国际财务治理课后习题答案(第六章)

CHAPTER6INTERNATIONALPARITYRELATIONSHIPSSUGGESTEDANSWERSANDSOLUTIONSTOEND-OF-CHAPTERQUESTIONSANDPROBLEMSQUESTIONSGiveafulldefinitionofarbitrage.Answer:Arbitragecanbedefinedastheactofsimultaneouslybuyingandsellingthesameorequivalentassetsorcommoditiesforthepurposeofmakingcertain；guaranteedprofits.Discusstheimplicationsoftheinterestrateparityfortheexchangeratedetermination.Answer:Assumingthattheforwardexchangerateisroughlyanunbiasedpredictorofthefuturespotrate,IRPcanbewrittenas:S=[(1+I£)/(l+I$)]E[St+iIt].Theexchangerateisthusdeterminedbytherelativemterestrates,andtheexpectedfiitiuespotrate,conditionalonalltheavailableuiformation,It,asofthepresenttune・On亡thuscansaythatexpectationisself-fxilfilling・Sincetheinformationsetwillbecontinuouslyupdatedasnewshitthemarket,theexchangeratewillexhibitalughlydynamic,randombehavior.Explaintheconditionsunderwhichtheforwardexchangeratewillbeanunbiasedpredictorofthefiitiuespotexchangerate・Answer:Theforwardexchangeratewillbeanunbiasedpredictorofthefiiturespotrateif(I)theriskpremiumisinsigmficantand(ii)foreignexchangemarketsareHiformationallvefficient・Explainthepurchasmgpowerparity,boththeabsoluteandrelativeversions.Whatcausesthedeviationsfromthepurchasmgpowerparity?Answer:Theabsoluteversionofpurchasmgpowerparity(PPP):s=pypf.Therelativeversionis:PPPcanbeviolatediftherearebarrierstouiternationaltrade01ifpeopleindifTerentcountrieshavedifferentconsumptiontaste.PPPisthelawofonepriceappliedtoastandardconsumptionbasket.8.Explaintherandomwalkmodelforexchangerateforecasting.Canitbeconsistentwiththetecluucalanalysis?JAnswer:Theraiidomwalkmodelpredictsthatthecuirentexcliangeratewillbethebestpredictorofthefutureexchangerate.Ailunplicationofthemodelisthatpasthistoryoftheexchangerateisofnovalueinpredictingfutureexchangerate.Themodelthusisinconsistentwiththetecluucalanalysiswhichtriestoutilizepasthistoryuipredictingthefiituieexchangeirate.*9.Deriveandexplainthemonetaryapproachtoexchangeratedetermination・Answer:ThemonetaryapproachisassociatedwiththeClucagoSchoolofEconomics・Itisbasedontwotenets:purcliasingpowerparityandthequantitytheoryofmoney.Combingthesetwotheoriesallowsforstating,say,theS/£spotexchangerateas:S($/£)=(M^M£)(Vs^£)(y^ys),whereMdenotesthemoneysupply,Vthevelocityofmoney,andythenationalaggiegateoutput.Thetheoryholdsthatwhatmattersinexchangeratedetermmationare:Therelativemoneysupply,Therelativevelocitiesofmonies,andTherelativenationaloutputs・10.CFAquestion:1997,Level3.A.Explainthefollowingtliieeconceptsofpurchasingpowerpaiitv(PPP):a.Thelawofoneprice・b・AbsolutePPP.c.RelativePPP.E.EvaluatetheusefulnessofrelativePPPinpredictingmovementsmforeignexchangerateson:Short-termbasis(forexample,tlueemontlis)Long-termbasis(forexample,sixveais)Answer:A.a.Thelawofoneprice(LOP)referstotheinternationalarbitrageconditionforthestandardconsumptionbasket.LOPrequuesthattheconsumptionbasketshouldbeselluigforthesamepriceinagivencurrencyacrosscountries・A.b.AbsolutePPPholdsthatthepricelevelinacountryisequaltothepricelevelinanothercountiytimestheexchangeratebetweenthetwocountries・A.c.RelativePPPholdstliattherateofexchangeratechangebetweenapairofcountliesisaboutequaltothedifferenceininflationratesofthetwocountries.E.a.PPPisnotuseftilforpredictmgexchangeratesontheshoil-termbasismauilvbecauseinternationalconmioditvarbitrageisatmie-consunuiigprocess.E.b.PPPisusefulforpredictingexchangeratesonthelong-termbasis.PROBLEMSSupposethatthetreasurerofIBMhasanextracashreseiveofSi00.000.000tomvestforsixmontlis.Thesix-monthmterestrateis8percentperamiuniintheUnitedStatesand6percentperannummGermany・Currently,thespotexchangerateis€1.01perdollarandthesix-monthforwardexchangerateis€0.99perdollar・ThetreasurerofIBMdoesnotwishtobearaiivexchangerisk.Whereshouldhe/slieinvesttomaximizethereturn?Themarketconditionsaresummarizedasfollows:Is=4%;i€=3.5%;S=€1.01/S;F=€0.99/$.If$100,000,000isinvestedintheU.S.,thematurityvaluemsixmonthswillbe$104,000,000=S100.000.000(1+.04).Alternatively,Si00.000.000canbeconvenedintoeurosandinvestedattheGermaninterestrate,withtheeuromaturityvaluesoldfonvard.Iiithiscasethedollarmaturityvaluewillbe$105,590,909=($100,000,000x1.01)(l+.035)(1/0.99)Clearly,itisbettertomvestS100.000.000iiiGermanywithexchangeriskhedging・WliileyouwerevisituigLondon,youpurchasedaJaguarfor£35,000,payablemtlueemonths.YouhaveenoughcashatyouibankhiNewYorkCity,wliichpays0.35%interestpermonth,compoundingmontlily,topayforthecair.Currently,thespotexchangerateisS1.45/£andthetluee-monthfonvardexchangerateisS1.40/£・IiiLondon,themoneymarketinterestrateis2.0%foratluee-monthinvestment.TherearetwoalternativewaysofpayingforyourJaguar・KeepthefluidsatvourbankintheU.S.andbuy£35,000forvs-aid・BuyaceitampoundamountspottodayandinvesttheamountintheU.K.fortlueemonthssothatthematurityvaluebecomesequalto£35,000.Evaluateeachpaymentmethod.Wliichmethodwouldyouprefer?Why?Solution:Theproblemsituationissunmianzedasfollows:A，P=£35.000payableinthieemonthsixv=0.35%/month.compoundingmontlilyiLD=2.0%fortlueemonthsS=$l・45/£;F=S1.40/£.Optiona:Whenyoubuy£35,000fdns-aid?youwillneedS49.000intlueemontlistofulfillthefonvardcontract.Thepresentvalueof$49,000iscomputedasfollows:$49,000/(1.0035)'=$48,489.Thus,thecostofJaguarasoftodayis$48,489・Optionb:Thepresentvalueof£35.000is£34,314=£35,000/(1.02).Tobuy£34,314today,itwillcost$49,755=34,314x1.45・ThusthecostofJaguarasoftodayis$49,755・Youshoulddefinitelychoosetouse"optionan,andsaveS1.266,winchisthedifferencebehveen$49,755andS48489・Currently,thespotexchangerateisS1.50/£andthetluee-monthforwardexchangerateis$1.52/£.Thetluee-monthinterestrateis8.0%perannumintheU.S.and5.8%perannumintheU.K.AssumethatyoucanborrowasmuchasSi,500,000or£1,000,000.Deteniiniewhetherthemterestrateparityiscurrentlyholdmg・IftheIRPisnotholding,howwouldyoucanyoutcoveredinterestarbitrage?Showallthestepsanddeteniiniethearbitrageprofit.ExplainhowtheIRPwillberestoredasaresultofcoveredaibitiageactivities・Solution:Let'ssxmmianzethegivendatafirst:S=$1.5/£;F=$1.52/£;Is=2.0%;If=1.45%Credit=SI,500,000or£1,000.000.(1+Is)=1.02(l+If)(F/S)=(1.0145)(1.52/1.50)=1.0280Thus.IRPisnotholdingexactly・“7J(1)BorrowSi,500.000;repaymentwillbeS1,530,000.Buy£1,000.000spotusmg$1,500,000.Invest£1.000,000atthepoundinterestrateof1.45%;maturityvaluewillbe£1,014,500.Sell£1.014,500fbrwaidfor$1,542,040Aibitiageprofitwillbe$12.040Followingthearbitragetransactionsdescribedabove.Thedollarinterestratewillrise;Thepoundmterestratewillfall;Thespotexcliangeratewillrise;Theforwaidexchangeratewillfhll.TheseadjustmentswillcontmueuntilIRPholds.Supposethatthecuirentspotexchangelateis€0.80/$andthetluee-monthforwardexchangerateis€0.7813/$・Thetluee-monthmterestrateis5.6percentperamiuniintheUnitedStatesand5.40percentperannuminFiance・Assumethatyoucanborrowupto$1,000,000or€800,000.Showhowtorealizeacertainprofitviacoveredinterestarbitrage,assunuiigthatyouwanttorealizeprofitmtermsofU.S・dollars.Alsodeterminethesizeofyouiarbitrageprofit.Assumethatyouwanttorealizeprofitmtermsofeuios・Showthecoveredarbitrageprocessanddeterminethearbitrageprofitineuros・Solution:(1+is)=1.014<(F/S)(1+i€)=1.053・Thus,onehastoborrowdollarsandinvestineurostomakearbitrageprofit.1・Borrow$1,000,000andrepayS1,014.000hithieemonths.2・SellS1.000,000spotfor€1”60,000.3.Invest€1,060,000attheeurointerestrateof1.35%fortlireemonthsandreceive€1,074,310atmaturity・4・Sell€L074?310forwardforSL053?245.Aibitrageprofit=Sh053,245-$1,014200=$39,245.Followthefiistthieestepsabove・Butthelaststep,involvingexchangeriskhedgmg,willbedifferent.Buy$1,014,000fonvardfor€1,034,280.Ai-bitrageprofit=€1,074,310-€1,034,280=€40,030IntheissueofOctober23,1999.theEconomistreportstliattheinterestrateperaimumis5.93%intheUmtedStatesand70.0%mTurkey.WhydoyoutlunktheinterestrateissoliighinTurkey?Basedonthereportedinterestrates,howwouldyoupredictthechangeoftheexchangeratebetweentheU.S.dollai-andtheTurkishlua?Solution:AlugliTurkishinterestratemustreflectalughexpectedinflationinTuikev.AccordingtointernationalFishereffect(IFE),wehaveE(e)=is-iLira=5.93%-70.0%=-64.07%TheTurkishlirathusisexpectedtodepreciateagainsttheU.S.dollarbyabout64%・AsofNovember1,1999、theexchangeratebetweentheBrazilianrealandU.S・dollarisRS1.95/S・TheconsensusforecastfortheU.S.andBrazilinflationratesforthenext1-yearperiodis2.6%and20.0%,respectively・HowwouldyouforecasttheexchangeratetobeataioundNovember1,2000?Solution:SuicetheinflationrateisquitehiglimBrazil,wemayusethepuichasiiigpowerparitytoforecasttheexchangerate・E(e)=E(tis)-E(krs)=2.6%-20.0%=-17.4%E(St)=S°(1+E(e))=(RS1.95/$)(1+0.174)=RS2.29/S(CFAquestion)OnmiAdvisors,aninternationalpensionfundmanager,usestheconceptsofpuichasmgpowerparity(PPP)andtheInternationalFisherEffect(DFE)toforecastspotexchangerates.Onmigathersthefinancialinformationasfollows:BasepricelevelCurrentU.S.pricelevelCurrentSouthAfiicanpricelevelBaserandspotexchangerateCurrentrandspotexchangerateExpectedannualU.S.uiflationExpectedannualSouthAfiicanmflationExpectedU.S.one-yearinterestrateExpectedSoutliAfiicanone-yearinterestrateill5%8%105$0.175S0.15810%7%100Calculatethefollowingexchangerates(ZARandUSDrefertotheSoutliAfiicanandU.S.dollar,respectively)・ThecunentZARspotrateinUSDthatwouldhavebeenforecastbyPPP・UsingtheIFE,theexpectedZARspotratemUSDoneyearfromnow.UsingPPP,theexpectedZARspotrateinUSDfouryearsfromnow.Solution:ZARspotrateunderPPP=[1.05/1.ll](0.175)=$0.1655/rand・ExpectedZARspotrate=[1.10/1.08](0.158)=$0.1609/rand.ExpectedZARunderPPP=[(1.07)4/(1.05)4](0.158)=S0.1704/raiid・Supposethatthecurrentspotexchangerateis€1.50/£andtheone-yearfbnvardexchangerateis€1.60/£.Theone-yearinterestrateis5.4%meurosand5.2%inpounds・Youcanborrowatmost€1,000,000ortheequivalentpoundamount,i.e.,£666,667,atthecun'entspotexchangerate.Showhowyoucanrealizeaguaranteedprofitfiomcoveredmterestarbitrage.Assumethatyouareaeuio-basedmvestor.Alsodeterminethesizeofthearbitrageprofit.Discusshowtheinterestrateparitymayberestoredasaresultoftheabovetiansactions.Supposeyouareapound-basedinvestor.Showthecoveredarbitrageprocessanddeterminethepoundprofitamount・Solution:First,notethat(1+i€)=1.054islessthan(F/S)(l+ie)=(1.60/1.50)(1.052)=1.1221.Youshouldthusborrowmeurosandlendinpounds.Bonow€1,000,000andpromisetorepay€1,054,000inoneyeai\Buy£666,667spotfor€1,000,000.Invest£666,667atthepoundinterestrateof5.2%;thematiuityvaluewillbe£701,334.Tohedgeexcliangerisk,sellthematurityvalue£701,334fonvardinexchangefor€1,122,134.Thearbitrageprofitwillbethedifferencebetween€1,122,134and€1,054,000,i.e.?€68,134.Asaresultoftheabovearbitragetransactions,theeuromterestratewillrise,thepoundinterestratewillfall.Iiiaddition,thespotexchangerate(eurosperpound)willriseandthefonvaidratewillfall.Theseadjustmentswillcontinueuntiltheinterestrateparityisrestored.Thepound-basedmvestorwillcarryoutthesametransactions1),2)、and3)ina.Buttohedge,he/shewillbuy€1,054,000fonvardinexchangefor£658,750.Thearbitrageprofitwillthenbe£42,584=£701,334-£658,750.Duetotheintegratednatuieofthekcapitalmarkets,investorsinboththeU.S.andU.K.requuethesamerealinterestrate,2.5%,ontheii*lending・Thereisaconsensusincapitalmaiketsthattheannualinflationrateislikelytobe3.5%hitheU.S.and1.5%intheU.K.forthenexttlueeyears・Thespotexchangerateiscuirentlv$1.50/£・ComputethenominalmterestrateperaimummboththeU.S.andU.K.,assumingthattheFishereffectholds.Whatisyourexpectedfiituiespotdollar-poundexchangerateintlueeyearsfromnow?Canyouinferthefonvaiddollai-poundexchangerateforone-yearmaturity?Solution・NominalratemUS=(1+p)(1+E(兀s))-1=(1.025)(1.035)一1=0.0609or6.09%・NonuiialratemUK=(1+p)(1+E(7i£))一1=(1.025)(1.015)一1=0.0404or4.04%.E(St)=[(1.0609)7(1.0404)3](1.50)=S1.5904/£.F=[1.0609/1.0404](1.50)=$1.5296/£.Turkeyvs.U.S.MiniCase:TurkishLiraandthePuichasmgPowerParityVeritasEmerguigMaiketFundspecializeshiinvestinginemerguigstockmarketsoftheworld.Mi.HenryMobaus,anexperiencedhandininternationalinvestmentandyourboss,iscurrentlymterestedmTuikishstockmarkets・HetluiiksthatTurkeywilleventuallybeinvitedtonegotiateitsmembershipintheEuropeanUnion.Ifthishappens,itwillboostthestockpricesinTurkey.But,atthesametime,heisquiteconcernedwiththevolatileexchangeratesoftheTurkishcunency.HuwouldliketounderstandwhatdrivestheTurkishexchangerates・SincetheinflationrateismuchhighermTurkeythanmtheU.S.,hethuiksthatthepuichasmgpowerparitymaybeholdingatleasttosomeextent・Asaresearchassistantforhim、youwereassignedtochecktliisout.Inotherwords,youhavetostudyandprepareareportonthefollowingquestion:DoesthepurcliasingpowerparityholdfortheTurkishlua-U.S.dollarexchangerate?Amongothertlmigs,Mr.Mobauswouldlikeyoutodothefollowing:PlotthepastexchangeratechangesagainstthedifferentialuiflationratesbetweenTurkeyandtheU.S.forthelastfouryears.Regiesstherateofexcliangeratechangesontheinflationratedifferentialtoestimatethemterceptandtheslopecoefficient,andinteiprettheregressionresults・Datasource:YoumaydownloadtheconsumerpriceindexdatafortheU.S.andTurkeyfiomthefollowingwebsite:,"hotfile”(Excelfbmiat).Youmaydownloadtheexchangeratedatafromthewebsite:pacificm亡ice.ubc.ca/xr'data.litml・Solution:a.Inthecurrentsolution,weusethemontlilydatafromJanuary1999一December2002・0.15a))sniJO①6UPUOJOa)-Ea:-0.05-0.05-■♦••z/Z•池•zz♦♦“纶亠0.01/~':•/0.100.050.000.1500.050.1InLTurkey-lnf_US=1.47b.Weregressexchangeratechanges(e)ontlieinflationratedifferentialandestunatetheintercept(a)andslopecoefficient(P):et=d+p(Inf.Tuikev-InfLUS)+st&=-0.011(t=-0.649)B=1.472(t=3.095)Theestimatedinterceptismsignificantlydifferentfiomzero,whereastheslopecoefficientispositiveandsignificantlydifferentfromzeio.Infact,theslopecoefficientismsignificantlydifferentfromunity.[Notetliatt-statisticsforp=1is0.992=(1.472一1)/0.476wheres.e.is0.476]Illotherwords,wecamiotrejectthehypothesisthattheinterceptiszeroandtheslopecoefficientisone.Theresultsaiethussupportiveofpuichasiiigpowerparity・Discusstheimplicationsofthedeviationsfromthepurchasingpowerparityforcountries'competitivepositionsintheworldmarket.Answer:IfexchangeratechangessatisfyPPP,competitivepositionsofcountrieswillreniauiunaffectedfollowingexchangeratechanges・Otherwise,exchangeratechangeswillaffectrelativecompetitivenessofcountries.Ifacountry'sciuTencyappreciates(depreciates)bymorethaniswarrantedbyPPP,thatwillhurt(strengthen)thecountry'scompetitivepositionmtheworldmarket.ExplainandderivetheinternationalFishereffect.Answer:TheinternationalFishereffectcanbeobtauiedbycombiiuiigtheFishereffectandtherelativeversionofPPPinitsexpectationalfbnn.Specifically,theFishereffectholdsthatE（兀s）=Is-Ps,E（K£）=If-pi•Assumingthattherealmterestrateisthesamebetweenthetwocountlies,i.e.,ps=pf.andsubstitutmgtheaboveresultsintothePPP.i.e.,E（e）=E（兀E（兀f）,weobtauithemternationalFishereffect:E（e）=Is-If.Researchersfoundthatitisveiydifficulttoforecastthefutureexchangeratesmoreaccuratelythantheforwardexchangerateorthecuirentspotexchangerate.Howwouldyoumteipretthisfiiidmg?Answer:Thisimpliestliatexcliangemarketsaremfbrmationallyefficient.Thus,unlessonehasprivateinformationthatisnotyetreflectedinthecurrentmaiketrates,itwouldbedifficulttobeatthemarket.