国际财务管理（英文版·原书第9版） 答案Solutions-Manual-第6章　国际平价关系与汇率预测　

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CHAPTER6INTERNATIONALPARITYRELATIONSHIPSANDFORECASTINGFOREIGNEXCHANGERATES

ANSWERS&SOLUTIONSTOEND-OF-CHAPTERQUESTIONSANDPROBLEMS

QUESTIONS

1.Giveafulldefinitionofarbitrage.

Answer:Arbitragecanbedefinedastheactofsimultaneouslybuyingandsellingthesameorequivalentassetsorcommoditiesforthepurposeofmakingcertain,guaranteedprofits.

2.Discusstheimplicationsoftheinterestrateparityfortheexchangeratedetermination.

Answer:Assumingthattheforwardexchangerateisroughlyanunbiasedpredictorofthefuturespotrate,IRPcanbewrittenas:

S=[(1+i£)/(1+i$)]E[St+1It].

Theexchangerateisthusdeterminedbytherelativeinterestrates,andtheexpectedfuturespotrate,conditionalonalltheavailableinformation,It,asofthepresenttime.Onethuscansaythatexpectationisself-fulfilling.Sincetheinformationsetwillbecontinuouslyupdatedasnewshitthemarket,theexchangeratewillexhibitahighlydynamic,randombehavior.

3.Explaintheconditionsunderwhichtheforwardexchangeratewillbeanunbiasedpredictorofthefuturespotexchangerate.

Answer:Theforwardexchangeratewillbeanunbiasedpredictorofthefuturespotrateif(i)theforwardriskpremiumisinsignificantand(ii)foreignexchangemarketsareinformationallyefficient.

4.Explainthepurchasingpowerparity,boththeabsoluteandrelativeversions.Whatcausesthedeviationsfromthepurchasingpowerparity?

Answer:Theabsoluteversionofpurchasingpowerparity(PPP):

S=P$/P£.

Therelativeversionis:

e=$-£.

PPPcanbeviolatediftherearebarrierstointernationaltradeorifpeopleindifferentcountrieshavedifferentconsumptiontaste.PPPisthelawofonepriceappliedtoastandardconsumptionbasket.

5.Discusstheimplicationsofthedeviationsfromthepurchasingpowerparityforcountries’competitivepositionsintheworldmarket.

Answer:IfexchangeratechangessatisfyPPP,competitivepositionsofcountrieswillremainunaffectedfollowingexchangeratechanges.Otherwise,exchangeratechangeswillaffectrelativecompetitivenessofcountries.Ifacountry’scurrencyappreciates(depreciates)bymorethaniswarrantedbyPPP,thatwillhurt(strengthen)thecountry’scompetitivepositionintheworldmarket.

6.ExplainandderivetheinternationalFishereffect.

Answer:TheinternationalFishereffectcanbeobtainedbycombiningtheFishereffectandtherelativeversionofPPPinitsexpectationalform.Specifically,theFishereffectholdsthat

E($)=i$-$,

E(£)=i£-£.

Assumingthattherealinterestrateisthesamebetweenthetwocountries,i.e.,$=£,andsubstitutingtheaboveresultsintothePPP,i.e.,E(e)=E($)-E(£),weobtaintheinternationalFishereffect:E(e)=i$-i£.

7.Researchersfoundthatitisverydifficulttoforecastthefutureexchangeratesmoreaccuratelythantheforwardexchangerateorthecurrentspotexchangerate.Howwouldyouinterpretthisfinding?

Answer:Thisimpliesthatexchangemarketsareinformationallyefficient.Thus,unlessonehasprivateinformationthatisnotyetreflectedinthecurrentmarketrates,itwouldbedifficulttobeatthemarket.

8.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,and

3.Therelativenationaloutputs.

10.Explainthefollowingthreeconceptsofpurchasingpowerparity(PPP):

a.Thelawofoneprice.

b.AbsolutePPP.

c.RelativePPP.

Answer:

a.Thelawofoneprice(LOP)referstotheinternationalarbitrageconditionforthestandardconsumptionbasket.LOPrequiresthattheconsumptionbasketshouldbesellingforthesamepriceinagivencurrencyacrosscountries.

b.AbsolutePPPholdsthatthepricelevelinacountryisequaltothepricelevelinanothercountrytimestheexchangeratebetweenthetwocountries.

c.RelativePPPholdsthattherateofexchangeratechangebetweenapairofcountriesisaboutequaltothedifferenceininflationratesofthetwocountries.

11.EvaluatetheusefulnessofrelativePPPinpredictingmovementsinforeignexchangerateson:

Short-termbasis(forexample,threemonths)

Long-termbasis(forexample,sixyears)

Answer.

a.PPPisnotusefulforpredictingexchangeratesontheshort-termbasismainlybecause

internationalcommodityarbitrageisatime-consumingandcostlyprocess.

b.PPPismoreusefulforpredictingexchangeratesonthelong-termbasis.

PROBLEMS

1.SupposethatthetreasurerofIBMhasanextracashreserveof$100,000,000toinvestforsixmonths.Thesix-monthinterestrateis8percentperannumintheUnitedStatesand7percentperannuminGermany.Currently,thespotexchangerateis€1.01perdollarandthesix-monthforwardexchangerateis€0.99perdollar.ThetreasurerofIBMdoesnotwishtobearanyexchangerisk.Whereshouldhe/sheinvesttomaximizethereturn?

Solution: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=£35,000payableinthreemonths

iNY=0.35%/month,compoundingmonthly

iLD=2.0%forthreemonths

S=$1.45/£;F=$1.40/£.

Optiona:

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)=1.0280

Thus,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$1,542,040

Arbitrageprofitwillbe$12,040(=$1,542,040-$1,530,000).

c.Followingthearbitragetransactionsdescribedabove,

Thedollarinterestratewillrise;

Thepoundinterestratewillfall;

Thespotexchangeratewillrise;

Theforwardexchangeratewillfall.

TheseadjustmentswillcontinueuntilIRPisrestored.

4.Currently,thespotexchangerateis$0.85/A$andtheone-yearforwardexchangerate

is$0.81/A$.One-yearinterestis3.5%intheUnitedStatesand4.2%inAustralia.

Youmayborrowupto$1,000,000orA$1,176,471,whichisequivalentto$1,000,000

atthecurrentspotrate.

DetermineifIRPisholdingbetweenAustraliaandtheUnitedStates.

IfIRPisnotholding,explainindetailhowyouwouldrealizecertainprofitinU.S.dollarterms.

ExplainhowIRPwillberestoredasaresultofarbitragetransactionsyoucarryoutabove.

Solution:

(1+i$)=1.035

(1+iA$)(F/S)=(1.042)(0.81/0.85)=0.9930

Thus,IRPisnotholdingexactly.

(1)BorrowA$1,176,471andrepayA$1,225,883inoneyear.

(2)SellspotA$1,176,471for$1,000,000.

(3)Invest$1,000,000intheUS.Thematurityvaluewillbe$1,035,000.

(4)BuyA$1,225,883forwardfor$992,965.

Arbitrageprofit=$1,035,000-$992,965=$42,035.

5.Supposethatthecurrentspotexchangerateis€0.80/$andthethree-monthforwardexchangerateis€0.7813/$.Thethree-monthinterestrateis5.60percentperannumintheUnitedStatesand5.40percentperannuminFrance.Assumethatyoucanborrowupto$1,000,000or€800,000.

a.Showhowtorealizeacertainprofitviacoveredinterestarbitrage,assumingthatyouwanttorealizeprofitintermsofU.S.dollars.Alsodeterminethesizeofyourarbitrageprofit.

b.Assumethatyouwanttorealizeprofitintermsofeuros.Showthecoveredarbitrageprocessanddeterminethearbitrageprofitineuros.

Solution:

(1+i$)=1.014<(F/S)(1+i€)=1.0378.Thus,onehastoborrowdollarsandinvestineurostomakearbitrageprofit.

Borrow$1,000,000andrepay$1,014,000inthreemonths.

Sell$1,000,000spotfor€800,000.

Invest€800,000attheeurointerestrateof1.35%forthreemonthsandreceive€810,800atmaturity.

Sell€810,800forwardfor$1,037,758.

Arbitrageprofit=$1,037,758-$1,014,000=$23,758.

Followthefirstthreestepsabove.Butthelaststep,involvingexchangeriskhedging,willbedifferent.Specifically,fortheeuro-basedinvestor,thesourceofcurrencyriskisthedollarpayable,$1,014,000.Thus,he/sheneedstobuy$1,014,000forwardfor€792,238.

Arbitrageprofit=€810,800-€792,238=€18,562.

6.IntheOctober23,1999issue,theEconomistreportsthattheinterestrateperannumis5.93%intheUnitedStatesand70.0%inTurkey.WhydoyouthinktheinterestrateissohighinTurkey?Basedonthereportedinterestrates,howwouldyoupredictthechangeoftheexchangeratebetweentheU.S.dollarandtheTurkishlira?

Solution:AhighTurkishinterestratemustreflectahighexpectedinflationinTurkey.AccordingtointernationalFishereffect(IFE),wehave

E(e) =i$-iLira

=5.93%-70.0%=-64.07%

TheTurkishlirathusisexpectedtodepreciateagainsttheU.S.dollarbyabout64%.

7.AsofNovember1,1999,theexchangeratebetweentheBrazilianrealandU.S.dollarisR$1.95/$.TheconsensusforecastfortheU.S.andBrazilinflationratesforthenext1-yearperiodis2.6%and20.0%,respectively.WhatwouldyouforecasttheexchangeratetobeataroundNovember1,2000?

Solution:SincetheinflationrateisquitehighinBrazil,wemayusethepurchasingpowerparitytoforecasttheexchangerate.

E(e) =E($)-E(R$)

=2.6%-20.0%

=-17.4%

R$isexpectedtodepreciatebyabout17.4%againsttheUSdollar.Thus,theexpectedexchangeratewouldbe

E(ST) =So(1+E(e))

=(R$1.95/$)(1+0.174)

=R$2.29/$

8.(CFAquestion)OmniAdvisors,aninternationalpensionfundmanager,usestheconceptsofpurchasingpowerparity(PPP)andtheInternationalFisherEffect(IFE)toforecastspotexchangerates.Omnigathersthefinancialinformationasfollows:

Basepricelevel100

CurrentU.S.pricelevel105

CurrentSouthAfricanpricelevel111

Baserandspotexchangerate$0.175

Currentrandspotexchangerate$0.158

ExpectedannualU.S.inflation7%

ExpectedannualSouthAfricaninflation5%

ExpectedU.S.one-yearinterestrate10%

ExpectedSouthAfricanone-yearinterestrate8%

Calculatethefollowingexchangerates(ZARandUSDrefertotheSouthAfricanrandandU.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.

9.Supposethatthecurrentspotexchangerateis€1.50/₤andtheone-yearforwardexchangerateis€1.60/₤.Theone-yearinterestrateis5.4%ineurosand5.2%inpounds.Youcanborrowatmost€1,000,000ortheequivalentpoundamount,i.e.,₤666,667,atthecurrentspotexchangerate.

Showhowyoucanrealizeaguaranteedprofitfromcoveredinterestarbitrage.Assumethatyouareaeuro-basedinvestor.Alsodeterminethesizeofthearbitrageprofit.

Discusshowtheinterestrateparitymayberestoredasaresultoftheabove

transactions.

Supposeyouareapound-basedinvestor.Showthecoveredarbitrageprocessand

determinethepoundprofitamount.

Solution:

a.First,notethat(1+i€)=1.054islessthan(F/S)(1+i€)=(1.60/1.50)(1.052)=1.1221.

Youshouldthusborrowineurosandlendinpounds.

Borrow€1,000,000andpromisetorepay€1,054,000inoneyear.

Buy₤666,667spotfor€1,000,000.

Invest₤666,667atthepoundinterestrateof5.2%;thematurityvaluewillbe₤701,334.

Tohedgeexchangerisk,sellthematurityvalue₤701,334forwardinexchangefor€1,122,134.Thearbitrageprofitwillbethedifferencebetween€1,122,134and€1,054,000,i.e.,€68,134.

b.Asaresultoftheabovearbitragetransactions,theeurointerestratewillrise,thepound

interestratewillfall.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.

10.Duetotheintegratednatureoftheircapitalmarkets,investorsinboththeU.S.andU.K.requirethesamerealinterestrate,2.5%,ontheirlending.Thereisaconsensusincapitalmarketsthattheannualinflationrateislikelytobe3.5%intheU.S.and1.5%intheU.K.forthenextthreeyears.Thespotexchangerateiscurrently$1.50/£.

ComputethenominalinterestrateperannuminboththeU.S.andU.K.,assumingthattheFishereffectholds.

Whatisyourexpectedfuturespotdollar-poundexchangerateinthreeyearsfromnow?

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/₤.

11.AfterstudyingIrisHamson’screditanalysis,GeorgeDaviesisconsideringwhetherhecanincreasetheholdingperiodreturnonYucatanResort’sexcesscashholdings(whichareheldinpesos)byinvestingthosecashholdingsintheMexicanbondmarket.AlthoughDavieswouldbeinvestinginapeso-denominatedbond,theinvestmentgoalistoachievethehighestholdingperiodreturn,measuredinU.S.dollars,ontheinvestment.

DaviesfindsthehigheryieldontheMexicanone-yearbond,whichisconsideredtobefreeofcreditrisk,tobeattractivebutheisconcernedthatdepreciationofthepesowillreducetheholdingperiodreturn,measuredinU.S.dollars.Hamsonhaspreparedselectedeconomicandfinancialdata,giveninExhibit3-1,tohelpDaviesmakethedecision.

SelectedEconomicandFinancialDataforU.S.andMexico

ExpectedU.S.InflationRate 2.0%peryear

ExpectedMexicanInflationRate 6.0%peryear

U.S.One-yearTreasuryBondYield 2.5%

MexicanOne-yearBondYield 6.5%

NominalExchangeRates

Spot 9.5000Pesos=U.S.$1.00

One-yearForward 9.8707Pesos=U.S.$1.00

HamsonrecommendsbuyingtheMexicanone-yearbondandhedgingtheforeigncurrencyexposureusingtheone-yearforwardexchangerate.Sheconcludes:“ThistransactionwillresultinaU.S.dollarholdingperiodreturnthatisequaltotheholdingperiodreturnoftheU.S.one-yearbond.”

CalculatetheU.S.dollarholdingperiodreturnthatwouldresultfromthetransactionrecommendedbyHamson.Showyourcalculations.StatewhetherHamson’sconclusionabouttheU.S.dollarholdingperiodreturnresultingfromthetransactioniscorrectorincorrect.AfterconductinghisownanalysisoftheU.S.andMexicaneconomies,DaviesexpectsthatboththeU.S.inflationrateandtherealexchangeratewillremainconstantoverthecomingyear.BecauseoffavorablepoliticaldevelopmentsinMexico,however,heexpectsthattheMexicaninflationrate(inannualterms)willfallfrom6.0percentto3.0percentbeforetheendoftheyear.Asaresult,DaviesdecidestoinvestYucatanResorts’cashholdingsintheMexicanone-yearbondbutnottohedgethecurrencyexposure.

Calculatetheexpectedexchangerate(pesosperdollar)oneyearfromnow.Showyourcalculations.Note:YourcalculationsshouldassumethatDaviesiscorrectinhisexpectationsabouttherealexchangerateandtheMexicanandU.S.inflationrates.

CalculatetheexpectedU.S.dollarholdingperiodreturnontheMexicanone-yearbond.Showyourcalculations.Note:YourcalculationsshouldassumethatDaviesiscorrectinhisexpectationsabouttherealexchangerateandtheMexicanandU.S.inflationrates.

Solution:

TheU.S.dollarholdingperiodreturnthatwouldresultfromthetransactionrecommendedbyHamsonis2.5%.Theinvestorcanbuy“x”amountofpesosatthe(indirect)spotexchangerate,investthese“x”pesosintheMexicanbondmarketandhave“x×(1+YMEX)”pesosinoneyear,andconvertthesepesosbackintodollarsusingthe(indirect)forwardexchangerate.Interestrateparityassertsthatthetwoholdingperiodreturnsmustbeequal,whichcanberepresentedbytheformula:

(1+YUS)=Spot×(1+YMEX)×(1/Forward)

where“Spot”and“Forward”areinindirectterms.TheleftsideoftheequationrepresentstheholdingperiodreturnforaU.S.dollar-denominatedbond.Ifinterestrateparityholds,the“YUS”termalsocorrespondstotheU.S.dollarholdingperiodreturnforthecurrency-hedgedMexicanone-yearbond.Therightsideoftheequationistheholdingperiodreturn,indollarterms,foracurrency-hedgedpeso-denominatedbond.

SolvingforYUS:

(1+YUS)=9.5000×(1+0.065)×(1/9.8707)

(1+YUS)=9.5000×1.065×0.1013

(1+YUS)=1.0249

YUS=1.0249–1.0000=0.0249=2.5%

ThusYUS=2.5%,whichisthesameyieldasontheone-yearU.S.bond.Hamson’sconclusionabouttheU.S.dollarholdingperiodreturniscorrect.

Theexpectedexchangerateoneyearfromnowis9.5931.Theratecanbecalculatedbyusingtheformula:

(1+%ΔRUS)=(1+%ΔSUS)×[(1+%ΔPUS)/(1+%ΔPMEX)]

=(S1/S0)×[(1+%ΔPUS)/(1+%ΔPMEX)]

whereRUSistherealU.S.dollarexchangerate,Siisthenominalspotexchangerateinperiodi,and%ΔPistheinflationrate.Notethatthecurrencyquotesareinindirectform.SolvingforS1(theexpectedexchangerateoneyearfromnow):

(1+0.0000)=(S1/9.5000)×[(1+0.02)/(1+0.03)]

1.0000=(S1/9.5000)×0.9903

1.0098=S1/9.5000

S1=9.5931

TheexpectedU.S.dollarholdingperiodreturnontheMexicanone-yearbondis5.47%.Thereturncanbecalculatedasshownbelow,usingtheformulainPartAandthecurrentspotexchangerateandexpectedone-yearspotexchangeratecalculatedinPartB.

Holdingperiodreturn=[(1+YMEX)×(1+%Δpeso’svalue)]–1

=[(1+YMEX)×(S0/S1)]–1

=[(1+0.065)×(9.5000/9.5931)]–1

=(1.065×0.9903)–1

=5.47%

12.JamesClarkisaforeignexchangetraderwithCitibank.Henoticesthefollowingquotes.

Spotexchangerate SFr1.2051/$

Six-monthforwardexchangerate SFr1.1922/$

Six-month$interestrate 2.5%peryear

Six-monthSFrinterestrate 2.0%peryear

Istheinterestrateparityholding?Youmayignoretransactioncosts.

Isthereanarbitrageopportunity?Ifyes,showwhatstepsneedtobetakentomakearbitrageprofit.AssumingthatJamesClarkisauthorizedtoworkwith$1,000,000,computethearbitrageprofitindollars.

Solution:

Forsixmonths,iSFr=1.0%andi$=1.25%.thespotexchangerateis$0.8298/SFrandthe

forwardrateis$0.8388/SFr.Thus,

(1+i$)=1.0125and(F/s)(1+iSFr)=(0.8388/0.8298)(1.01)=1.02095

BecausetheleftandrightsidesofIRParenotequal,IRPisnotholding.

b. BecauseIRPisnotholding,thereisanarbitragepossibility:Because1.0125<1.02095,wecansaythattheSFrinterestratequoteismorethanwhatitshouldbeasperthequotesfortheotherthreevariables.Equivalently,wecanalsosaythatthe$interestratequoteislessthanwhatitshouldbeasperthequotesfortheotherthreevariables.Therefore,thearbitragestrategyshouldbebasedonborrowinginthe$marketandlendingintheSFrmarket.Thestepswouldbeasfollows:

Borrow$1,000,000forsixmonthsat1.25%.Needtopayback$1,000,000×(1+0.0125)=$1,012,500sixmonthslater.

Convert$1,000,000toSFratthespotratetogetSFr1,205,100.

LendSFr1,205,100forsixmonthsat1.0%.WillgetbackSFr1,205,100×(1+0.01)=SFr1,217,151sixmonthslater.

SellSFr1,217,151sixmonthsforward.Thetransactionwillbecontractedasofthecurrentdatebutdeliveryandsettlementwillonlytakeplacesixmonthslater.So,sixmonthslater,exchangeSFr1,217,151forSFr1,217,151/SFr1.1922/$=$1,020,929.

Thearbitrageprofitsixmonthslateris$1,020,929–$1,012,500=$8,429.

13.Supposeyouconductcurrencycarrytradebyborrowing$1millionatthestartofeachyearandinvestinginNewZealanddollarforoneyear.One-yearinterestratesandtheexchangeratebetweentheU.S.dollar($)andNewZealanddollar(NZ$)areprovidedbelowfortheperiod2000–2009.Notethatinterestratesareone-yearinterbankratesonJanuary1steachyear,andthattheexchangerateistheamountofNewZealanddollarperU.S.dollaronDecember31eachyear.TheexchangeratewasNZ$1.9088/$onJanuary1,2000.Filloutthecolumns(4)–(7)andcomputethetotaldollarprofitsfromthiscarrytradeovertheten-yearperiod.Also,assessthevalidityofuncoveredinterestrateparitybasedonyoursolutionofthisproblem.YouareencouragedtouseExcelprogramtotacklethisproblem.

(1)

(2)

(3)

(4)

(5)

(6)

(7)

Year

iNZ$

i$

SNZ$/$

iNZ$-i$

eNZ$/$

(4)-(5)

$Profit

2000

6.53

6.50

2.2599

2001

6.70

6.00

2.4015

2002

4.91

2.44

1.9117

2003

5.94

1.45

1.5230

2004

5.88

1.46

1.3845

2005

6.67

3.10

1.4682

2006

7.28

4.84

1.4182

2007

8.03

5.33

1.2994

2008

9.10

4.22

1.7112

2009

5.10

2.00

1.3742

Datasource:Datastream.

Solution:

(1)

(2)

(3)

(4)

(5)

(6)

(7)

Year

iNZ$

i$

SNZ$/$

iNZ$-i$

eNZ$/$

(4)-(5)

$Profit

2000

6.53

6.50

2.2599

0.03

18.40

-18.37

-183655

2001

6.70

6.00

2.4015

0.7

6.27

-5.57

-55680

2002

4.91

2.44

1.9117

2.47

-20.40

22.87

228676

2003

5.94

1.45

1.5230

4.49

-20.33

24.82

248220

2004

5.88

1.46

1.3845

4.42

-9.10

13.52

135159

2005

6.67

3.10

1.4682

3.57

6.05

-2.48

-24790

2006

7.28

4.84

1.4182

2.44

-3.40

5.84

58438

2007

8.03

5.33

1.2994

2.7

-8.38

11.08

110810

2008

9.10

4.22

1.7112

4.88

31.69

-26.81

-268106

2009

5.10

2.00

1.3742

3.1

-19.69

22.79

227922

Notes:

1.Interestratesareinterbank1-yearratesonJanuary1stofeachyearandmeasuredinpercentterms.

2.Spotexchangerates,SNZ$/$,aremeasuredonDecember31stofeachyearandspotexchangerateswas

NZ$1.9088perUS$onJanuary1,2000.

3.AlldataarefromDatastream.

Ifuncoveredinterestrateparityholds,profitfromcarrytradeshouldbeinsignificantlydifferentfromzero.Butsincetheprofitincolumn(7)substantiallydiffersfromzeroeachyear,uncoveredIRPdoesnotappeartohold.

MiniCase:TurkishLiraandthePurchasingPowerParity

VeritasEmergingMarketFundspecializesininvestinginemergingstockmarketsoftheworld.Mr.HenryMobaus,anexperiencedhandininternationalinvestmentandyourboss,iscurrentlyinterestedinTurkishstockmarkets.HethinksthatTurkeywilleventuallybeinvitedtonegoti