2e e-04-9e (0.7) -(0.15) -(0.08) -(0.04) -(0.22) -(0.62) -(0.01) -(0) R RM This able repors he resuls of esimaing equaion (10). The sample period ranges from Ocober 2006 o March 2017 and he esimaion is based on monhly daa covering 114 observaions. Numbers in parenheses represen p-values based on Newey-Wes (HAC) covariance esimaors. R 2 M denoes he R 2 when including only forward ineres raes.

29 Table 8: Baseline Regression Swap Raes 26 Model: rx (i,s) +1 = δ(i) 0 + γ (i) MF (s) + δ (i) (Euro) 1 CF + δ (i) (Counry,i) 2 CF + ε (i) +1 -Ausria -Belgium -France -Ireland -Ialy -Neherl. -Porugal -Spain δ (i) e e (0.71) -(0.29) -(0.82) -(0.22) -(0.08) -(0.88) -(0.31) -(0.23) γ (i) e-04-4e-04-5e (0.18) -(0.77) -(0.65) -(0.95) -(0.13) -(0.07) -(0.72) -(0.08) γ (i) (0.6) -(0.2) -(0.07) -(0.12) -(0.77) -(0.01) -(0.05) -(0.49) γ (i) (0.46) -(0.27) -(0.51) -(0.91) -(0.75) -(0.05) -(0.18) -(0.03) δ (i) e (0.18) -(0) -(0.41) -(0) -(0) -(0) -(0) -(0.01) δ (i) (0.01) -(0.67) -(0) -(0.44) -(0) -(0) -(0.9) -(0.03) R R 2 M This able repors he resuls of esimaing equaion (15) where excess holding period reurns are based on swap raes. The sample period ranges from Ocober 2006 o March 2017 and he esimaion is based on monhly daa covering 114 observaions. Numbers in parenheses represen p-values based on Newey-Wes (HAC) covariance esimaors. R 2 M denoes he R2 of a regression wihou credi risk facors.