国际财务管理课后习题答案第六章

CHAPTER6INTERNATIONAL PARITYRELATIONSHIPSSUGGESTED ANSWERSAND SOLUTIONSTO END-OF-CHAPTERQUESTIONS ANDPROBLEMSQUESTIONS1Give afull definitionof arbitrage.oAnswerArbitrage can be definedas theact ofsimultaneously buyingand sellingthe sameor equivalentassetsor commoditiesfor thepurpose ofmaking certain,guaranteed profits.Discuss the implications of the interest rate parityfor the exchange ratedetermination.2oAnswer:Assuming that the forward exchange rate is roughlyan unbiased predictor of the future spot rate,IRP can be writtenas S=[1+I/1+1$]E[S i|It].£l+The exchange rate isthus determinedby therelative interest rates,and the expected futurespot rate,conditional onall theavailable information,L，as of the present time Onethus cansay thatexpectation isself-fulfilling.Since theinformation setwill becontinuously updatedas newshit themarket,the exchangerate will exhibita highlydynamic,random behavior.Explain theconditions underwhich the forwardexchange rate will be an unbiasedpredictor of the future3ospot exchange rateAnswer:The forwardexchange ratewill beanunbiasedpredictor of the futurespot rateif Ithe riskpremiumis insignificantand ii foreign exchangemarkets areinformationally efficient.

4.Explain the purchasing power parity,both theabsolute andrelative versions.What causes the deviationsfrom the purchasing power parity5o In the issueof October23,1999,the Economistreports that the interest rate per annum is593%in the United States and

70.0%in Turkey.Why doyou thinkthe interest rate isso high in TurkeyBased onthereported interest rates,how would you predictthe changeof the exchange rate between the U.S.dollar and the TurkishliraSolution:A highTurkish interest rate mustreflect ahigh expectedinflation in Turkey oAccording tointernational Fisher effectIFE,we haveEe=i$——iLira=5o93%-

70.0%=—

64.07%The Turkishlira thus is expectedto depreciateagainst the U.S dollarby about64%6o Asof November1,1999,the exchange ratebetween the Brazilianreal andU So dollar isR$1o95/$oThe consensusforecast for theU.S andBrazil inflation rates for the next1-year periodis

2.6%and200%,respectively oHow wouldyou forecast theexchange rate tobe ataround November1,2000SolutionSince the inflation rate is quitehighinBrazil,we mayuse thepurchasing power parity toforecastthe exchange rateE e=E7iS-E兀R$=2o6%—20o0%=—17o4%E ST=S O1+Ee二R$lo95/$=R$

2.29/$1+0o174CFA questionOmni Advisors,an internationalpension fundmanager,usestheconcepts ofpurchasing7opower parity PPP and the InternationalFisher EffectIFE toforecast spot exchange ratesOmnigathers thefinancial informationas followsBase price level100Current U S.price level105Current South African pricelevel111Base randspot exchange rate$0o175Current randspot exchange rate$

0.158Expected annualU.S inflation7%Expected annualSouthAfricaninflation5%Expected Uo So one—year interest rate10%Expected SouthAfrican one—year interestrate8%Calculate the following exchange rates ZARand USDrefer to the SouthAfrican andU dollar,respectivelySooa.The currentZAR spot rate in USD thatwould havebeen forecastby PPP.Using theIFE,the expectedZAR spotrate inUSD oneyear fromnowbo oUsingPPP,theexpectedZAR spotrate inUSD four years fromnow.CoSolution:a.ZAR spotrate under PPP=[

1.05/

1.11]

0.175=$

0.1655/rand.b.Expected ZARspotrate=[

1.10/108]

0.158=$01609/rand.o CoExpected ZARunderPPP=[lo074/

1.054]

0.158=$01704/randooSuppose that the current spot exchange rate is€

1.50/£and the one-year forwardexchange rate is€

1.60/£o8oThe one-year interestrate is

5.4%in euros and

5.2%in poundsYou canborrow atmost€1,000,000or theo，，equivalent poundamount,£666,667at the currentspot exchange rate.ioCoa.Show howyou canrealize aguaranteed profitfrom covered interest arbitrage.Assume thatyou are aeuro-based investorAlso determine the size of thearbitrage profit0ob.Discuss howthe interestrate paritymay berestored asa resultof theabove transactions.c.Suppose youareapound-based investorShow the covered arbitrage process anddetermine the poundprofit amount.Solution:a First,note thatl+i=

1.054is lessthan F/S l+i=k60/

1.50k052=

1.

1221.You shouldthus borrowo€€in eurosand lendin poundso1Borrow€1000000and promiseto repay€1,054,000in oneyear.952Buy£666,667spot for€1,000,

000.3Invest£666,667at the pound interestrate of

5.2%;the maturity value will be£701,

334.4To hedgeexchange risk,sell the maturity value£701,334forward inexchange fbr€1,122,134Thearbitrage profit will bethe differencebetween€1,122,134and€1,054,000,i e，€68,134o As a resultoftheabove arbitrage transactions,the euro interestratewill rise,thepound interestratewill fall.boIn addition,the spot exchange rateeuros perpound will rise and theforwardratewill fall.Theseadjustments will continue untilthe interestrate parityis restored.c.The pound-based investorwill carryout the same transactions1,2,and3in a.But tohedge,he/she willbuy€1,054,000forward inexchange for£658,

750.The arbitrage profit willthen be£42,584=£701,334—£658,

7509.Due tothe integratednature oftheir capitalmarkets,investors inboth theU.So andU.K requirethe samerealinterestrate,

2.5%,on theirlending.There is a consensusin capitalmarkets that the annualinflation rateislikely tobe

3.5%in theU.S.and15%in theU.K.for thenext three years.The spotexchange rate isocurrently$150/£.a.Compute thenominal interestrate per annum inboth theU・S andU K.,assuming that the Fisher effect holds.b.What isyour expectedfuturespotdollar-pound exchange rate in threeyearsfrom nowc.Can youinfer theforward dollar—pound exchange rate forone—year maturitySolution.aoNominal rateinUS=1+p1+ETI$-1=10251o035—1=00609or

6.09%oNominal ratein UK=l+p1+E-1=k

0251.015—1=00404or404%.兀»Ob.E ST=[

1.06093/104043]

1.50=$

1.5904/£oc.F=[lo0609/

1.0404]

1.50=$

1.5296/£.Mini Case:Turkish Liraand thePurchasing PowerParityVeritas EmergingMarket Fundspecializes ininvesting inemerging stockmarkets ofthe world.Mr.HenryMobaus,an experiencedhand ininternational investmentand yourboss,is currentlyinterested inTurkishstock markets.He thinksthat Turkeywill eventuallybe invitedto negotiateits membershipin theEuropeanUnion Ifthis happens,it willboost thestock pricesinTurkeyBut,atthesame time,he isquite concerned0with thevolatile exchange rates ofthe Turkishcurrency Hewould liketo understandwhat drivestheoTurkish exchange rates.Since the inflationrate is muchhigher inTurkey thanin theU S・,he thinksthat thepurchasing powerparitymay beholding atleast tosome extent.Asaresearch assistantfor him,you wereassignedto checkthis outo In otherwords,you haveto studyandprepare areport onthefollowingquestionDoes thepurchasing powerparity holdfor theTurkishlira-U.Sodollarexchange rateAmong otherthings,Mr Mobauswould likeyou todo thefollowing:Plot thepast exchange rate changesagainst thedifferential inflation rates betweenTurkeyand theU.S for the lastfouryears.Regress therate ofexchange rate changes ontheinflationrate differentialto estimatethe interceptand theslope coefficient,and interpretthe regressionresults.Data sourceYou maydownload theconsumer price index datafortheUS.and Turkeyfromthefollowingwebsitehttp:〃,2987,en264920118511111,00html,“hot file”Excel format.You maydownload theexchange ratedata fromthe website:http//pacifiCocommerce.ubco ca/xr/data htmlooSolution—

0.15a.Inthe current solution,we usethe monthlydata fromJanuary1999-December2002obo Weregress exchange rate changeseontheinflationrate differentialand estimatethe interceptaandslope coefficient3:Turkey vs.U.S.e=a+P Inf_Turkey-Inf_US+€tt=—

0.011t=-

0.649B=L472t=

3.095The estimatedintercept isinsignificantly differentfrom zero,whereas the slopecoefficient is positiveandsignificantly differentfrom zerooIn fact,the slopecoefficient isinsignificantly differentfrom unityo[Note thatt-statistics forB=1is

0.992=

1.472-1/

0.476where se.is

0.476]In otherwords,we cannotrejectthe hypothesisthat theintercept iszero and theslopecoefficientisone Theresults arethus supportiveofpurchasing powerparity.

00.

050.1lnf_Turkey-lnf_US.os.Is5054Uo5o000505o Discusstheimplicationsofthedeviations fromthepurchasing powerparityfbr countries9competitivepositions in the worldmarket0AnswerIf exchangerate changessatisfy PPP,competitive positionsof countrieswill remainunaffectedfollowing exchangeratechangesOtherwise,exchangeratechanges willaffect relativecompetitiveness ofocountries.If a countrys currencyappreciates depreciatesby morethan iswarranted byPPP,that willhurtstrengthen thecountrys competitiveposition in the worldmarket0Explain andderive the internationalFisher effect.60AnswerThe internationalFisher effectcanbeobtained bycombining the Fishereffectand therelativeversion ofPPP inits expectationalform Specifically,theFishereffect holds thatE7l5=1$一p$,E兀£=1£-p£Assuming thatthe realinterestrate is thesame betweenthe two countries,i e.,p$=p£,and substitutingtheabove resultsinto thePPP,i.e,Ee=ETU$—Eg,we obtain the internationalFishereffectEe=1$—IfoResearchers foundthat it is verydifficult toforecastthefuture exchangerates moreaccurately thanthe7oforward exchangerate orthe currentspotexchangerate.How wouldyou interpretthis findingAnswer:This impliesthat exchangemarkets areinformationally efficient.Thus,unless one has private，information thatis notyet reflectedin thecurrent marketrates itwould bedifficult tobeat themarket.AnswerThe absoluteversion ofpurchasingpowerparity PPPS=P$/P£The relativeversion isC—-7l£oPPP canbe violatedif thereare barriersto internationaltrade orif peoplein differentcountries havedifferentconsumption taste.PPP isthe law of one price appliedto astandard consumption basket.

8.Explain therandom walk model forexchangerateforecasting Canit beconsistent withthe technicaloanalysisAnswer:The randomwalkmodelpredicts thatthecurrentexchangeratewill bethe bestpredictorofthefuture exchangerate.An implicationofthemodel isthat past history oftheexchangerateisof novalue inpredictingfuture exchangerate.The modelthusisinconsistent withthe technicalanalysis whichtries toutilizepasthistoryin predictingthefutureexchangerate*

9.Derive andexplain themonetary approachto exchangerate determinationAnswerThe monetaryapproach isassociated withthe ChicagoSchool ofEconomics oIt isbased ontwotenetspurchasingpowerparity andthe quantitytheory ofmoney.Combing thesetwo theoriesallows forstating,say,the$/£spotexchangerate as:S$/£=M$/MQ V,/Vy£今where Mdenotes the money supply,V thevelocity ofmoney,and ythe nationalaggregate outputo Thetheory holdsthat whatmatters inexchangeratedetermination are:1o The relative moneysupply,

2.Therelativevelocities ofmonies,and3oTherelative nationaloutputs

10.CFA question:1997,Level

3.A.Explain thefollowing threeconcepts ofpurchasingpowerparityPPPa The lawof oneprice.obo Absolute PPPoCo RelativePPPoB.Evaluate theusefulness ofrelative PPPin predictingmovements inforeign exchangerates ona.Short—term basisfor example,three monthsb.Long-term basisfor example,six yearsAnswer:A.a.Thelawofoneprice LOPrefers totheinternationalarbitrage conditionforthestandard consumptionbasket.LOP requiresthattheconsumptionbasketshould beselling forthesamepriceina givencurrencyacross countriesoA.b.AbsolutePPP holdsthatthe pricelevel inacountryis equal tothepricelevelin anothercountry timestheexchangeratebetweenthetwo countriesA.Co RelativePPPholdsthattherate ofexchangeratechange betweena pairof countriesis aboutequalto the difference ininflationratesofthetwocountries.B.a PPP is notuseful forpredicting exchangerates onthe short-term basismainly becauseinternationalcommodity arbitrageisatime-consuming processoBob.PPPisuseful forpredicting exchangerates onthe long-term basisoPROBLEMS

1.Suppose thatthe treasurerof IBMhas anextra cashreserve of$100,000,000to investfor six months.The six—month interestrateis8percent perannum inthe UnitedStates and6percent perannum inGermany.Currently,the spotexchangerateis€

1.01per dollarandthesix-month forwardexchangerateis€

0.99per dollarThe treasurerof IBMdoes notwish tobear anyexchange risk.Where shouldhe/she investtomaximize thereturn Themarket conditionsare summarized as followsI=4%；i=

3.5%；S=€

1.01/$；F=€0o99/$.$€If$100,000,000is investedintheUoS.，thematurity value insixmonthswill be$104,000,000=$100,000,0001+040oAlternatively,$100,000,000canbeconverted intoeurosandinvested atthe Germaninterestrate,with theeuromaturityvaluesold forward oInthis casethe dollarmaturityvaluewill be$105,590,909=$100,000,000x lo011+.0351/

0.99Clearly,itisbetter toinvest$100,000,000in Germanywith exchangerisk hedgingo

2.While youwere visitingLondon,you purchaseda Jaguarfor£35,000,payable in three monthsYouohave enoughcash at your bank in NewYork City,which pays

0.35%interest permonth,compoundingmonthly,to payforthecar Currently,the spotexchangerateis$145/£andthethree month forwardo一exchangerateis$1o40/£In London,themoneymarket interestrateis2o0%for athree-monthoinvestmento Thereare twoalternative waysof payingfor yourJaguar.a Keepthe fundsatyourbankintheUS.and buy£35,000forward obBuy a certain poundamount spottoday andinvest theamount intheU.K.for threemonths sothat thematurityvalue becomesequalto£35,

000.Evaluate eachpayment method.Which methodwouldyouprefer WhySolution:The problemsituation issummarizedas follows:A/P=£35,000payable inthree monthsINY=

0.35%/month,compounding monthlyILD=

2.0%for threemonthsS=$

1.45/£;F$140/£.二Option aWhen youbuy£35,000forward,you willneed$49,000inthreemonths tofulfill theforward contractoThe present value of$49,000is computedasfollows$49,000/lo00353$48,

489.二Thus,the cost of Jaguar as of today is$48,489Option bThepresentvalueof£35,000is£34,314=£35,000/

1.

02.To buy£34,314today,itwillcost$49,755=34,314x

1.

45.Thus thecostofJaguarasoftodayis$49,

755.You shoulddefinitely chooseto use“option a”,and save$1,266,which isthedifferencebetween$49,755and$

484893.Currently,the spotexchangerateis$

1.50/£andthethree-month forwardexchangerateis$

1.52/£.Thethree-month interestrateis80%perannum intheU.S.and

5.8%perannum intheU KAssume thatyouocan borrowas muchas$1,500,000or£1,000,000a.Determine whetherthe interestrate parityis currentlyholding0b.If the IRP isnot holding,how wouldyou carryout coveredinterest arbitrageShow allthe stepsanddeterminethearbitrage profit.c.Explain howtheIRPwill berestored asa resultof coveredarbitrage activities.SolutionLef ssummarize thegiven datafirst:S=$

1.5/£;F=$lo52/£;I$=2o0%；I=k45%£Credit=$1,500,000or£l,000,000a.1+I$=lo021+IF/S=lo

01451.52/

1.50=lo0280£Thus,IRP isnot holdingexactly.1Borrow$1,500,000;repayment will be$1,530,000bo o2Buy£1,000,000spot using$1,500,

000.3Invest£1,000,000atthepoundinterestrate of145%;omaturity valuewillbe£1,014,5004Sell£1,014,500forward for$1,542,040Arbitrage profitwillbe$12,040Following thearbitragetransactionsdescribed above,The dollarinterestratewill rise;CoThe poundinterestratewill fall；The spotexchangeratewillrise；The forwardexchangeratewillfall.These adjustmentswillcontinueuntil IRPholds.

4.Suppose thatthecurrentspotexchangerateis€0o80/$andthethree-monthforwardexchangerateis€0o7813/$The three—month interestrateis

5.6percent perannuminthe UnitedStatesand540percento perannuminFrance.Assume thatyou canbonow upto$1,000,000or€800,

000.a.Show howto realizeacertainprofit viacoveredinterestarbitrage,assuming thatyou wantto realizeprofitin terms of US.dollarso Alsodeterminethesizeofyour arbitrageprofit.Assume thatyou wantto realizeprofit intermsofeuroso Showthecoveredarbitrageprocessand determinebothearbitrageprofitin euros.Solution b.1+i$=

1.014F/S1+if=

1.

053.Thus,onehasto borrowdollars andinvest ineuros tomakearbitrage profito

1.Borrow$1,000,000and repay$1,014,000inthreemonths.

2.Sell$1,000,000spot fbr€1,060,

000.

3.Invest€1,060,000attheeurointerestrate of135%for threemonths andreceive€1,074,310at0maturity.

4.Sell€l,074,310forward for$1,053,

245.Arbitrage profit=$1,053,245—$1,014,000=$39,

245.c.Follow thefirst threesteps aboveoBut thelast step,involving exchangerisk hedging,willbedifferent.

5.Buy$1,014,000forward for€1,034,280Arbitrage profit=€1,074,310—€1,034,280=€40,030。