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INTERNATIONALFINANCIALMANAGEMENTEUN/RESNICKSecondEdition5ChapterFiveInternationalParityRelationships&ForecastingExchangeRatesChapterObjective:Thischapterexaminesseveralkeyinternationalparityrelationships,suchasinterestrateparityandpurchasingpowerparity. ChapterOutlineInterestRateParityPurchasingPowerParityTheFisherEffectsForecastingExchangeRates1 ChapterOutlineInterestRateParityCoveredInterestArbitrageIRPandExchangeRateDeterminationReasonsforDeviationsfromIRPPurchasingPowerParityTheFisherEffectsForecastingExchangeRates2 ChapterOutlineInterestRateParityPurchasingPowerParityPPPDeviationsandtheRealExchangeRateEvidenceonPurchasingPowerParityTheFisherEffectsForecastingExchangeRates3 ChapterOutlineInterestRateParityPurchasingPowerParityTheFisherEffectsForecastingExchangeRates4 ChapterOutlineInterestRateParityPurchasingPowerParityTheFisherEffectsForecastingExchangeRatesEfficientMarketApproachFundamentalApproachTechnicalApproachPerformanceoftheForecasters5 InterestRateParityInterestRateParityDefinedCoveredInterestArbitrageInterestRateParity&ExchangeRateDeterminationReasonsforDeviationsfromInterestRateParity6 InterestRateParityDefinedIRPisanarbitragecondition.IfIRPdidnothold,thenitwouldbepossibleforanastutetradertomakeunlimitedamountsofmoneyexploitingthearbitrageopportunity.Sincewedon’ttypicallyobservepersistentarbitrageconditions,wecansafelyassumethatIRPholds.7 InterestRateParityDefinedSupposeyouhave$100,000toinvestforoneyear.YoucaneitherinvestintheU.S.ati$.Futurevalue=$100,000(1+ius)tradeyourdollarsforyenatthespotrate,investinJapanati¥andhedgeyourexchangerateriskbysellingthefuturevalueoftheJapaneseinvestmentforward.Thefuturevalue=$100,000(F/S)(1+i¥)Sincebothoftheseinvestmentshavethesamerisk,theymusthavethesamefuturevalue—otherwiseanarbitragewouldexist.(F/S)(1+i¥)=(1+ius)8 InterestRateParityDefinedFormally,(F/S)(1+i¥)=(1+ius)orifyouprefer,IRPissometimesapproximatedas9 IRPandCoveredInterestArbitrageIfIRPfailedtohold,anarbitragewouldexist.It’seasiesttoseethisintheformofanexample.Considerthefollowingsetofforeignanddomesticinterestratesandspotandforwardexchangerates.SpotexchangerateS($/£)=$1.25/£360-dayforwardrateF360($/£)=$1.20/£U.S.discountratei$=7.10%Britishdiscountratei£=11.56%10 IRPandCoveredInterestArbitrageAtraderwith$1,000toinvestcouldinvestintheU.S.,inoneyearhisinvestmentwillbeworth$1,071=$1,000(1+i$)=$1,000(1.071)Alternatively,thistradercouldexchange$1,000for£800attheprevailingspotrate,(notethat£800=$1,000÷$1.25/£)invest£800ati£=11.56%foroneyeartoachieve£892.48.Translate£892.48backintodollarsatF360($/£)=$1.20/£,the£892.48willbeexactly$1,071.11 AccordingtoIRPonlyone360-dayforwardrate,F360($/£),canexist.ItmustbethecasethatF360($/£)=$1.20/£Why?IfF360($/£)$1.20/£,anastutetradercouldmakemoneywithoneofthefollowingstrategies:InterestRateParity &ExchangeRateDetermination12 ArbitrageStrategyIIfF360($/£)>$1.20/£i.Borrow$1,000att=0ati$=7.1%.ii.Exchange$1,000for£800attheprevailingspotrate,(notethat£800=$1,000÷$1.25/£)invest£800at11.56%(i£)foroneyeartoachieve£892.48iii.Translate£892.48backintodollars,ifF360($/£)>$1.20/£,£892.48willbemorethanenoughtorepayyourdollarobligationof$1,071.13 ArbitrageStrategyIIIfF360($/£)<$1.20/£i.Borrow£800att=0ati£=11.56%.ii.Exchange£800for$1,000attheprevailingspotrate,invest$1,000at7.1%foroneyeartoachieve$1,071.iii.Translate$1,071backintopounds,ifF360($/£)<$1.20/£,$1,071willbemorethanenoughtorepayyour£obligationof£892.48.14 YouareaU.S.importerofBritishwoolensandhavejustorderednextyear’sinventory.Paymentof£100Misdueinoneyear.IRPandHedgingCurrencyRiskIRPimpliesthattherearetwowaysthatyoufixthecashoutflowa)Putyourselfinapositionthatdelivers£100Minoneyear—alongforwardcontractonthepound.Youwillpay(£100M)(1.2/£)=$120Mb)Formaforwardmarkethedgeasshownbelow.SpotexchangerateS($/£)=$1.25/£360-dayforwardrateF360($/£)=$1.20/£U.S.discountratei$=7.10%Britishdiscountratei£=11.56%15 IRPandaForwardMarketHedgeToformaforwardmarkethedge:Borrow$112.05millionintheU.S.(inoneyearyouwillowe$120million).Translate$112.05millionintopoundsatthespotrateS($/£)=$1.25/£toreceive£89.64million.Invest£89.64millionintheUKati£=11.56%foroneyear.Inoneyearyourinvestmentwillhavegrownto£100million—exactlyenoughtopayyoursupplier.16 ForwardMarketHedgeWheredothenumberscomefrom?Weoweoursupplier£100millioninoneyear—soweknowthatweneedtohaveaninvestmentwithafuturevalueof£100million.Sincei£=11.56%weneedtoinvest£89.64millionatthestartoftheyear.Howmanydollarswillittaketoacquire£89.64millionatthestartoftheyearifS($/£)=$1.25/£?17 ReasonsforDeviationsfromIRPTransactionsCostsTheinterestrateavailabletoanarbitrageurforborrowing,ib,mayexceedtheratehecanlendat,il.Theremaybebid-askspreadstoovercome,Fb/Sa1competitivenessofdomesticcountrydeteriorateswithcurrencydepreciations.21 EvidenceonPPPPPPprobablydoesn’tholdpreciselyintherealworldforavarietyofreasons.Haircutscost10timesasmuchinthedevelopedworldasinthedevelopingworld.Film,ontheotherhand,isahighlystandardizedcommoditythatisactivelytradedacrossborders.Shippingcosts,aswellastariffsandquotascanleadtodeviationsfromPPP.PPP-determinedexchangeratesstillprovideavaluablebenchmark.22 TheFisherEffectsAnincrease(decrease)intheexpectedrateofinflationwillcauseaproportionateincrease(decrease)intheinterestrateinthecountry.FortheU.S.,theFishereffectiswrittenas:i$=$+E($)Where$istheequilibriumexpected“real”U.S.interestrateE($)istheexpectedrateofU.S.inflationi$istheequilibriumexpectednominalU.S.interestrate23 InternationalFisherEffectIftheFishereffectholdsintheU.S.i$=$+E($)andtheFishereffectholdsinJapan,i¥=¥+E(¥)andiftherealratesarethesameineachcountry$=¥thenwegettheInternationalFisherEffectE(e)=i$-i¥.24 InternationalFisherEffectIftheInternationalFisherEffectholds,E(e)=i$-i¥andifIRPalsoholdsthenforwardparityholds.25 EquilibriumExchangeRateRelationships$-£IRPPPPFEFRPPPIFEFP26 ForecastingExchangeRatesEfficientMarketsApproachFundamentalApproachTechnicalApproachPerformanceoftheForecasters27 EfficientMarketsApproachFinancialMarketsareefficientifpricesreflectallavailableandrelevantinformation.Ifthisisso,exchangerateswillonlychangewhennewinformationarrives,thus:St=E[St+1]andFt=E[St+1|It]Predictingexchangeratesusingtheefficientmarketsapproachisaffordableandishardtobeat.28 FundamentalApproachInvolveseconometricstodevelopmodelsthatuseavarietyofexplanatoryvariables.Thisinvolvesthreesteps:step1:Estimatethestructuralmodel.step2:Estimatefutureparametervalues.step3:Usethemodeltodevelopforecasts.Thedownsideisthatfundamentalmodelsdonotworkanybetterthantheforwardratemodelortherandomwalkmodel.29 TechnicalApproachTechnicalanalysislooksforpatternsinthepastbehaviorofexchangerates.Clearlyitisbaseduponthepremisethathistoryrepeatsitself.ThusitisatoddswiththeEMH30 PerformanceoftheForecastersForecastingisdifficult,especiallywithregardtothefuture.Asawhole,forecasterscannotdoabetterjobofforecastingfutureexchangeratesthantheforwardrate.ThefounderofForbesMagazineoncesaid:“Youcanmakemoremoneysellingadvicethanfollowingit.”31 EndChapterFive32
