國(guó)際財(cái)務(wù)治理課后習(xí)題答案(第六章)

CHAPTER6INTERNATIONALPARITYRELATIONSHIPS

SUGGESTEDANSWERSANDSOLUTIONSTOEND-OF-CHAPTER

QUESTIONSANDPROBLEMS

QUESTIONS

Giveafulldefinitionofarbitrage.

Answer:Arbitragecanbedefinedastheactofsimultaneouslybuyingandsellingthesameorequivalentassetsorcommoditiesforthepurposeofmakingcertain,guaranteedprofits.

Discusstheimplicationsoftheinterestrateparityfortheexchangeratedetermination.

Answer:Assumingthattheforwardexchangerateisroughlyanunbiasedpredictorofthefuturespotrate,IRPcanbewrittenas:

s=[(1+I￡)/(l+I$)]E[St+iIt].

Theexchangerateistliusdeterminedbytherelativeinterestrates,andtheexpectedfiitiuespotrate,conditionalonalltheavailableinformation,It,asofthepresenttune.Onethuscansaythatexpectationisself-fiilfilling.Sincetheinformationsetwillbecontinuouslyupdatedasnewshitthemarket,theexchangeratewillexhibitalughlydynamic,randombehavior.

Explaintheconditionsunderwhichtheforwardexchangeratewillbeanunbiasedpredictorofthefiitiuespotexchangerate.

Answer:Theforwardexchangeratewillbeanunbiasedpredictorofthefiitiuespotrateif(I)theriskpreiniuniisinsigmficantand(ii)foreignexchangemarketsareHifbnnationallyefficient.

Explainthepurchasmgpowerparity,boththeabsoluteandrelativeversions.Whatcausesthedeviationsfromthepurchasmgpowerparity?

Answer:Theabsoluteversionofpurchasuigpowerparity(PPP):s=pypf.

Therelativeversionis:

PPPcanbeviolatediftherearebarrierstomternationaltrade01ifpeopleindifferentcountrieshavedifferentconsumptiontaste.PPPisthelawofonepriceappliedtoastandardconsumptionbasket.

8.Explaintherandomwalkmodelforexchangerateforecasting.Canitbeconsistentwiththetechnicalanalysis?

J

Answer:Therandomwalkmodelpredictsthatthecuirentexcliangeratewillbethebestpredictorofthefutureexchangerate.Ailunplicationofthemodelisthatpasthistoryoftheexchangerateisofnovalueinpredictingfutureexchangerate.Themodelthusisinconsistentwiththetechnicalanalysiswhichtriestoutilizepasthistoryuipredictingthefiitureexchangerate.

*9.Deriveandexplainthemonetaryapproachtoexchangeratedetermination.

Answer:ThemonetaryapproachisassociatedwiththeClucagoSchoolofEconomics.Itisbasedontwotenets:purcliasingpowerparityandthequantitytheoryofmoney.Combingthesetwotheoriesallowsfbrstating,say,theS/￡spotexchangerateas:

S($/￡)=

whereMdenotesthemoneysupply,Vthevelocityofmoney,andythenationalaggiegateoutput.Thetheoryholdsthatwhatmattersmexchangeratedetermmationare:

Therelativemoneysupply,

Therelativevelocitiesofmonies,and

Therelativenationaloutputs.

CFAquestion:1997,Level3.

Explainthefollowingthieeconceptsofpurchasingpowerpaiity(PPP):

Thelawofoneprice.

AbsolutePPP.

RelativePPP.

EvaluatetheusefulnessofrelativePPPinpredictingmovementsmforeignexchangerateson:a.Shoit-termbasis(fbrexample,tlueemontlis)b.Long-termbasis(fbrexample,sixyeais)

Answer:

A.a.Thelawofoneprice(LOP)referstotheinternationalarbitrageconditionfbrthestandardconsumptionbasket.LOPrequuesthattheconsumptionbasketshouldbesellmgfbrthesamepriceinagivencurrencyacrosscountries.

A.b.AbsolutePPPholdsthatthepricelevelinacountryisequaltothepricelevelinanothercountiytimestheexchangeratebetweenthetwocountries.

c.RelativePPPholdstliattherateofexchangeratechangebetweenapairofcountliesisaboutequal

tothedifferenceininflationratesofthetwocountries.

a.PPPisnotuseftilforpredictmgexchangeratesontheshort-termbasismauilybecauseinternationalcommodityarbitrageisatune-consuninigprocess.

b.PPPisusefulforpredictingexchangeratesonthelong-term

basis.

PROBLEMS

SupposethatthetreasurerofIBMhasanextracashreseiveofSi00.000.000tomvestfbrsixmontlis.Thesix-monthmterestrateis8percentperannumintheUnitedStatesand6percentperannummGermany.Currently,thespotexchangerateis€1.01perdollarandthesix-monthforwaidexchangerateis€0.99perdollar.ThetreasurerofIBMdoesnotwishtobearaiiyexchangerisk.Whereshouldhe/sheinvesttomaximizetheretuin?

Themarketconditionsaresummarizedasfollows:

Is=4%;i€=3.5%;S=€1.01/S;F=€0.99/$,

If$100,000,000isinvestedintheU.S.,thematurityvaluemsixmonthswillbe$104,000,000=$100,000,000(1+.04).

Alternatively,Si00.000.000canbeconvertedintoeurosandinvestedattheGermaninterestrate,withtheeuromaturityvaluesoldfbnvard.Inthiscasethedollai'matuiityvaluewillbe

$105,590,909=($100,000,000x+.035)(1/0.99)

Clearly,itisbettertomvest$100,000,000inGermanywithexchangeriskhedging.

WliileyouwerevisitingLondon,youpurchasedaJaguarfbr￡35,000,payablemtlueemonths.YouhaveenoughcashatyouibankmNewYorkCity,wliichpays0.35%mterestpermonth,compoundingmontlily,topayfbrthecar.Cuirently,thespotexchangerateisS1.45/￡andthetluee-monthfonvardexchangerateisS1.40/￡,InLondon,themoneymarketinterestrateis2.0%fbratluee-monthinvestment.TherearetwoalternativewaysofpayingfbryourJaguar.

KeepthefluidsatyourbankintheU.S.andbuy￡35,000fbrwaid.

BuyaceitampoundamountspottodayandinvesttheamountintheU.K.fbrtlireemonthssothatthematurityvaluebecomesequalto￡35,000.

Evaluateeachpaymentmethod.Wliichmethodwouldyouprefer?Why?

Solution:Theproblemsituationissunmianzedasfollows:

A，P=￡35.000payableinthreemonths

ixy=0.35%/month,compoundingmontlily

Ild=2.0%fortlueemonths

S=$L45/￡;F=S1.40/￡.

Optiona:

Whenyoubuy￡35,000fbrwaid,youwillneedS49.000intlueemontlistofulfillthefbnvardcontiact.

Thepresentvalueof$49,000iscomputedasfollows:

$49.000/(1.0035)3=S48,489.

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”，andsave51,266,winchisthedifferencebehveen$49,755andS48489.

Currently,thespotexchangerateisS1.50/￡andthetliree-monthforwaidexchangerateisS1.52/￡.Thetliiee-monthinterestrateis8.0%perannumintheU.S.and5.8%perannumintheU.K.AssumethatyoucanborrowasmuchasSi,500.000or￡1,000,000.

Deteniiuiewhetherthemterestrateparityiscurrentlyholdmg.

IftheIRPisnotholding,howwouldyoucanyoutcoveredinterestarbitrage?Showallthestepsanddeteniiuiethearbitrageprofit.

ExplainhowtheIRPwillberestoredasaresultofcoveredaibitiageactivities.

Solution:Let'ssunmiarizethegivendatafirst:

S=$1.5/￡;F=$1.52/￡;Is=2.0%;If=1.45%

Credit=$1,500,000or￡1,000.000.

(l+Is)=1.02

(l+If)(F/S)=(1.0145)(1.52/1.50)=1.0280

Thus.IRPisnotholdingexactly.

(1)BorrowSi,500.000:lepaymentwillbe81,530,000.

Buy￡1.000.000spotusmg$1,500,000.

Invest￡1.000,000atthepoundinterestrateof1.45%;

niaturityvaluewillbe￡1.014,500.

Sell￡1,014,500fbrwaidfor$1,542,040

Aibitiageprofitwillbe$12,040

Followingthearbitragetransactionsdescribedabove.

Thedollarinterestratewillrise;

Thepoundinterestratewillfall;

Thespotexcliangeratewillrise;

Thefbnvaidexchangeratewillfall.

TheseadjustmentswillcontmueuntilIRPholds.

Supposethatthecuirentspotexchangerateis€0.80/$andthetluee-monthforwardexchangerateis€0.7813/S.Thethiee-monthmterestrateis5.6percentperannumintheUnitedStatesand5.40percentperannuminFrance.Assumethatyoucanborrowupto$1,000,000or€800,000.

Showhowtorealizeacertainprofitviacoveredinterestarbitrage,assunuiigthatyouwanttorealizeprofitmtermsofU.S.dollars.Alsodeterminethesizeofyourarbitrageprofit.

Assumethatyouwanttorealizeprofitintermsofeuios.Showthecoveredarbitrageprocessanddeteniihiethearbitrageprofitineuros.

Solution:

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

Borrow$1,000,000andrepayS1.014,000mthieemonths.

Sell$1,000,000spotfor€1,060,000.

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

Sell€1074,310forwardfbr51,053,245.

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

Followthefiisttlueestepsabove.Butthelaststep,involvingexchangeriskhedgmg,willbedifferent.

5.Buy$1,014,000fbnvardfor€1,034,280.

Aibiti-ageprofit=€1,074,310-€L0345280=

€40,030

IntheissueofOctober23,1999.theEconomistreportstliattheinterestrateperannumis5.93%inthe

UmtedStatesand70.0%mTurkey.WhydoyoutlunktheinterestrateissolughinTurkey?Basedonthe

reportedinterestrates,howwouldyoupredictthechangeoftheexchangeratebenveentheU.S.dollai-

andtheTurkishlua?

Solution:AlugliTurkishinterestratemustreflectalughexpectedinflationinTuikey.AccordingtointernationalFishereffect(IFE),wehave

E(e)=i5-iun

=5.93%-70.0%=-64.07%

TheTurkishlirathusisexpectedtodepreciateagainsttheU.S.dollarbyabout64%.

AsofNovember1,1999,theexchangeratebetweentheBrazilianrealandU.S.dollarisRS1.95/S.TheconsensusforecastfortheU.S.andBrazilinflationratesfbrthenext1-yearperiodis2.6%and20.0%,respectively.HowwouldyouforecasttheexchangeratetobeataioundNovember1,2000?

Solution:SmcetheinflationrateisquiteluglimBrazil,wemayusethepuichasmgpowerparitytoforecasttheexchaneerate.

E(e)=E(ks)-E(krs)

=2.6%-20.0%

=-17.4%

E(St)=So(l+E(e))

=(RS1.95/$)(1+0.174)

=RS2.29/S

(CFAquestion)OmniAdvisors,aninternationalpensionfundmanager,usestheconceptsofpuichasmgpowerparity(PPP)andtheInternationalFisherEffect(EFE)toforecastspotexchangerates.

Omnigathersthefinancialinformationasfollows:

Basepricelevel 100

105

111

50,175

S0.158

7%

5%

10%

8%

CurrentU.S.pricelevel

CurrentSouthAfricanpricelevel

Baserandspotexchangerate

Currentrandspotexchangerate

ExpectedannualU.S.uiflation

ExpectedannualSouthAfiicanuiflation

ExpectedU.S.one-yearinterestrate

ExpectedSoutliAfiicanone-yearinterestrate

Calculatethefollowingexchangerates(ZARandUSDrefertotheSouthAfricanandU.S.dollar,respectively).

ThecurrentZARspotrateinUSDthatwouldhavebeenforecastbyPPP.

UsingtheIFE.theexpectedZARspotratemUSDoneyearfromnow.

UsmgPPP,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)=$0.1704/rand.

Supposethatthecurrentspotexchangerateis€1.50/￡andtheone-yearfbnvardexchangerateis€1.60/￡.Theone-yearinterestrateis5.4%meurosand5.2%inpounds.Youcanborrowatmost€1,000,000ortheequivalentpoimdamount,i.e.,€666,667)atthecun'entspotexchangerate.

Showhowyoucanrealizeaguaranteedprofitfromcoveredmterestarbitrage.Assumethatyouareaeuro-basedmvestor.Alsodeterminethesizeofthearbitrageprofit.

Discusshowtheinterestrateparitymayberestoredasaresultoftheabovetiansactions.

Supposeyouareapound-basedinvestor.Showthecoveredarbitrageprocessanddeterminethepoundprofitamount.

Solution:

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

Youshouldthusborrowmeurosandlendinpounds.

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

Buy￡666,667spotfor€1,000,000.

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

Tohedgeexcliangerisk,sellthematurityvalue￡701,334fonvardinexchangefor€1,122,134.Thearbitrageprofitwillbethedifferencebetween€1,122,134and€1,054,000,i.e.,€68,134.

Asaresultoftheabovearbitragetransactions,theeuromterestratewillrise,thepound

interestratewillfall.Iiiaddition,thespotexchangerate(eurosperpound)willriseandthefbnvaidratewillfall.Theseadjustmentswillcontinueuntiltheinterestrateparityisrestored.

Thepound-basedmvestorwillcarryoutthesametransactions1),2),and3)ina.Buttohedge,he/shewillbuy€1,054,000forwardmexchangefor￡658,750.Thearbitrageprofitwillthenbe￡42,584=￡701,334-￡658,750.

Duetotheintegratednatuieoftheircapitalmarkets,investorsinboththeU.S.andU.K.requuethesamerealinterestrate,2.5%,ontheklending.Thereisaconsensusincapitalmaiketsthattheannualinflationrateislikelytobe3.5%mtheU.S.and1.5%mtheU.K.fbrthenexttlireeyears.ThespotexchangerateisciuTently51.50/￡,

ComputethenominalmterestrateperannummboththeU.S.andU.K.,assumingthattheFishereffectholds.

Whatisyourexpectedfiituiespotdollar-poundexchangerateintlueeyearsfromnow?

Canyouinferthefbnvaiddollai-poundexchangeratefbrone-yearmaturity?

Solution.

NominalratemUS=(1+p)(1+E(兀s))—1=(1.025)(1.035)-1=0.0609or6.09%.

NonuiialratemUK=(1+p) -1=(1.025)(1.015)-1=0.0404or4.04%.

E(St)=[(1.0609)7(1.0404)5](1.50)=$1.5904住.

F=[1.0609/1.0404](1.50)=$1.5296/￡.

MiniCase:TurkishLiraandthePuichasmgPowerParity

VeritasEmergmgMaiketFundspecializesminvestinginemerguigstockmarketsoftheworld.Mr.HenryMobaus,anexperiencedhandininternationalinvestmentandyourboss,iscurrentlymterestedmTurkishstockmarkets.HetluiiksthatTurkeywilleventuallybeinvitedtonegotiateitsmembershipintheEuropeanUnion.Ifthishappens,itwillboostthestockpricesinTurkey.But,atthesametime,heisquiteconcernedwiththevolatileexchangeratesoftheTurkishcurrency.HewouldliketounderstandwhatdrivestheTurkishexchangerates.SincetheinflationrateismuchhighermTurkeythanmtheU.S.,hethuiksthatthepuichasmgpowerparitymaybeholdingatleasttosomeextent.Asaresearchassistantfbrhim,youwereassignedtochecktillsout.Inotherwords,youhavetostudyandpreparearepoilonthefollowingquestion:DoesthepurcliasingpowerparityholdfbrtheTurkishlua-U.S.dollarexchangerate?Amongothertlinigs,Mr.Mobauswouldlikeyoutodothefollowing:

Plotthepastexchangeratechangesagainstthedifferentialuiflationratesbetween

TurkeyandtheU.S.forthelastfouryears.

Regiesstherateofexcliangeratechangesontheinflationratedifferentialtoestimatethemterceptandtheslopecoefficient,andinteiprettheregressionresults.

Datasource:YoumaydownloadtheconsumerpriceindexdatafbrtheU.S.andTurkeyfiomthefollowingwebsite:)“hotfile”(Excelfbniiat).Youmaydownloadtheexchangeratedatafromthewebsite:pacificmerce.ube.ca-xr/data.htnil.

Solution:

Inthecurrentsolution,weusethemontlilydatafromJanuary1999-December2002.

-0.05

-0.05

Turkeyvs.U.S.

0 0.05 0.1 0.15

Inf-Turkey-lnf_US

5ooo??oo

Weregressexchangeratechanges(e)ontlieinflationratedifferentialandestunatetheintercept(a)andslopecoefficient(0):

et=a4-p(Inf.Tuikey-Inf_US)+8ta=-0.01l(t=-0.649)6=1.4720=3095)

Theestimatedinterceptismsignificantlydifferentfromzero,whereastheslopecoefficientispositiveandsignificantlydifferentfr