国际财务管理(英文版)课后习题答案7

国际财务管理(英文版)课后习题答案7

CHAPTER6INTERNATIONALPARITYRELATIONSHIPSSUGGESTEDANSWERSANDSOLUTIONSTOEND-OF-CHAPTERQUESTIONSANDPROBLEMSQUESTIONS1.Giveafulldefinitionofarbitrage.Answer:Arbitragecanbedefinedastheactofsimultaneouslybuyingandsellingthesameorequivalentassetsorcommoditiesforthepurposeofmakingcertain,guaranteedprofits.2.Discusstheimplicationsoftheinterestrateparityfortheexchangeratedetermination.Answer:Assumingthattheforwardexchangerateisroughlyanunbiasedpredictorofthefuturespotrate,IRPcanbewrittenas:S=[(1+I£)/(1+I$)]E[St+1|It].Theexchangerateisthusdeterminedbytherelativeinterestrates,andtheexpectedfuturespotrate,conditionalonalltheavailableinformation,It,asofthepresenttime.Onethuscansaythatexpectationisself-fulfilling.Sincetheinformationsetwillbecontinuouslyupdatedasnewshitthemarket,theexchangeratewillexhibitahighlydynamic,randombehavior.3.Explaintheconditionsunderwhichtheforwardexchangeratewillbeanunbiasedpredictorofthefuturespotexchangerate.Answer:Theforwardexchangeratewillbeanunbiasedpredictorofthefuturespotrateif(I)theriskpremiumisinsignificantand(ii)foreignexchangemarketsareinformationallyefficient.4.Explainthepurchasingpowerparity,boththeabsoluteandrelativeversions.Whatcausesthedeviationsfromthepurchasingpowerparity?IM-12nAnswer:Theabsoluteversionofpurchasingpowerparity(PPP):S=P$/P£.Therelativeversionis:e=p$-p£.PPPcanbeviolatediftherearebarrierstointernationaltradeorifpeopleindifferentcountrieshavedifferentconsumptiontaste.PPPisthelawofonepriceappliedtoastandardconsumptionbasket.5.Discusstheimplicationsofthedeviationsfromthepurchasingpowerparityforcountries’competitivepositionsintheworldmarket.Answer:IfexchangeratechangessatisfyPPP,competitivepositionsofcountrieswillremainunaffectedfollowingexchangeratechanges.Otherwise,exchangeratechangeswillaffectrelativecompetitivenessofcountries.Ifacountry’scurrencyappreciates(depreciates)bymorethaniswarrantedbyPPP,thatwillhurt(strengthen)thecountry’scompetitivepositionintheworldmarket.6.ExplainandderivetheinternationalFishereffect.Answer:TheinternationalFishereffectcanbeobtainedbycombiningtheFishereffectandtherelativeversionofPPPinitsexpectationalform.Specifically,theFishereffectholdsthatE(p$)=I$-r$,E(p£)=I£-r£.Assumingthattherealinterestrateisthesamebetweenthetwocountries,i.e.,r$=r£,andsubstitutingtheaboveresultsintothePPP,i.e.,E(e)=E(p$)-E(p£),weobtaintheinternationalFishereffect:E(e)=I$-I£.7.Researchersfoundthatitisverydifficulttoforecastthefutureexchangeratesmoreaccuratelythantheforwardexchangerateorthecurrentspotexchangerate.Howwouldyouinterpretthisfinding?Answer:Thisimpliesthatexchangemarketsareinformationallyefficient.Thus,unlessonehasprivateinformationthatisnotyetreflectedinthecurrentmarketrates,itwouldbedifficulttobeatthemarket.IM-12n8.Explaintherandomwalkmodelforexchangerateforecasting.Canitbeconsistentwiththetechnicalanalysis?Answer:Therandomwalkmodelpredictsthatthecurrentexchangeratewillbethebestpredictorofthefutureexchangerate.Animplicationofthemodelisthatpasthistoryoftheexchangerateisofnovalueinpredictingfutureexchangerate.Themodelthusisinconsistentwiththetechnicalanalysiswhichtriestoutilizepasthistoryinpredictingthefutureexchangerate.*9.Deriveandexplainthemonetaryapproachtoexchangeratedetermination.Answer:ThemonetaryapproachisassociatedwiththeChicagoSchoolofEconomics.Itisbasedontwotenets:purchasingpowerparityandthequantitytheoryofmoney.Combingthesetwotheoriesallowsforstating,say,the$/£spotexchangerateas:S($/£)=(M$/M£)(V$/V£)(y£/y$),whereMdenotesthemoneysupply,Vthevelocityofmoney,andythenationalaggregateoutput.Thetheoryholdsthatwhatmattersinexchangeratedeterminationare:1.Therelativemoneysupply,2.Therelativevelocitiesofmonies,and3.Therelativenationaloutputs.10.CFAquestion:1997,Level3.A.Explainthefollowingthreeconceptsofpurchasingpowerparity(PPP):a.Thelawofoneprice.b.AbsolutePPP.c.RelativePPP.B.EvaluatetheusefulnessofrelativePPPinpredictingmovementsinforeignexchangerateson:a.Short-termbasis(forexample,threemonths)b.Long-termbasis(forexample,sixyears)Answer:A.a.Thelawofoneprice(LOP)referstotheinternationalarbitrageconditionforthestandardconsumptionbasket.LOPrequiresthattheconsumptionbasketshouldbesellingforthesamepriceinagivencurrencyacrosscountries.IM-12nA.b.AbsolutePPPholdsthatthepricelevelinacountryisequaltothepricelevelinanothercountrytimestheexchangeratebetweenthetwocountries.A.c.RelativePPPholdsthattherateofexchangeratechangebetweenapairofcountriesisaboutequaltothedifferenceininflationratesofthetwocountries.B.a.PPPisnotusefulforpredictingexchangeratesontheshort-termbasismainlybecauseinternationalcommodityarbitrageisatime-consumingprocess.B.b.PPPisusefulforpredictingexchangeratesonthelong-termIM-12nbasis.PROBLEMS1.SupposethatthetreasurerofIBMhasanextracashreserveof$100,000,000toinvestforsixmonths.Thesix-monthinterestrateis8percentperannumintheUnitedStatesand6percentperannuminGermany.Currently,thespotexchangerateis€1.01perdollarandthesix-monthforwardexchangerateis€0.99perdollar.ThetreasurerofIBMdoesnotwishtobearanyexchangerisk.Whereshouldhe/sheinvesttomaximizethereturn?Themarketconditionsaresummarizedasfollows:I$=4%;i€=3.5%;S=€1.01/$;F=€0.99/$.If$100,000,000isinvestedintheU.S.,thematurityvalueinsixmonthswillbe$104,000,000=$100,000,000(1+.04).Alternatively,$100,000,000canbeconvertedintoeurosandinvestedattheGermaninterestrate,withtheeuromaturityvaluesoldforward.Inthiscasethedollarmaturityvaluewillbe$105,590,909=($100,000,000x1.01)(1+.035)(1/0.99)Clearly,itisbettertoinvest$100,000,000inGermanywithexchangeriskhedging.2.WhileyouwerevisitingLondon,youpurchasedaJaguarfor£35,000,payableinthreemonths.YouhaveenoughcashatyourbankinNewYorkCity,whichpays0.35%interestpermonth,compoundingmonthly,topayforthecar.Currently,thespotexchangerateis$1.45/£andthethree-monthforwardexchangerateis$1.40/£.InLondon,themoneymarketinterestrateis2.0%forathree-monthinvestment.TherearetwoalternativewaysofpayingforyourJaguar.(a)KeepthefundsatyourbankintheU.S.andbuy£35,000forward.(b)BuyacertainpoundamountspottodayandinvesttheamountintheU.K.forthreemonthssothatthematurityvaluebecomesequalto£35,000.Evaluateeachpaymentmethod.Whichmethodwouldyouprefer?Why?Solution:Theproblemsituationissummarizedasfollows:A/P=£35,000payableinthreemonthsiNY=0.35%/month,compoundingmonthlyiLD=2.0%forthreemonthsS=$1.45/£;F=$1.40/£.IM-12nOptiona:Whenyoubuy£35,000forward,youwillneed$49,000inthreemonthstofulfilltheforwardcontract.Thepresentvalueof$49,000iscomputedasfollows:$49,000/(1.0035)3=$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“optiona”,andsave$1,266,whichisthedifferencebetween$49,755and$48489.3.Currently,thespotexchangerateis$1.50/£andthethree-monthforwardexchangerateis$1.52/£.Thethree-monthinterestrateis8.0%perannumintheU.S.and5.8%perannumintheU.K.Assumethatyoucanborrowasmuchas$1,500,000or£1,000,000.a.Determinewhethertheinterestrateparityiscurrentlyholding.b.IftheIRPisnotholding,howwouldyoucarryoutcoveredinterestarbitrage?Showallthestepsanddeterminethearbitrageprofit.c.ExplainhowtheIRPwillberestoredasaresultofcoveredarbitrageactivities.Solution:Let’ssummarizethegivendatafirst:S=$1.5/£;F=$1.52/£;I$=2.0%;I£=1.45%Credit=$1,500,000or£1,000,000.a.(1+I$)=1.02(1+I£)(F/S)=(1.0145)(1.52/1.50)=1.0280Thus,IRPisnotholdingexactly.b.(1)Borrow$1,500,000;repaymentwillbe$1,530,000.(2)Buy£1,000,000spotusing$1,500,000.(3)Invest£1,000,000atthepoundinterestrateof1.45%;maturityvaluewillbe£1,014,500.(4)Sell£1,014,500forwardfor$1,542,040Arbitrageprofitwillbe$12,040IM-12nc.Followingthearbitragetransactionsdescribedabove,Thedollarinterestratewillrise;Thepoundinterestratewillfall;Thespotexchangeratewillrise;Theforwardexchangeratewillfall.TheseadjustmentswillcontinueuntilIRPholds.4.Supposethatthecurrentspotexchangerateis€0.80/$andthethree-monthforwardexchangerateis€0.7813/$.Thethree-monthinterestrateis5.6percentperannumintheUnitedStatesand5.40percentperannuminFrance.Assumethatyoucanborrowupto$1,000,000or€800,000.a.Showhowtorealizeacertainprofitviacoveredinterestarbitrage,assumingthatyouwanttorealizeprofitintermsofU.S.dollars.Alsodeterminethesizeofyourarbitrageprofit.b.Assumethatyouwanttorealizeprofitintermsofeuros.Showthecoveredarbitrageprocessanddeterminethearbitrageprofitineuros.Solution:a.(1+i$)=1.014<(F/S)(1+i€)=1.053.Thus,onehastoborrowdollarsandinvestineurostomakearbitrageprofit.1.Borrow$1,000,000andrepay$1,014,000inthreemonths.2.Sell$1,000,000spotfor€1,060,000.3.Invest€1,060,000attheeurointerestrateof1.35%forthreemonthsandreceive€1,074,310atmaturity.4.Sell€1,074,310forwardfor$1,053,245.Arbitrageprofit=$1,053,245-$1,014,000=$39,245.b.Followthefirstthreestepsabove.Butthelaststep,involvingexchangeriskhedging,willbedifferent.5.Buy$1,014,000forwardfor€1,034,280.Arbitrageprofit=€1,074,310-€1,034,280=€40,030IM-12n5.IntheissueofOctober23,1999,theEconomistreportsthattheinterestrateperannumis5.93%intheUnitedStatesand70.0%inTurkey.WhydoyouthinktheinterestrateissohighinTurkey?Basedonthereportedinterestrates,howwouldyoupredictthechangeoftheexchangeratebetweentheU.S.dollarandtheTurkishlira?Solution:AhighTurkishinterestratemustreflectahighexpectedinflationinTurkey.AccordingtointernationalFishereffect(IFE),wehaveE(e)=i$-iLira=5.93%-70.0%=-64.07%TheTurkishlirathusisexpectedtodepreciateagainsttheU.S.dollarbyabout64%.6.AsofNovember1,1999,theexchangeratebetweentheBrazilianrealandU.S.dollarisR$1.95/$.TheconsensusforecastfortheU.S.andBrazilinflationratesforthenext1-yearperiodis2.6%and20.0%,respectively.HowwouldyouforecasttheexchangeratetobeataroundNovember1,2000?Solution:SincetheinflationrateisquitehighinBrazil,wemayusethepurchasingpowerparitytoforecasttheexchangerate.E(e)=E(p$)-E(pR$)=2.6%-20.0%=-17.4%E(ST)=So(1+E(e))=(R$1.95/$)(1+0.174)=R$2.29/$IM-12n7.(CFAquestion)OmniAdvisors,aninternationalpensionfundmanager,usestheconceptsofpurchasingpowerparity(PPP)andtheInternationalFisherEffect(IFE)toforecastspotexchangerates.Omnigathersthefinancialinformationasfollows:Basepricelevel100CurrentU.S.pricelevel105CurrentSouthAfricanpricelevel111Baserandspotexchangerate$0.175Currentrandspotexchangerate$0.158ExpectedannualU.S.inflation7%ExpectedannualSouthAfricaninflation5%ExpectedU.S.one-yearinterestrate10%ExpectedSouthAfricanone-yearinterestrate8%Calculatethefollowingexchangerates(ZARandUSDrefertotheSouthAfricanandU.S.dollar,respectively).a.ThecurrentZARspotrateinUSDthatwouldhavebeenforecastbyPPP.b.UsingtheIFE,theexpectedZARspotrateinUSDoneyearfromnow.c.UsingPPP,theexpectedZARspotrateinUSDfouryearsfromnow.Solution:a.ZARspotrateunderPPP=[1.05/1.11](0.175)=$0.1655/rand.b.ExpectedZARspotrate=[1.10/1.08](0.158)=$0.1609/rand.c.ExpectedZARunderPPP=[(1.07)4/(1.05)4](0.158)=$0.1704/rand.8.Supposethatthecurrentspotexchangerateis€1.50/₤andtheone-yearforwardexchangerateis€1.60/₤.Theone-yearinterestrateis5.4%ineurosand5.2%inpounds.Youcanborrowatmost€1,000,000ortheequivalentpoundamount,i.e.,₤666,667,atthecurrentspotexchangerate.a.Showhowyoucanrealizeaguaranteedprofitfromcoveredinterestarbitrage.Assumethatyouareaeuro-basedinvestor.Alsodeterminethesizeofthearbitrageprofit.b.Discusshowtheinterestrateparitymayberestoredasaresultoftheabovetransactions.c.Supposeyouareapound-basedinvestor.Showthecoveredarbitrageprocessanddeterminethepoundprofitamount.IM-12nSolution:a.First,notethat(1+i€)=1.054islessthan(F/S)(1+i€)=(1.60/1.50)(1.052)=1.1221.Youshouldthusborrowineurosandlendinpounds.1)Borrow€1,000,000andpromisetorepay€1,054,000inoneyear.2)Buy₤666,667spotfor€1,000,000.3)Invest₤666,667atthepoundinterestrateof5.2%;thematurityvaluewillbe₤701,334.4)Tohedgeexchangerisk,sellthematurityvalue₤701,334forwardinexchangefor€1,122,134.Thearbitrageprofitwillbethedifferencebetween€1,122,134and€1,054,000,i.e.,€68,134.b.Asaresultoftheabovearbitragetransactions,theeurointerestratewillrise,thepoundinterestratewillfall.Inaddition,thespotexchangerate(eurosperpound)willriseandtheforwardratewillfall.Theseadjustmentswillcontinueuntiltheinterestrateparityisrestored.c.Thepound-basedinvestorwillcarryoutthesametransactions1),2),and3)ina.Buttohedge,he/shewillbuy€1,054,000forwardinexchangefor₤658,750.Thearbitrageprofitwillthenbe₤42,584=₤701,334-₤658,750.9.Duetotheintegratednatureoftheircapitalmarkets,investorsinboththeU.S.andU.K.requirethesamerealinterestrate,2.5%,ontheirlending.Thereisaconsensusincapitalmarketsthattheannualinflationrateislikelytobe3.5%intheU.S.and1.5%intheU.K.forthenextthreeyears.Thespotexchangerateiscurrently$1.50/£.a.ComputethenominalinterestrateperannuminboththeU.S.andU.K.,assumingthattheFishereffectholds.b.Whatisyourexpectedfuturespotdollar-poundexchangerateinthreeyearsfromnow?c.Canyouinfertheforwarddollar-poundexchangerateforone-yearmaturity?Solution.a.NominalrateinUS=(1+ρ)(1+E(π$))–1=(1.025)(1.035)–1=0.0609or6.09%.NominalrateinUK=(1+ρ)(1+E(π₤))–1=(1.025)(1.015)–1=0.0404or4.04%.b.E(ST)=[(1.0609)3/(1.0404)3](1.50)=$1.5904/₤.c.F=[1.0609/1.0404](1.50)=$1.5296/₤.IM-12nMiniCase:TurkishLiraandthePurchasingPowerParityVeritasEmergingMarketFundspecializesininvestinginemergingstockmarketsoftheworld.Mr.HenryMobaus,anexperiencedhandininternationalinvestmentandyourboss,iscurrentlyinterestedinTurkishstockmarkets.HethinksthatTurkeywilleventuallybeinvitedtonegotiateitsmembershipintheEuropeanUnion.Ifthishappens,itwillboostthestockpricesinTurkey.But,atthesametime,heisquiteconcernedwiththevolatileexchangeratesoftheTurkishcurrency.HewouldliketounderstandwhatdrivestheTurkishexchangerates.SincetheinflationrateismuchhigherinTurkeythanintheU.S.,hethinksthatthepurchasingpowerparitymaybeholdingatleasttosomeextent.Asaresearchassistantforhim,youwereassignedtocheckthisout.Inotherwords,youhavetostudyandprepareareportonthefollowingquestion:DoesthepurchasingpowerparityholdfortheTurkishlira-U.S.dollarexchangerate?Amongotherthings,Mr.Mobauswouldlikeyoutodothefollowing:PlotthepastexchangeratechangesagainstthedifferentialinflationratesbetweenTurkeyandtheU.S.forthelastfouryears.Regresstherateofexchangeratechangesontheinflationratedifferentialtoestimatetheinterceptandtheslopecoefficient,andinterprettheregressionresults.Datasource:YoumaydownloadtheconsumerpriceindexdatafortheU.S.andTurkeyfromthefollowingwebsite:http://www.oecd.org/home/0,2987,en_2649_201185_1_1_1_1_1,00.html,“hotfile”(Excelformat).Youmaydownloadtheexchangeratedatafromthewebsite:http://pacific.commerce.ubc.ca/xr/data.html.Solution:a.Inthecurrentsolution,weusethemonthlydatafromJanuary1999–December2002.IM-12nb.Weregressexchangeratechanges(e)ontheinflationratedifferentialandestimatetheintercept(α)andslopecoefficient(β):Theestimatedinterceptisinsignificantlydifferentfromzero,whereastheslopecoefficientispositiveandsignificantlydifferentfromzero.Infact,theslopecoefficientisinsignificantlydifferentfromunity.[Notethatt-statisticsforβ=1is0.992=(1.472–1)/0.476wheres.e.is0.476]Inotherwords,wecannotrejectthehypothesisthattheinterceptiszeroandtheslopecoefficientisone.Theresultsarethussupportiveofpurchasingpowerparity.IM-12