国际投资学在线试题库英文版M02SOLN969506TBC02.docx
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国际投资学在线试题库英文版M02SOLN969506TBC02.docx
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国际投资学在线试题库英文版M02SOLN969506TBC02
Chapter2
ForeignExchangeParityRelations
Note:
InthesixtheditionofGlobalInvestments,theexchangeratequotationsymbolsdifferfrompreviouseditions.Weadoptedtheconventionthatthefirstcurrencyisthequotedcurrencyintermsofunitsofthesecondcurrency.
Forexample,€:
$=1.4indicatesthatoneeuroispricedat1.4dollars.Inpreviouseditionsweusedthereversedconvention$/€=1.4,meaning1.4dollarspereuro.
Allproblemsinthistestbankstillusetheoldconventionandhavenotbeenadaptedtoreflectthenewquotationsymbolsusedinthe6thedition.
QuestionsandProblems
1.ThecurrentSwissfranc/U.S.dollarspotexchangerateis2Swissfrancsperdollar,orCHF/$=2.
Theexpectedinflationoverthecomingyearis2%inSwitzerlandand5%intheUnitedStates.
Whatistheexpectedvalueforthespotexchangerateayearfromnow,accordingtopurchasingpowerparity?
Solution
Accordingtothepurchasingpowerparityrelation,whichstatesthatspotexchangerateadjustsperfectlytoinflationdifferentialbetweentwocountries,theexpectedvaluefortheexchangerate,
ayearfromnow,isgivenby:
CHF/$.
2.ThespotexchangerateisCHF/$=2.00.Theone-yearinterestrateisequalto4%inSwitzerlandand8%intheUnitedStates.Whatshouldthecurrentvalueoftheforwardexchangeratebe?
Solution
Accordingtotheinterestrateparityrelation,theforwarddiscount(orpremium)isequaltotheinterestratedifferential.WithFbeingthecurrentvalueoftheone-yearforwardexchangerate,
wehave:
CHF/$.
3.The¥/€spotexchangerateis130yenpereuro.InflationratesinJapanandGermanyaresimilar.Overthepastyearthe¥/€ratemovedfrom110to130.IsthisgoodnewsorbadnewsforJapanesefirmscompetingwithGermanfirmsintheautomobilemarket?
Solution
TheweakeningoftheyenagainsttheeuroisgoodnewsforJapanesecompetitorsintheautomobilemarket.ForthesameamountofeurosearnedfromtheirsalesinGermany(forinstance€1billion),theJapanesecompanieswillhavethepossibilitytoconverttheirearningsintoagreateramountofyen(130billionyen)thantheyusedto(110billionyen).Also,theirrelativecoststructureimprovescomparedtotheirGermancompetitors.
4.Shouldnominalinterestratesbeequalacrosscountries?
Whyorwhynot?
Solution
Thenominalinterestratecanbedefinedasthesum(ormorepreciselythecompounding)oftherealinterestrateandtheexpectedinflationrateoverthetermoftheinterestrate.AlthoughtheinternationalFisherrelationclaimsthatrealinterestratesareequalacrosstheworld,weknowthatexpectedinflationcanbeverydifferentfromonecountrytoanother.Therefore,thereisnoreasonwhynominalinterestratesshouldbeequalacrosscountries.
5.Shouldrealinterestratesbeequalacrosscountries?
Canafinancialarbitragetakeplaceincaseofsignificantandpersistentrealinterestratedifferences?
Toanswerthisquestion:
a.Firstassumethatexchangeratesarefullypredictableandfollowpurchasingpowerparity(PPP).
b.ThenassumethattheyareuncertainbutthatPPPholds.
c.Finally,assumethatexchangeratesareuncertainandthatPPPdoesnothold.
Solution
Notnecessarily.Thiscanbeshownbyobservingthatnorisk-freearbitragecanexploitdifferencesinrealinterestrates.Let’sstartwithasimpleworldandprogressivelyaddmorecomplexrealities.AssumethattherealratesoneurosandU.S.dollarsarerespectively2%and4%.Let’susethelinearapproximation:
a.ExchangerateisfullypredictableandPPPholds.
Differencesinrealinterestratescanbearbitragedaway.Onecansimplyborrowin€,transferthe€in$atthespotexchangerateandlendthe$.Itcaneasilybeseenthatthisstrategyyieldsexactlytherealinterestratedifferential(2%)withoutanycapitalinvestment.
SincetheexchangerateisfullypredictableandfollowsPPP,weknowforsurethatitsfuturedepreciationisexactlyequaltothe(certain)expectedinflationdifferential.Thenetresultontheinvestmentstrategyistherealinterestratedifferential.
b.ExchangerateisuncertainbutPPPholds.
Weknowthatthefutureexchangeratewillexactlyreflecttheobservedfutureinflationdifferential(PPP)butwearenotsureaboutfutureinflationrates.Theinterestratedifferentialisequaltotherealinterestratedifferentialplustheexpectedinflationdifferential,whiletheexchangeratedepreciationwillbeequaltotheex-postrealizedinflationdifferential.Thedeviationbetweenexpectedandrealizedinflationmakestheabovearbitrageuncertain.However,thedeviationislikelytobesmallforshorthorizons,soarbitragewillinsurethattheshort-termrealinterestratedifferentialissmall.
c.PPPdoesnothold.
Realexchangeratescanbeveryvolatileintheshortrun.Norisklessarbitragecantakeplacetotakeadvantageofrealinterestratedifferentials.
6.Herearesomestatistics:
GBP(£)
CHF
Inflation(annualrate)
10%
4%
One-yearinterestrate
12%
?
%
Spotexchangerate(CHF/£)
3%
Expectedexchangerate(inoneyear)
?
%
One-yearforwardexchangerate(CHF/£)
?
%
Basedonthelinearapproximationofinternationalparityrelations,replacethequestionmarkswiththeappropriateanswers.
Solution
Assumingthatinternationalparityrelationshold,herearetheappropriateanswers(linearapproximation):
GBP(£)
CHF
Inflation(annualrate)
10%
4%
One-yearinterestrate
12%
6%
Spotexchangerate(CHF/£)
3%
Expectedexchangerate(inoneyear)
2.84%
One-yearforwardexchangerate(CHF/£)
2.84%
Calculationscanalsobeperformedwithoutthelinearapproximation.
7.Pafisasmallcountry.ItscurrencyisthepifandtheexchangeratewiththeU.S.dollarwas2pifs
perdollarin1980.Theinflationindexesin1980wereequalto100intheUnitedStatesandinPaf.Twentyyearslater,theinflationindexeswereequalto400intheUnitedStatesand200inPaf.Thecurrentexchangerateis0.9pifsperdollar.
a.WhatshouldthecurrentexchangeratebeifPPPprevailed?
b.IsthePifover/undervaluedaccordingtoPPP?
Solution
a.Accordingtothepurchasingpowerparityrelation,whichstatesthatthespotexchangerateadjustsperfectlytoinflationdifferentialbetweentwocountries,theexpectedvaluefortheexchangerate,twentyyearsfromnow,isgivenby:
Pif/$.
b.AccordingtoPPP,thePifisovervalued.
8.FundamentalValueBasedonAbsolutePPP.Ideally,onewouldliketocomparedirectlytheprice
ofgoodsintwocountriestoseeifanexchangerateconformstoabsolutePPP,orwhetheritisovervaluedorundervaluedinrealterms.AsmentionedinChapter2,thiscanonlybedoneforsomeindividualgoodsthatareclearlycomparable(“lawofoneprice”),andtheestimationfordifferentgoodscanleadtoopposingconclusions.InChapter2,weprovideananalysisbasedonthewell-knownBigMacreportofTheEconomist.Ofcourse,theBigMacisaveryparticularproductandafundamentalPPPvaluecanbecomputedonawiderangeofproducts.Theresultsareoftenconflicting.Forexample,onecanlookatproductionpricesratherthanconsumptionprices.Somestudiesareconductedbylookingatlaborcosts.Ratherthanlookingatunitlaborcostsforunskilledworkers,asisoftendone,theexhibitbelowreportstheaverageannualremunerationofthechiefexecutiveofficer(CEO)ofindustrialcompanieswithannualrevenuesof$250millionto$500millionintenselectedareasoftheworld.ThefiguresarealsofromApril1998.Theyincludeallformsofcompensation,suchasbonuses,perks,andstockoptions,butarenotadjustedfordifferenttaxesorcostsofliving.
ThefirstcolumngivesthetotalCEOcompensationmeasuredinU.S.dollarsusingtheactualexchangerate,whichisindicatedinthesecondcolumn.ThethirdcolumngivesthefundamentalPPPvalueofeachcurrency,impliedbythenationalCEOcompensations.ItistheexchangeratewiththedollarthatwouldmakeCEOcompensationidenticalinallcountries.Thefourthcolumngivestheactualovervaluation(ifpositive)orundervaluation(ifnegative)ofthelocalcurrencyrelativetoitsfundamentalvalueintermsofCEOcompensation.
EXHIBIT:
DeterminingaFundamentalPPPValueBasedonCEOs’Remuneration
TotalCompensation
inUS$
Actual
ExchangeRate
(1US$=)
FundamentalPPPValue
(1US$=)
Undervaluation
in%
SouthKorea
150,711
1474
207
-86
Germany
398,430
1.84
0.68
-63
Japan
420,855
135
53
-61
Mexico
456,902
8.54
3.64
-57
Canada
498,118
1.42
0.66
-54
France
520,389
6.17
2.99
-51
U.K.
645,540
0.6024
0.3626
-40
HongKong
680,616
7.75
4.92
-37
Brazil
701,219
1.14
0.75
-35
U.S.A.
1,072,400
1
1
Source:
TotalcompensationdatacomesfromTowersPerrin,1998.
Whatconclusionscanyoudrawfromthisexhibit?
Solution
ThereisawidedispersioninthedollarremunerationofCEOsacrosstheworld.AmericanCEOsarethebestpaid,followedbytheirBrazilianandHongKongcounterparts.KoreanandGermanCEOshaveverylowcompensationsrelativetoAmericans.TheimpliedPPPexchangeratessuggestthatallcurrenciesarestronglyundervaluedrelativetotheU.S.dollar.Theyreflectabasicinternationaldifferenceinmanagementcultureacrosstheworld,ratherthananenormousdollarovervaluation.Actually,recentinternationalmergers(e.g.,theacquisitionofAmocobyBritishPetroleum,ortheacquisitionofChryslerbyDaimlerBenz)highlighttheproblem,asGermanandBritishmanagersareenviousoftheirU.S.counterparts,whothemselvesfearlosingpartoftheirremuneration.Itis
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