Term Structure of Interest Rates: The Theories

Transcription

1 Handou 03 Econ 333 Abdul Munasb Trm Srucur of Inrs Ras: Th Thors Trm Srucur Facs Lookng a Fgur, w obsrv wo rm srucur facs Fac : Inrs ras for dffrn maurs nd o mov oghr ovr m Fac : Ylds on shor-rm bond mor volal han ylds on long-rm bonds Fgur : Trm Srucur of h Trasury Ras Fgur, on h ohr hand, gvs us h followng rm srucur fac Fac 3: Long-rm yld nds o b hghr han shor rm ylds yld curvs usually ar upward slopng Fgur : Trasury Yld Curv

2 To xplan hs facs w shall mak us of a hr hors of rm srucur of nrs ras Th Expcaons Thory, whch can xplan Facs and, canno xplan Fac 3 vry wll Th Sgmnd Mark Thory, can xplan Fac 3 bu canno xplan Facs and Th Lqudy Prmum Thory, whch combns boh h xpcaons hory and h sgmnd mark hory, can xplan all h hr facs Th Expcaons Thory Th ky assumpon bhnd hs hory s ha buyrs of bonds do no prfr bonds of on maury ovr anohr, so hy wll no hold any quany of a bond f s xpcd rurn s lss han ha of anohr bond wh a dffrn maury Bonds ha hav hs characrsc ar sad o b prfc subsus No ha wha maks long rm bonds dffrn from h shor rm bonds ar h nflaon and nrs ra rsks Thrfor, hs hory ssnally assums away nflaon and nrs ra rsks To s wha h assumpon ha bonds wh dffrn maurs ar prfc subsus lads o; consdr h followng wo nvsmn srags: : Buy $ of on-yar bond h shor bond and whn maurs buy anohr onyar bond : Buy $ of wo-yar bond h long bond and hold Accordng o h xpcaons hory, hy ar prfc subsus and hr xpcd rurns mus b qual To calcula hs xpcd rurns, frs a fw noaons: nrs ra on -pd bond a, xpcaon a abou h nrs ra on -pd bond a prod, nrs ra on -pd bond a From Invsmn Sragy, h xpcd rurn, 0 bcaus,, From Invsmn Sragy, h xpcd rurn, 0 bcaus,, By xpcaons hory, Tha s, nrs ra on h long bond s h avrag of h nrss on shor bonds xpcd ovr h lf of h long bond Mor gnrally, for n-prod bonds, n n n

3 Consdr a fw numrcal xampls Suppos, on-yar ras ovr h nx fv yars ar 5%, 6%, 7%, 8% and 9% Thn, nrs ra on h wo-yar long bond s 5% 6% 55% And, nrs ra on fv-yar long bond s, 5% 6% 7% 8% 9% 7% 5 Thus, nrs ras for wo o fv yar long bonds ar, 5%, 55%, 6%, 65% and 7%, whch, ssnally, s h yld curv Accordng o h xpcaons hory, long-rm ras ar all avrags of xpcd fuur shor-rm ra If changs so wll n for n,3,4,, c Thus, nrs ras of dffrn maurs wll mov oghr Fac Also, an avrag smoohns ou larg volals Thrfor, f h currn shor-rm ra changs say, h xpcd shor ra of jus h nx yar, wll hav vry ll mpac on a long-rm ra say, h 0-yar ra Thus, shor rm ras ar mor volal Fac Expcaons hory canno xplan why long-rm ylds ar normally hghr han shor-rm ylds, n ohr words, why h yld curv s usually upward slopng If h shor ras ar low now, hy ar xpcd o go up n h fuur In ha cas h yld curv wll b upward slopng On h ohr hand, f h shor ras ar hgh now, hy ar xpcd o go down and n ha cas h yld curv wll b downward slopng Now, a a gvn pon n m, shor-rm ylds ar as lkly o b hgh as hy ar o b low Thrfor, hy ar as lkly o go up as hy ar o go down n h fuur Tha mans ha h xpcaons hory prdcs ha h yld curvs ar as lkly o b upward slopng as hy ar o b downward slopng Thus, h xpcaons hory canno xplan why h yld curv s usually upward slopng 3 Sgmnd Marks Thory Ths hory assums ha marks for dffrn-maury bonds ar complly sgmnd Th nrs ra for ach bond wh a dffrn maury s hn drmnd by h supply of and dmand for h bond wh no ffcs from h xpcd rurns on ohr bonds wh ohr maurs In ohr words, longr bonds ha hav assocad wh hm nflaon and nrs ra rsks ar complly dffrn asss han h shorr bonds Thus, h bonds of dffrn maurs ar no subsus a all, so h xpcd rurns from a bond of on maury has no ffc on h dmand for a bond of anohr maury Bcaus bonds of shorr holdng prods hav lowr nflaon and nrs ra rsks, sgmnd mark hory prdcs ha yld on longr bonds wll gnrally b hghr, whch xplans why h yld curv s usually upward slopng Fac 3 Howvr, snc marks for dffrn-maury bonds ar complly sgmnd, hr s no rason why h shor and long ylds should mov oghr And, bcaus of h sam rason, h sgmnd mark hory also canno xplan why h shor-rm ylds should b mor volal han h longr-rm ylds

4 4 Th Lqudy Prmum Thory Throughou our dscusson of bonds, w mphaszd ha vn h dfaul-fr bonds ar rsky bcaus of uncranly abou nflaon and fuur nrs ras Th rason for h ncras n nflaon rsk ovr m s clar-cu Th bondholdrs car abou h purchasng powr of h rurn h ral rurn hy rcv from bonds, no jus h nomnal dollar valu of h coupon paymns Uncrany abou nflaon cras uncrany abou a bond s ral rurn, makng h bond a rsky nvsmn Th furhr w look no h fuur, h grar h uncranly abou h lvl of nflaon, whch mpls ha a bond s nflaon rsk ncrass wh s m o maury Inrs-ra rsk arss from a msmach bwn nvsor s nvsmn horzon and a bond s m o maury If a bondholdr plans o sll a bond pror o maury, changs n h nrs ra gnra capal gans or losss Th longr h rm of h bond, h grar h prc changs for a gvn chang n nrs ras and h largr h ponal for capal losss As n cas of nflaon, h rsk ncrass wh h rm o maury, so h compnsaon mus ncras as wh Th buyr of long-rm bonds would rqur compnsaon for h rsks hy ar akng buyng long-rm bonds Th lqudy prmum hory vws bonds of dffrn maurs as subsus, bu no prfc subsus Invsors prfr shor rahr han long bonds bcaus hy ar fr of nflaon and nrs ra rsks Thrfor, hy mus b pad posv lqudy rm prmum, l n, o hold long-rm bonds Th yld, hrfor, has wo pars, on ha s rsk fr gvn by h formula accordng o h xpcaons hory and anohr ha s a prmum for holdng a longr-rm bond Thus, h yld on an n-prod bond s, n n ln n As a numrcal xampl, consdr h followng on-yar nrs ras ovr h nx fv yars: 5%, 6%, 7%, 8% and 9% Suppos nvsors prfrncs for holdng shor-rm bonds gvs us followng lqudy prmums for on o fv-yar bonds, rspcvly: 0%, 05%, 05%, 075% and 0% Thn, nrs ra on h wo-yar bond s, 5% 6% 05% 575% And, nrs ra on h fv-yar bond s, 5% 6% 7% 8% 9% 0% 8% 5 Inrs ras on on o fv-yar bonds, hus, ar: 5%, 575%, 65%, 75% and 8% As you can s, lqudy prmum hors produc yld curvs ha mor sply upward slopd Lk h xpcaons hory, h lqudy prmum hory prdcs ha nrs ras of dffrn maurs wll mov oghr bcaus h long-rm ras ar ssnally d o h shor-rm ras Long ras wll also b lss volal bcaus par of h long ra, whch s jus an avrag of h shor ras, wll smoohn ou h volaly n h shor ras And fnally, snc h rsk prmum ncrass wh m o maury, h lqudy prmum hory lls us ha h yld curv wll normally slop upwards, only rarly wll ld fla or slop downwards

5 As an llusraon, suppos ha h shor ras ar xpcd o b h sam for h nx 30 yars As Fgur 3 shows, h xpcaon hory wll prdc a fla yld curv, whl h lqudy prmum hory wll prdc an upward slopng yld curv Fgur 3: Yld Curvs Prdcd by Two Thors Fgur 4: Shfs n Yld Curvs Prdcd by h Two Thors Suppos ha h shor ras ar xpcd o fall hroughou h 30 yars n h fuur In ha cas h yld curv prdcd by h xpcaon hory wll b downward slopng bu h yld curv prdcd by h lqudy prmum hory can sll b upward slopng In Fgur 4, whn shor ras r xpcd dcln, h yld curvs wll shf

6 black rd Evn whn h yld curv from Expcaons hory s ngavly slopd, h yld curv from Lqudy Prmum hory can sll b posvly slopd Ths handou has bn prpard usng Frdrc Mshkn s Mony, Bankng, and Fnancal Marks 8h don, and Sphn Ccch s Mony, Bankng, and Fnancal Marks