國際財務(wù)管理課后習(xí)題答案chapter-6

CHAPTER6INTERNATIONALPARITYRELATIONSHIPS

SUGGESTEDANSWERSANDSOLUTIONSTOEND-OF-CHAPTER

QUESTIONSANDPROBLEMS

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)theriskpremiumisinsignificantand(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.CFAquestion:1997,Level3.

Explainthefollowingthreeconceptsofpurchasingpowerparity(PPP):

a.Thelawofoneprice.

b.AbsolutePPP.

c.RelativePPP.

EvaluatetheusefulnessofrelativePPPinpredictingmovementsinforeignexchangerateson:

Short-termbasis(forexample,threemonths)

Long-termbasis(forexample,sixyears)

Answer:

a.Thelawofoneprice(LOP)referstotheinternationalarbitrageconditionforthestandardconsumptionbasket.LOPrequiresthattheconsumptionbasketshouldbesellingforthesamepriceinagivencurrencyacrosscountries.

b.AbsolutePPPholdsthatthepricelevelinacountryisequaltothepricelevelinanothercountry

timestheexchangeratebetweenthetwocountries.

c.RelativePPPholdsthattherateofexchangeratechangebetweenapairofcountriesisaboutequal

tothedifferenceininflationratesofthetwocountries.

a.PPPisnotusefulforpredictingexchangeratesontheshort-termbasismainlybecause

internationalcommodityarbitrageisatime-consumingprocess.

B.b.PPPisusefulforpredictingexchangeratesonthelong-termbasis.

PROBLEMS

1.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=￡35,000payableinthreemonths

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

c.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:

(1+i$)=1.014<(F/S)(1+i€)=1.053.Thus,onehastoborrowdollarsandinvestineurostomakearbitrageprofit.

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

Sell$1,000,000spotfor€1,060,000.

Invest€1,060,000attheeurointerestrateof1.35%forthreemonthsandreceive€1,074,310atmaturity.

Sell€1,074,310forwardfor$1,053,245.

Arbitrageprofit=$1,053,245-$1,014,000=$39,245.

Followthefirstthreestepsabove.Butthelaststep,involvingexchangeriskhedging,willbedifferent.

Buy$1,014,000forwardfor€1,034,280.

Arbitrageprofit=€1,074,310-€1,034,280=€40,0305.IntheissueofOctober23,1999,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%.

6.AsofNovember1,1999,theexchangeratebetweentheBrazilianrealandU.S.dollarisR$1.95/$.TheconsensusforecastfortheU.S.andBrazilinflationratesforthenext1-yearperiodis2.6%and20.0%,respectively.HowwouldyouforecasttheexchangeratetobeataroundNovember1,2000?

Solution:SincetheinflationrateisquitehighinBrazil,wemayusethepurchasingpowerparitytoforecasttheexchangerate.

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

=2.6%-20.0%

=-17.4%

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

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

=R$2.29/$

7.(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(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.

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.

9.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/?.

MiniCase:TurkishLiraandthePurchasingPowerParity

VeritasEmergingMarketFundspecializesininvestinginemergingstockmarketsoftheworld.Mr.HenryMobaus,anexperiencedhandininternationalinvestmentandyourboss,iscurrentlyinterestedinTurkishstockmarkets.HethinksthatTurkeywilleventuallybeinvitedtonegotiateitsmembershipintheEuropeanUnion.Ifthishappens,itwillboostthestockpricesinTurkey.Bu