Decomposing the relationship between international bond markets

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1 Dcomposing h rlaionship bwn inrnaional bond marks Andrw Clar and Ilias Lkkos 1 1. Inroducion Th corrlaions bwn major ass classs ar of concrn and inrs o monary auhoriis and financial rgulaors alik h ponial for a worldwid dclin in consumpion which migh rsul from a dramaic fall in quiy mark walh could hav srious implicaions for boh h halh of financial insiuions and ha of h ral conomy. This concrn is rflcd in h acadmic liraur, whr an incrasing numbr of rsarchrs hav rid o undrsand h characrisics of hs linkags and h naur of h procsss by which informaion flows bwn marks. Prhaps h main caalys for his concrn in rcn yars was h quiy mark crash of Ocobr This vn mor han any ohr highlighd h high lvls of corrlaion bwn naional quiy marks a ims of xrm mark srss. Howvr, of qual imporanc is h rlaionship bwn inrnaional bond marks. Typically, monary auhoriis ar abl o influnc dircly only h vry shor nd of h rm srucur. Nvrhlss, givn ha h long bond ra is drmind by xpcaions abou fuur shor-rm ral inrs ras and inflaion, a crdibl monary policy should riggr a ransmission mchanism hrough which monary policy acions ar passd hrough o h whol of h rm srucur. As h covariaion bwn govrnmn bond ras in diffrn counris incrass, h abiliy of monary auhoriis o influnc h rm srucur may dclin, and hnc hir abiliy o conrol domsic inflaion may also dclin. Corrlaion bwn bond marks may aris hrough a numbr of channls, for xampl: if hr is a world pric of risk; if ral ras ar drmind by global facors; or if hr is a fligh o qualiy in ims of financial srss. Uncondiional masurs of h corrlaions bwn major inrnaional bond marks showd ha h linkags bwn hs marks incrasd from h 1960s unil h arly 1980s, bu, according o Solnik al. (1996) and Chrisiansn and Pigo (1997), hs corrlaions hav no xhibid a clar rnd sinc his im. Howvr, whil simpl uncondiional, rolling masurs of inrnaional bond mark corrlaions may no hav bn rnding up in rcn ims, h qusion of how much conrol monary auhoriis can bring o bar upon h shap of h yild curv hrough changs in shor ras sill rmains. Anohr issu rlas o h xn (in rms of duraion and magniud) o which h slop of h yild curv is influncd by inrnaional facors during priods of financial crisis. Finally, anohr imporan and rlad issu is h xn o which comovmns in long bond ras, or indd h componns of hs comovmns, chang during priods of financial mark srss. This papr addrsss all of hs issus. Using h inuiion from h raional xpcaions hypohsis of h rm srucur (REHTS), w dcompos h long bond ras of Grmany, h Unid Kingdom and h Unid Sas ino hir rspciv fundamnal and risk prmium componns. 2 Th dcomposiion is achivd by using h 1 2 W would lik o hank Rogr Clws, Nicola Andrson, Jams Proudman, Nikolaos Panigirzoglou and paricipans a h BIS Auumn 1999 Ming of Cnral Bank Economiss for commns on an arlir draf of his papr. W would lik o poin ou ha h viws xprssd in his papr ar hos of h auhors and do no ncssarily rprsn hos of h Bank of England. s: andrw.clar@bankofngland.co.uk and ilias.lkkos@bankofngland.co.uk Our chniqu dos no allow us o disinguish bwn mor prmann risk prmium componns and mporary conagion ffcs. Howvr, for xposiional simpliciy w us h rm risk prmium in his papr o man som combinaion of h wo. 196

2 Campbll and Shillr (1987) VAR mhodology. Each VAR which w sima conains boh domsic and forign condiioning variabls, which mans ha w can spara ha porion of h varianc of h slop of h yild curv which is influncd by domsic facors from ha porion which is drivn by inrnaional facors. W hn urn our anion o calculaing a condiional masur of inrnaional bond mark covariaion, dcomposing his masur ino is fundamnal and risk prmia componns, by invoking h REHTS. W xnd our analysis o considr h rlaionships bwn srling and US dollar swap marks, a rlaionship which o our knowldg has no bn considrd in his conx by prvious rsarchrs. Finally, bcaus w sima ach of h VARs on a rolling basis, w can monior h im variaion in boh h varianc and h covarianc dcomposiions. Our rsuls suggs ha hr hav bn priods associad wih financial mark criss whn h slops of h govrnmn yild curvs sudid hr ar drmind mor by inrnaional han by domsic facors, for xampl during h srling xchang ra crisis of Howvr, our vidnc suggss in gnral ha onc h crisis has passd, h yild curvs bcom dominad by domsic facors onc again. Wih rspc o h covarianc bwn bond yilds, w find ha whil h oal covarianc bwn h marks is fairly sabl ovr im, h componns of his covarianc can vary considrably ovr im. Th rs of h papr is organisd as follows: in Scion 2 w brifly oulin rlvan acadmic liraur on h opic of financial mark linkags; in Scion 3 w dscrib our mhodology; in Scion 4 w prsn h daa usd hr; in Scion 5 w prsn our rsuls; and finally, Scion 6 concluds h papr. 2. Brif liraur rviw On of h main spurs o rsarch ino financial mark linkags was h Ocobr 1987 sock mark crash. Koumos and Booh (1995) (amongs ohrs) find vidnc o suggs ha inrdpndncis bwn h world s hr major sock marks London, Nw York and Tokyo incrasd afr h 1987 crash. This apparn incras in h linkags bwn naional quiy marks could b du o h globalisaion of financ, and hnc o an incras in h prsnc of inrnaional invsors. Alrnaivly, volailiy ransmission could b h rsul of conagion, as proposd by King and Wadhwani (1990), whr, for xampl, agns do no assss h conomic implicaions of nws from an ovrsas mark for hir own and simply rspond by shooing firs and asking qusions lar (s Shillr al. (1991)). Whil som arly sudis of h informaional linkags bwn marks invsigad h inrdpndncis bwn condiional firs momns (s, for xampl, Eun and Shim (1989), King and Wadhwani (1990) or Koch and Koch (1991)), mor rcn sudis hav focusd upon h rlaionships bwn condiional firs and scond momns. Engl al. (1990) xamin h phnomnon of volailiy clusring in forign xchang marks, making h disincion bwn wha hy rm o b ha wav and mor showr ffcs: h formr rfrring o volailiy which is no ransmid o ohr marks, h lar rfrring o volailiy which is ransfrrd bwn marks. Th Engl al. sudy finds mor vidnc for mor showr han for ha wav bhaviour in h forign xchang daa in hir sudy. Using daily daa on London, Nw York and Tokyo sock indics, Koumos and Booh (1995) sima a mulivaria E-GARCH modl o s for spillovr ffcs bwn h condiional firs and scond momns of rurns in hs marks. Whil hy find clar vidnc of such spillovrs, hy also find ha h volailiy ransmission is asymmric, wih ngaiv shocks from on mark having a largr impac upon h volailiy of anohr mark han quivaln posiiv shocks. Following King and Wadhwani (1990), ohr sudis hav couchd h volailiy ransmission issu as a signal xracion problm, whr agns in h local mark hav o xrac from any nws vn ha porion of h nws which is rlvan o hir mark. For xampl, Lin al. (1994) dcompos rurn surpriss from on mark ino is global and local componns using Kalman filring chniqus. 197

3 An alrnaiv approach o h analysis of h rlaionship bwn naional quiy marks can b found in Ammr and Mi (1996), who us a varian of h Campbll and Shillr (1987) varianc dcomposiion for quiis o analys h rlaionship bwn US and UK sock rurns. From 1957 o 1989 hy find ha hr was an incras in h corrlaion boh bwn xpcd dividnds and bwn risk prmiums in hs wo counris, bu ha hs corrlaions hav changd lil sinc Finally, som rsarchrs hav also considrd h rlaionship bwn bond and sock marks. Shillr and Blrai (1992) and Campbll and Ammr (1993) invsiga h rlaionship bwn bond and sock marks using h VAR approach of Campbll and Shillr (1987) o dcompos ass rurns. Shillr and Blrai find ha h ngaiv rlaionship obsrvd bwn ral sock prics and long-rm inrs ras is much biggr in magniud compard o h rlaionship implid by h simpl raional xpcaions prsn valu modl. Using a similar VAR dcomposiion for US daa, Campbll and Ammr (1993) find ha sock rurns ar drivn mainly by nws abou fuur sock rurns, whil bond rurns ar prdominanly drivn by inflaion, hus xplaining h low corrlaion bwn h rurns on hs wo long-rm asss. To our knowldg, far fwr rsarchrs hav invsigad h rlaionships bwn inrnaional bond marks (for an xcpion o his gnral rul, s Dahlquis al. (1999)). Th purpos of his papr, hn, is o add o h liraur on financial mark linkags by considring h links bwn fixd incom marks. 3. Mhodology 3.1 Srucural dcomposiion of bond mark covariaion W bgin by oulining a dcomposiion of h covariaion bwn long-rm bond ras. To achiv his mor srucural approach o h linkags bwn inrnaional bond marks, w mak us of h REHTS. In is original form h REHTS dfins currn long-rm inrs ras as an avrag of xpcd fuur shor-rm ras plus a consan risk prmium. Givn h ovrwhlming mpirical vidnc agains h pur xpcaions hypohsis, w adop a mor gnral vrsion of h REHTS ha allows for a im-varying, risk prmium (s Evans and Lwis (1994)). For pur discoun bonds w can wri: (1) R k, = R k, + RPk, whr R, is h yild on a k-mauriy pur discoun bond and k associad wih buying a long bond rlaiv o rolling ovr on-priod bonds. k-mauriy ra according o h xpcaions hypohsis givn by: RP, is h risk prmium a im k R k, is h horical 1 k 1 (2) R k, = Er1, + i k i= 0 whr E dnos h mark s xpcaions condiional upon informaion availabl a im and is h on-priod ra a im +i. Similarly w can dfin forign bond ras as: (3) k, = R k, RP k, R + r 1, + i Givn quaions (1) and (3), h covarianc bwn domsic and forign inrs ras can b wrin as: (4) Cov( R, R ) = Cov( R = Cov( R + RP, R, R + RP ) + Cov( R ), RP ) + Cov( RP, R ) + Cov( RP, RP ) 198

4 How can w inrpr hs componns? Th firs componn in xprssion (4) masurs ha par of h covariaion bwn wo bond marks which can b aribud o h covariaion in invsors xpcaions abou fuur shor-rm inrs ras in h wo counris. Givn ha hs xpcaions will rflc considraions abou h fuur pah of inflaion, ral inrs ras and h monary policy sanc in ach counry, w assum ha his componn rflcs h par of h oal covariaion du o conomic fundamnals bwn h wo conomis. If h wo conomis rack ach ohr hrough h businss cycl, w migh xpc h links bwn h wo bond marks o b qui srong. Th rmaining componns ar a dirc rsul of our us of h REHTS. In h absnc of a bond mark risk prmium h fully anicipad raional xpcaion of h long ra will qual h acual long ra. W can hrfor inrpr h diffrnc bwn R k and R k as h risk prmium rquird for holding govrnmn bonds, RP. Th scond (hird) componn hn rprsns h covariaion bwn domsic (forign) fundamnals and h forign (domsic) inrs ra risk prmium. Finally, h fourh componn masurs h covariaion bwn domsic and forign risk prmia. 3.2 Gnraing xpcaions of fuur long ras On difficuly in calculaing h covarianc dcomposiion givn by xprssion (4) is ha non of h long-rm inrs ra componns ar dircly obsrvabl. Sinc h componns of xprssion (4) dpnd upon long-horizon xpcaions of shor-rm inrs ras, w nd som way o condiion hs xpcaions. To his nd w us h vcor auorgrssion (VAR) mhodology o calcula mulipriod xpcaions of h long ra (s Campbll and Shillr (1987)). 3 Having chosn his VAR mhodology, h nx issu rlas o h choic of condiioning variabls. Campbll and Shillr (1987) us a wo-dimnsional vcor of sa variabls, which includs h changs in h shor ra and h slop of h rm srucur, in undraking his xrcis using US daa. An assumpion inhrn in such a formulaion is ha invsors xpcaions abou fuur shorrm ras ar affcd only by informaion concrning domsic fundamnals as rflcd in h shor ra and h slop of h rm srucur. Howvr, sinc h aim of his papr is o invsiga h linkags bwn naional bond marks, w condiion xpcaions abou fuur long ras on boh domsic and inrnaional masurs of h shor ra and h slop of h rm srucur. Our innion hn is o formula a VAR using informaion from h bond marks of Grmany, h Unid Kingdom and h Unid Sas in such a way ha inrs ra xpcaions ar joinly drmind, hus allowing for possibl inracions bwn domsic and inrnaional fundamnals. In ordr o achiv his inracion, w xpand h informaion s o includ informaion on hr diffrn rm srucurs. 4 As a rsul h vcor of sa variabls is dfind as: = 1 yar, 1yar, 1yar, (5) z [ r, r, r, Slop, Slop, Slop ] whr h suprscrips and rla o h firs and scond forign marks rspcivly. Having chosn h informaion s, w can follow Campbll and Shillr (1987) and dfin h horical slop of h rm srucur undr h xpcaions hypohsis, s k,, as: (6) s k, = R k, r1, Subsiuing (2) ino (5), w g: 1 k 1 (7) s k, = ( k i) E ( r1, + i+ 1) k i= 1 whr dnos h on-priod backward diffrnc opraor dfind as r 1, + i+ 1 = r1, + i+ 1 r1, + i. 3 4 For a mor daild discussion on alrnaiv mhodologis usd o valua mulipriod xpcaions of unobsrvd variabls and hir shorcomings rlaiv o h VAR approach, s Campbll and Ammr (1993). Th numbr of counris includd in h vcor of sa variabls is limid only by daa availabiliy. 199

5 Similar xprssions o (6) and (7) hold for k, s and k, s. To sima h xpcaions of fuur shor-ra changs, w assum ha h vcor of sa variabls dfind by (5) follows a firs-ordr VAR procss: (8) z = Az 1 + w whr z is h vcor of sa variabls givn by (5), A is h marix of h VAR cofficins and w is h vcor of rsiduals. By including h inrs ra changs rahr han h lvls, w nsur saionariy in h VAR. Furhrmor, for rasons of noaional simpliciy and compuaional convninc, w dman h variabls bfor including hm in h VAR. Finally, w no ha h assumpion of h firs-ordr VAR procss is no rsriciv. 5 Basd on his formulaion, h long-horizon xpcaions of changs in on-priod inrs ras j-priods in h fuur, j=1,...,k-1, can b simad by: (9) E ( r1, + j ) = h1 A z, (10) E ( r 1 + j ) = h A z and, (11) E ( r 1 + j ) = h A z T T T 2 T 3 T 2 j j j T 3 whr h 1 = [1,0,0,0,...], h = [0,1,0,0,...] and h = [0,0,1,0,...] ar usd o pick ou h firs, scond and hird lmn of h sa vcor. Onc h marix A of VAR cofficins is simad hn for ach, =1,...,T, h xpcaions of fuur changs in inrs ras can b gnrad using xprssions (9), (10) and (11), and h horical rm srucur slops by using xprssion (7). W can calcula h horical long-rm inrs ra by solving (6) wih rspc o R k,. Th diffrncs bwn h horical and acual long-rm ras provid an sima of h domsic and forign bond mark risk prmium, RP. Esimas of R,, RP k, and k, R, RP k, ar producd by a similar procdur. 6 Givn h simad horical long ras and h risk prmia, hn, for ach pair of counris, componns of h covarianc bwn acual inrs ras can b calculad according o xprssion (4). Our innion is no only o idnify h covarianc componns and h imporanc of domsic and inrnaional facors in drmining inrs ras, bu also o xamin how hs drivd variabls vary ovr our sampl priod. To capur his ffc, w adop a rolling simaion procdur whr h VAR dscribd abov is simad using on yar s worh of daa. W hn roll forward h simaion window by on wk and rpa h procdur oulind abov unil h nd of h sampl priod. By doing his, w can gnra a im sris of h componns of xprssion (4). Finally, h simaion of a VAR allows us o dcompos h varianc of h slops of boh h domsic and forign rm sprads, a procdur which is now common pracic in paprs using unrsricd VARs of h kind usd hr (s Sims (1980) for a dscripion of h chniqu). Th varianc dcomposiion provids us wih an sima of h proporion of h movmn in on variabl which can b aribud o shocks in ohr variabls in h VAR. Sinc w sima h VARs on a rolling basis, w also cra a im sris of his varianc dcomposiion allowing us, for xampl, o gaug h im-varying impac of shocks o ovrsas inrs ras on h slop of h UK yild curv. k k, 5 6 Campbll and Shillr (1988) dmonsra ha i is sraighforward o modify h modl o allow for a highr VAR ordr. Ths simas of h risk prmia will b accura providd ha w includ in our modl all h rlvan informaion ha invsors us o form hir xpcaions abou fuur inrs ras and ha h dynamics of h VAR ar corrcly spcifid. If hs condiions ar no m, simas of risk prmia will b biasd upwards. 200

6 3.3 Exnding h analysis o inrs ra swaps Inrs ra swaps ar conracs which allow wo counrparis o xchang fixd for floaing inrs ra paymns. Th fixd ra of h swap is usually dfind as h ra of h undrlying govrnmn bond plus a mark-up, known as h sprad. This sprad is ofn usd o mak infrncs abou dfaul risk in an conomy,.g. h srling (US dollar) swap sprad is ofn usd in h financial prss as a masur of dfaul risk in h Unid Kingdom (Unid Sas). I is possibl o xnd h VAR mhodology o invsiga h imporanc of domsic vrsus forign facors in drmining h siz of h swap sprad, nabling us, for xampl, o rac h im pah of h apparn crdi crunch which affcd inrs ra swap marks afr h rcn Russian db crisis. Th main aim of his analysis is o idnify priods whr condiions in inrnaional swap marks ovrrid domsic facors as h driving forc of swap sprads. During hs priods h inrpraion of h sprad as an indicaor of aggrga domsic dfaul risk 7 may b mislading. Prvious rsarch (s, for xampl, Sun al. (1993) or Minon (1997)) has shown ha long-rm swap sprads ar affcd by changs in h slop of h rm srucur. Hnc, w can dfin h following vcor of sa variabls: = 1 yar, 1yar, (12) z [ r, r, Slop, Slop, swap sprad, swap sprad ] Th analysis of swap sprads has bn limid o only wo counris purly du o daa availabiliy, as discussd in h following scion. Using h vcor of sa variabls givn in xprssion (12), w can again calcula h rolling varianc dcomposiion, as oulind in Scion Daa 4.1 Daa dscripion W sima h VARs using wkly on- and 10-yar US, UK and Grman inrs ras. Ths ar zro coupon inrs ras simad from h prics of coupon-paying govrnmn bonds using h Tabl 1 Dscripiv saisics Ras From To No. obs. Man S. dv. Min. Max. US inrs ras 1-yar 15 Augus Augus yar 15 Augus Augus Slop 15 Augus Augus UK inrs ras 1-yar 15 Augus Augus yar 15 Augus Augus Slop 15 Augus Augus Grman inrs ras 1-yar 9 Ocobr Augus yar 9 Ocobr Augus Slop 9 Ocobr Augus UK swap sprads 10-yar 15 Augus Augus US swap sprads 10-yar 15 Augus Augus S, for xampl, Swap sprads show a nw avrsion o risk, Financial Tims, 10 Augus 1999, p

7 Svnsson mhodology (Svnsson (1994, 1995)). 8 Th zro coupon daa availabl for h hr counris bgin on diffrn das: from January 1979 for h Unid Kingdom, from Augus 1990 for h Unid Sas and from Ocobr 1991 for Grmany. 9 Givn ha h VARs ar joinly simad for hr counris a a im, h simaion priod for ach VAR is s qual o h priod ovr which ovrlapping daa bwn h hr counris ar availabl. Dscripiv saisics for h daa usd ar givn in Tabl 1. In addiion, w xnd our analysis o inrs ra swap sprads. Only srling and US dollar swap ras wr availabl o us for a sufficin span of im. Th swap daa span h priod from Augus 1990 o Augus From zro coupon swap ras 10 w subrac h quivaln mauriy zro-coupon inrs ra simad from h appropria Svnsson yild curv o provid simas of h srling and dollar swap sprads. 5. Rsuls W now prsn h rsuls rlaing o various vrsions of h VAR oulind in Scion 4 abov. This VAR is simad using govrnmn bond mark daa for Grmany, h Unid Kingdom and h Unid Sas. W also sima h VAR givn in xprssion (12) using swap mark daa. W bgin by discussing h rsuls of h varianc dcomposiions of hs VARs and hn mov on o discuss h dcomposiion of h covarianc. 5.1 Varianc dcomposiion rsuls Govrnmn bond mark rsuls In Figur 1 w prsn h varianc dcomposiion for h slop of h US yild curv, basd upon a VAR which includs Grman, UK and US variabls. Th figur rpors h proporion of h varianc of h slop of h rm srucur ha can b aribud o shocks in h variabls of h VAR, 26 wks ino h fuur. 11 On known shorcoming of h VAR mhodology is ha h varianc dcomposiion rsuls may b influncd by h ordring of h variabls in h VAR. In our VAR h firs variabl in h sa vcor is h chang in shor-rm US inrs ras, followd by h chang in Grman and hn UK shor-rm ras, which ar followd in urn by h slops of h US, Grman and UK yild curvs. Th raison d êr for his ordring is ha shocks o shor-rm ras should affc h slops of h yild curvs. Th ordring of h counris, wih h Unid Sas firs hn Grmany and hn h Unid Kingdom, rflcs our priors of h imporanc of hs conomis and hir rspciv bond marks in a global sns Mor dails on h implmnaion of h Svnsson mhodology and h simaion of zro coupon rm srucurs ar providd in Appndix A. From January 1999 h Grman ras ar rplacd by uro inrs ras. Appndix B givs mor dails abou h simaion of zro coupon inrs ras simad from swap ras. Th varianc dcomposiion rsuls prsnd hr could b basd upon cofficins which ar poorly drmind. To s for his possibiliy, and o s for causaion bwn forign influncs on h domsic rm srucur, w s a null hypohsis ha h VAR cofficins rlaing o h forign variabls ar joinly insignifican, i.. ha hy do no hlp o prdic h domsic slop and inrs ra chang. W undrak his s on a rolling basis. In h inrss of brviy, w do no rpor h rsuls in dail hr; howvr, w find ha for all of h VARs prsnd in his papr h null hypohsis of no forign influnc on domsic inrs ras can b rjcd for h majoriy of h sampl priod considrd hr, and in paricular for h crisis priods. An alrnaiv way of inrpring hs rsuls is ha dual causaliy, in h Grangr causaliy sns of h rm, xiss bwn hs marks. Ths rsuls ar of cours availabl on rqus from h auhors. 202

8 Figur 1 shows ha on avrag 60% of h slop of h US yild curv is drmind by US variabls, and hrfor ha hr is a significan inrnaional componn in his slop on avrag, and during four priods in paricular. Th firs priod rlas o h srling xchang ra crisis whn h Unid Kingdom was forcd ou of h ERM in During his priod h Grman govrnmn bond mark was xring a considrabl influnc upon h US slop unil normal srvic was rsumd in arly Th scond priod of inrnaional influnc rlas o a priod of monary asing in Grmany in prparaion for h hird sag of EMU in This asing was followd by a wav of associad monary asings across ohr EU counris. This monary asing was also associad wih considrabl EU convrgnc rads across inrnaional bond marks a his im. Th hird priod appars o rla o h Asian crisis of 1997, whil h fourh rlas o h Russian db crisis of Ths las wo pisods wr of cours widly rcognisd as inrnaional criss, and hrfor w bliv ha h UK and Grman marks ar proxying hr for widr inrnaional influncs. Finally, and prhaps mos imporanly, w should no ha afr ach of hs four priods domsic facors gradually rurnd as h dominan influnc ovr h slop of h US yild curv. In Figur 2 w rpor h varianc dcomposiion rsuls for h slop of h Grman curv. On avrag, 70% of h slop of h Grman yild curv is drmind by h Grman variabls in h sysm. This is paricularly ru during h ERM crisis, whr h varianc in h Grman ras accound for almos 100% of h varianc in h yild curv. Th rsuls also indica ha h crisis in Asian financial marks in 1997 and h Russian db crisis in 1998 boh had a rlaivly larg influnc, via UK and US bond marks, upon h rm srucur of Grman govrnmn db. Finally, w migh also no ha hr has bn an incras in h influnc of US bond marks in h scond half of our sampl. Figur 3 rpors analogous rsuls for h facors influncing h slop of h UK yild curv. Th rsuls show ha h UK rm srucur is influncd h mos by inrnaional facors, wih jus lss han 40% of h slop on avrag bing drmind by h UK variabls in h sysm. Th Grman bond mark xrs a larg influnc on h UK bond mark in wo priods. Th firs priod coincids wih h ERM crisis in Th scond, spanning 1995 and 1996, coincids wih h loosning of Grman monary policy during his priod, as oulind abov. Inrsingly, hr ar also wo priods whr h US bond mark influncs h UK bond mark. Th firs follows h ERM xchang ra crisis priod in 1993 and Th scond priod arguably bgins bfor, bu rachs a pak during h financial crisis in Asian marks and rmains high unil h impac of h Russian db crisis dclins owards h middl of Finally, Figur 3 also shows h brif bu dramaic impac of h 203

9 Mxican crisis of 1994, rvaling islf as a sharp incras in h proporion of h volailiy of h UK yild slop which can b xplaind by US bond mark variabls. W could summaris hs rsuls as follows: h varianc of h slop of h UK yild curv appars o hav bn influncd mos by inrnaional bond mark facors, paricularly h US mark; whil h varianc of h slop of h US yild curv has ndd o hav bn influncd by domsic facors, hr hav bn significan priods of im whn is varianc has also bn affcd by inrnaional facors; finally, h varianc of h slop of h Grman yild curv appars o hav bn h mos domsically orinad of h hr marks sudid hr, paricularly during h arly 1990s This rsul is robus o alrnaiv VAR ordrings. 204

10 5.1.2 Swap mark rsuls Finally, w considr h varianc dcomposiion of h rlaionship bwn h US dollar and srling swap marks in Figurs 4 and 5. Th firs variabls in h VAR ar h changs in shor-rm ras, followd by h rm srucur slops and finally by h swap sprads. Th US dollar variabl always prcds is srling counrpar. Figur 4 shows ha h varianc of h US dollar swap sprad is virually unaffcd by h srling sprad, whil h slop of h UK yild curv on avrag drmins 15% of h varianc of h US dollar sprad. Th main facor affcing h US dollar swap sprad, ohr han own variaion, is movmns in h slop of h US rm srucur. This rflcs h way praciionrs pric inrs ra swaps rlaiv o govrnmn bond yilds wih similar mauriis. In conras o his rsul, Figur 5 shows ha h varianc of h srling swap sprad is influncd by h slop of h US yild curv. Prhaps mor imporanly, i is havily influncd by h US dollar swap sprad owards h nd of our sampl, a priod bginning wih h Asian financial crisis and xnding ino h priod surrounding h Russian db crisis. 205

11 Th rsuls wih rspc o h srling swap sprad should ac as a ponial warning for hos who bliv ha swap sprads ar an indicaor of domsic financial condiions. Whil his migh b ru for h US dollar swap mark, clarly a h nd of our sampl h srling swap sprad was bing mor havily influncd by dvlopmns in h US bond and US dollar swap marks han by UK facors. 5.2 Covarianc dcomposiion rsuls W now urn o h rsuls of dcomposing h covariancs bwn h major govrnmn bond marks. In Figur 6 w prsn h uncondiional covarianc bwn UK and US long bond ras. In kping wih h rsuls of Chrisiansn and Pigo (1997) and Solnik al. (1996), w find no sign of an obvious incras in h oal covariaion bwn hs wo marks during h 1990s, which is always posiiv, alhough vry clos o zro for much of h priod. Inrsingly his covarianc masur rachs a pak during 1994, no during h srling, Asian or Russian criss. Figur 6 also shows h covarianc ovr im bwn h REHTS-drivd masurs of xpcd long ras. Th fac ha his masur of covarianc dos no always rack h oal covarianc closly indicas ha a ims h covarianc bwn hs marks is influncd vry srongly by risk prmium ffcs. This corroboras our prvious findings ha a ims inrnaional facors xr considrabl influnc on h drminaion of h domsic inrs ras, ovrriding in many cass considraions abou domsic fundamnals. Thr ar wo such priods. Firsly, during h srling xchang ra crisis in la Th covarianc bwn h REHTS-drivd xpcaions of h wo long ras indicas ha h rlaionship should b srongly ngaiv, rflcing h fac ha h wo conomis wr a diffrn sags in h businss cycl. Howvr, sinc h oal covarianc is posiiv, his indicas ha hr wr srong risk prmium ffcs prsn a his im offsing h influnc of rspciv domsic conomic condiions. Th scond noabl dviaion bwn h wo sris occurs during h Asian conomic crisis, whr domsic conomic fundamnals wr implying a ngaiv covarianc, bu h impac of h crisis, which raisd h oal covarianc bwn h wo marks ovr his priod, combind o produc a posiiv rlaionship. Finally, w migh also no ha hr ar also ims whn h REHTS-drivd covarianc rm suggss a mor posiiv rlaionship bwn h wo marks han can b sn from h oal covarianc masur. In Figur 7 w prsn analogous rsuls for h US-Grman covarianc dcomposiion. Th oal covarianc bwn hs wo marks paks in Thr is a noicabl, bu small incras in his 206

12 variabl following h Asian crisis which prsiss unil h nd of our sampl. Again his masur is always posiiv and clos o zro for a significan porion of h sampl. Whn w considr h diffrnc bwn h oal covarianc and h REHTS-drivd masur for h Grman-US pair, h rsuls ar in sharp conras o hos involving h Unid Kingdom and h Unid Sas. Th REHTS-drivd masur, wih h xcpion of wo minor, shor-livd pisods in 1995 and in 1998, follows h oal covarianc masur fairly closly. Again his vidnc is consisn wih our prvious findings. Varianc dcomposiion rsuls showd ha, in conras o h Unid Kingdom, h US and Grman yild slops xhibi a smallr dgr of variaion du o inrnaional shocks. This rsul could b akn o indica ha h covarianc bwn hs wo marks is drivn mor by macroconomic fundamnals han by risk prmia. Th oal covarianc bwn h UK and Grman govrnmn bond marks, shown in Figur 8, rachs a pak in 1994 and rmains, posiiv, bu fairly low and sabl during our sampl priod. Th 207

13 srling, Asian and Russian criss again sm o hav had lil impac upon oal covarianc ovr his priod. Thr appar o b a las hr priods whr h REHTS-drivd covarianc componn divrgs subsanially from h oal masur. Th firs of hs priods occurs afr h Unid Kingdom s xi from h ERM in 1992, whn h REHTS masur is srongly posiiv, whil h oal covarianc masur rmains posiiv, bu small. This divrgnc suggss ha h covarianc bwn forign risk prmia and h REHTS masur of inrs ra xpcaions is vry ngaiv ovr his priod and analysis of his sris confirms his o b ru. During 1994, whn h oal covarianc masur is a is maximum, h REHTS-drivd masur is ngaiv for a priod, indicaing srong posiiv corrlaions bwn risk prmia. Finally, owards h nd of our sampl w s ha h REHTS masur is indicaing ha h marks should b posiivly corrlad whil h oal masur rmains low, onc again indicaing ha h risk-prmia-rlad covarianc componns ar ngaivly corrlad wih on anohr, and wih h REHTS masur. 6. Conclusions In his papr w xamin h significanc of domsic and inrnaional facors in drmining h slops of h US, Grman and UK yild curvs, and how h magniud of hir impac flucuas ovr h businss cycl. Our main finding is ha a ims of global financial urmoil, lik h srling xchang ra crisis of 1992, h Asian financial crisis of 1997 and h Russian db crisis of 1998, hs slops rspond mainly o inrnaional facors, prsumably as global invsors ralloca hir bond porfolio holdings and local invsors radjus hir xpcaions abou domsic inrs ras. W also xamin h dcomposiion of h covariancs bwn h US, Grman and UK long-rm inrs ras. Our dcomposiion of h covarianc bwn hs govrnmn bond marks indicas ha risk prmia and/or conagion ffcs hav playd an imporan rol during hs priods, moving h covarianc bwn h marks away from whr w migh hav xpcd i o b if inrnaional bond ras wr drmind solly by h REHTS arbirag. 208

14 Appndix A Th simaion of h rm srucur of inrs ras 13 Th rm srucurs of US Trasury zro coupon bonds ar providd by h Bank of England. Hr w provid a brif discussion of h rlvan issus., i=1,...,n, is h pric (clan pric plus accrud G P i, G inrs) of an ih mauriy bond a im. Th bond P i, pays a sram of cash flows, c ij, (including rdmpion paymns) a ims m ij. Th vcor of discoun bonds corrsponding o h coupon-paying bonds can b simad from h following non-linar modl: (A1) G P i, = cijδ( mij, ) + εij, i = 1,..., n j whr δ m, ) is a paramric discoun funcion wih paramr vcor = β, β, β, β, τ, ). ( ij ( τ2 Th funcional form slcd by h Bank of England is basd on h Svnsson (1994, 1995) gnralisaion of h Nlson and Sigl (1987) modl. According o Svnsson h rm srucur of zro coupon yilds is givn by: y( m, (A2) ) = β 0 m τ 1 + β1 m / τ 1 1 τ 1 + β2 m / τ1 1 + β3 m / τ and h discoun funcion is: m 1 m τ 2 2 m τ 1 m τ 2 (A3) δ ( m, y( m, ) = xp 100 ) m Equaions (A2) and (A3) ar subsiud in quaion (A1) and h paramr vcor a non-linar maximisaion algorihm. is simad via 13 This appndix is largly basd on h work undrakn by h Monary Insrumns and Marks division a h Bank of England. S Bianchi (1997) and Andrson al. (1996) for mor dails. 209

15 Appndix B Swap mark daa Th mos common yp of inrs ra swap is h fixd-o-floaing par swap. This is a conrac bwn wo counrparis o xchang fuur cash flows or quivalnly o xchang inrs ra risk posiions. On pary of h swap, namly h fixd payr, agrs o pay, on ach paymn day unil h mauriy of h swap, an amoun qual o a fixd inrs ra applid on a noional principal. In rurn, h fixd payr rcivs from h ohr counrpary, h floaing payr, cash flows basd on h sam noional principal bu calculad wih rspc o a floaing inrs ra,.g. Libor. Th paymns of hs cash flows usually occur ihr annually or smiannually. Th chniqu usd o infr h prics of zro coupon bonds from swap ras is calld boosrapping and is basd on h fac ha inrs ra swaps ar par insrumns wih zro n prsn valu. In h cas of US dollars, whr h swap cash flows occur annually, h prics of discoun bonds implid by h swap mark ar givn by: 1 1 s ( ) (B1) i αi ib = 1 1, 0, i b = 0, 1 + s α 1, whr s is h swap ra, i = 1,2, K, and h accrual facor is α i 1, i. 14 Th only problm is ha swaps ar availabl only for on, wo, hr, four, fiv, svn and 10 yars of mauriy. Thus, a linar inrpolaion has o b usd o g an sima of h missing swap ras. In h cas of pound srling swaps, whr h swap cash flows occur smiannually, h calculaions ar slighly mor complicad. 15 If h swaps mak smiannual paymns, hn w hav o us swap ras vry half a yar in ordr o calcula h zro bond prics for h corrsponding priod. Again a linar inrpolaion has o b usd o g an sima of h missing swap ras. Th only swap ra w ar no abl o calcula using linar inrpolaion is h s 1. 5 swap ra sinc h on-yar swap ra is no availabl and h corrsponding on-yar ra availabl from h mony mark is quod on a diffrn basis. As a rsul an adjusmn has o b mad: (B2) s 1 = α b 1 b 0,0.5 0,1 + α 0.5,1 b 0,1 and s 1. 5 can b calculad by inrpolaing bwn s 1 and s 2. Finally, h zro bond prics can b calculad using h boosrap mhod as in quaion (B1) bu now h indx i in h summaion is bing don smiannually such ha i = 1, 1.5, 2, 2.5,,. Basd on hos zro coupon bond prics, w can sima h implid annualisd yilds as: 16 α 0, 1 (B3) r 0, = 1 b0, In h cas of US dollar inrs ra swaps, h accrual facor is dfind as α 30 i 1, i =. 360 In h cas of srling swap marks, h swap day-coun convnion is 365 days pr yar. Thus, h accrual facor is i i 1 dfind as αi 1, i =. 365 i i 1 Th accrual facors now rfr o bonds and ar dfind a αi 1, i =

16 On-yar forward ras can b simad by: α, + 12m b0, (B4) f 0,, + 12m = 1 b0, + 12m 211

17 Bibliography Ammr, J and J Mi (1996): Masuring inrnaional conomic linkags wih sock mark daa. Journal of Financ, 51(5), pp , Dcmbr. Andrson, N, F Brdon, A Dacon, M Drry and G Murphy (1996): Esimaing and inrpring h yild curv. John Wily & Sons, London. Bianchi, M (1997): Esimaion of forward yild curvs from convnional and indx-linkd bonds. Mimo, Bank of England. Campbll, J Y and J Ammr (1993): Wha movs h sock and bond marks? A varianc dcomposiion for long-rm ass rurns. Journal of Financ; 48(1), pp. 3-37, March. Campbll, J Y and R J Shillr (1987): Coingraion and ss of prsn valu modls. Journal of Poliical Economy; 95, pp Campbll, J Y and R J Shillr (1988): Sock prics, arnings, and xpcd dividnds. Journal of Financ; 43(3), pp July. Chrisiansn, H and C Pigo (1997): Long-rm inrs ras in globalisd marks. OECD Working Papr Sris, Paris. Dahlquis, M, P Hördahl and P Sllin (1999): Masuring inrnaional volailiy spillovrs. This volum. Engl, R F, T Io and W Lin (1990): Mor showrs or ha wavs? Hroskdasic inra-daily volailiy in h forign xchang mark. Economrica, 58, pp Eun, C S and S Shim (1989): Inrnaional ransmission of sock mark movmns. Journal of Financial and Quaniaiv Analysis, 24, pp Evans, M D D and K K Lwis (1994): Do saionary prmia xplain i all? Evidnc from h rm srucur. Journal of Monary Economics, 33, pp King, M A and S Wadhwani (1990): Transmission of volailiy bwn sock marks. Rviw of Financial Sudis, 3(1), pp Koch, P D and T W Koch (1991): Evoluion in dynamic linkags across daily naional sock indxs. Journal of Inrnaional Mony and Financ, 10(2), pp , Jun. Koumos, G and G G Booh (1995): Asymmric volailiy ransmission in inrnaional sock marks. Journal of Inrnaional Mony and Financ, 14, pp Lin, W, R F Engl and T Io (1994): Do bulls and bars mov across bordrs? Inrnaional ransmission of sock rurns and volailiy. Rviw of Financial Sudis, 7, pp Minon, B A (1997): An mpirical xaminaion of basic valuaion modls for plain vanilla U.S. inrs ra swaps. Journal of Financial Economics, 44, pp Nlson, C R and A F Sigl (1987): Parsimonious Modling of Yild Curvs. Journal of Businss, 60(4), pp , Ocobr. Shillr, R J, F Konya and Y Tsusui (1991): Invsor bhaviour in h Ocobr 1987 sock mark crash: Th cas of Japan. Journal of h Japans and Inrnaional Economy, 5(1), pp. 1-13, March. Shillr, R J and A E Blrai (1992): Sock prics and bond yilds: Can hir comovmns b xplaind in rms of prsn valu modls? Journal of Monary Economics, 30(1), pp , Ocobr. Sims, C A (1980): Macroconomics and raliy. Economrica, 48(1), pp. 1-48, January. Solnik, B, C Boucrll and Y L Fur (1996): Inrnaional mark corrlaion and volailiy. Financial Analyss Journal, pp , Spmbr/Ocobr. 212

18 Sun, T S, S Sundarsun and C Wang (1993): Inrs ras swaps. An mpirical invsigaion. Journal of Financial Economics, 34, pp Svnsson, L (1994): Esimaing and inrpring forward ras: Swdn Working papr 114, Inrnaional Monary Fund. Svnsson, L (1995): Esimaing forward ras wih h xndd Nlson and Sigl mhod. Quarrly Rviw, Svrigs Riksbank. 213

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