--

CHAPTER6INTERNATIONALPARITYRELATIONSHIPS

SUGGESTEDANSWERSANDSOLUTIONSTOEND-OF-CHAPTER

QUESTIONSANDPROBLEMS

QUESTIONS

1.Giveafulldefinitionofarbitrage.

Answer:Arbitragecanbedefinedastheactofsimultaneouslybuyingandsellingthesameorequivalentassetsorcommoditiesforthepurposeofmakingcertain,guaranteedprofits.

2.Discusstheimplicationsoftheinterestrateparityfortheexchangeratedetermination.

Answer:Assumingthattheforwardexchangerateisroughlyanunbiasedpredictorofthefuturespotrate,IRPcanbewrittenas:

S=[(1+I)/(1+I)]E[SI].

￡$t+1t

Theexchangerateisthusdeterminedbytherelativeinterestrates,andtheexpectedfuturespotrate,conditionalonalltheavailableinformation,I,asofthepresenttime.Onethuscansaythatexpectationis

t

self-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.

--

--

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:

Therelativemoneysupply,

Therelativevelocitiesofmonies,and

Therelativenationaloutputs.

10.CFAquestion:1997,Level3.

A.Explainthefollowingthreeconceptsofpurchasingpowerparity(PPP):

Thelawofoneprice.

AbsolutePPP.

RelativePPP.

B.EvaluatetheusefulnessofrelativePPPinpredictingmovementsinforeignexchangerateson:

Short-termbasis(forexample,threemonths)

Long-termbasis(forexample,sixyears)

Answer:

A.a.Thelawofoneprice(LOP)referstotheinternationalarbitrageconditionforthestandardconsumptionbasket.LOPrequiresthattheconsumptionbasketshouldbesellingforthesamepriceinagivencurrencyacrosscountries.

--

--

A.b.AbsolutePPPholdsthatthepricelevelinacountryisequaltothepricelevelinanothercountrytimestheexchangeratebetweenthetwocountries.

A.c.RelativePPPholdsthattherateofexchangeratechangebetweenapairofcountriesisaboutequal

tothedifferenceininflationratesofthetwocountries.

B.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.

KeepthefundsatyourbankintheU.S.andbuy￡35,000forward.

BuyacertainpoundamountspottodayandinvesttheamountintheU.K.forthreemonthssothatthematurityvaluebecomesequalto￡35,000.

Evaluateeachpaymentmethod.Whichmethodwouldyouprefer?Why?

Solution:Theproblemsituationissummarizedasfollows:

A/P=￡35,000payableinthreemonths

i=0.35%/month,compoundingmonthly

NY

i=2.0%forthreemonths

LD

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.

Determinewhethertheinterestrateparityiscurrentlyholding.

IftheIRPisnotholding,howwouldyoucarryoutcoveredinterestarbitrage?Showallthestepsanddeterminethearbitrageprofit.

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.

Buy￡1,000,000spotusing$1,500,000.

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.

Showhowtorealizeacertainprofitviacoveredinterestarbitrage,assumingthatyouwanttorealizeprofitintermsofU.S.dollars.Alsodeterminethesizeofyourarbitrageprofit.

Assumethatyouwanttorealizeprofitintermsofeuros.Showthecoveredarbitrageprocessanddeterminethearbitrageprofitineuros.

Solution:

a.(1+i)=1.014<(F/S)(1+i

$

makearbitrageprofit.

€

)=1.053.Thus,onehastoborrowdollarsandinvestineurosto

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.

b.Followthefirstthreestepsabove.Butthelaststep,involvingexchangeriskhedging,willbedifferent.

5.Buy$1,014,000forwardfor€1,034,280.

Arbitrageprofit=€1,074,310-€1,034,280=€40,030

--

--

5.IntheissueofOctober23,1999,theEconomistreportsthattheinterestrateperannumis5.93%inthe

UnitedStatesand70.0%inTurkey.WhydoyouthinktheinterestrateissohighinTurkey?Basedonthereportedinterestrates,howwouldyoupredictthechangeoftheexchangeratebetweentheU.S.dollar

andtheTurkishlira?

Solution:AhighTurkishinterestratemustreflectahighexpectedinflationinTurkey.AccordingtointernationalFishereffect(IFE),wehave

E(e)=i-i

$Lira

=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(S)=S(1+E(e))

To

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

=R$2.29/$

--

--

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

asepricelevel

urrentU.S.pricelevel105CurrentSouthAfricanpricelevel111

Baserandspotexchangerate$0.175Currentrandspotexchangerate$0.158ExpectedannualU.S.inflation7%ExpectedannualSouthAfricaninflation5%

ExpectedU.S.one-yearinterestrate10%ExpectedSouthAfricanone-yearinterestrate8%

100

Calculatethefollowingexchangerates(ZARandUSDrefertotheSouthAfricanandU.S.dollar,respectively).

ThecurrentZARspotrateinUSDthatwouldhavebeenforecastbyPPP.

UsingtheIFE,theexpectedZARspotrateinUSDoneyearfromnow.

UsingPPP,theexpectedZARspotrateinUSDfouryearsfromnow.

Solution:

ZARspotrateunderPPP=[1.05/1.11](0.175)=$0.1655/rand.

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.

c.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(S)=[(1.0609)3/(1.0404)

T

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.But,atthesametime,heisquiteconcernedwiththevolatileexchangeratesoftheTurkishcurrency.HewouldliketounderstandwhatdrivestheTurkishexchangerates.SincetheinflationrateismuchhigherinTurkeythanintheU.S.,hethinksthatthepurchasingpowerparitymaybeholdingatleasttosomeextent.Asaresearchassistantforhim,youwereassignedtocheckthisout.Inotherwords,youhavetostudyandprepareareportonthefollowingquestion:DoesthepurchasingpowerparityholdfortheTurkishlira-U.S.dollarexchangerate?Amongotherthings,Mr.Mobauswouldlikeyoutodothefollowing:

Plotthepastexchangeratechangesagainstthedifferentialinflationratesbetween

TurkeyandtheU.S.forthelastfouryears.

Regresstherateofexchangeratechangesontheinflationratedifferentialtoestimate

theinterceptandtheslopecoefficient,andinterprettheregressionresults.

Datasource:YoumaydownloadtheconsumerpriceindexdatafortheU.S.andTurkeyfromthefollowingwebsite:,“hotfile”(Excelformat).Youmaydownloadtheexchangeratedatafromthewebsite:.

Solution:

a.Inthecurrentsolution,weusethemonthlydatafromJanuary1999–December2002.

--

)

/

f

?

f

t

?

?

--

Turkeyvs.U.S.

e

(

$

L

T

o

e

g

n

a

h

C

0.15

0.10

0.05

β1.47

o

e

a

R

0.00

-0.05

α?0.011

-0.0500.050.10.15

Inf_Turkey-Inf_US

b.Weregressexchangeratechanges(e)ontheinflationratedifferentialandestimatethe

intercept(α)andslopecoefficient(β):

eα?β(Inf_Turkey-Inf_US)ε

tt

α?0.011(t-0.649)

β1.472(t3.095)

Theestimatedinterceptisinsignificantlydifferentfromzero,whereastheslopecoefficientispositiveandsignificantlydifferentfromzero.