Exercise-06-solution

ExerciseSix:ExchangeRateTheory–PPPandIRP1.TherealexchangerateisdefinedtobeE(CPI*/CPI).IfPPPholds,whatistherateofchangeoftheCPIwhentheforeigninflationrateis3percentperyearand1)thenominalexchangerateisfixed?2)thedomesticcurrencyisdepreciatingat7percentperyear?3)thedomesticcurrencyisappreciatingat3percentperyear?Answer:R=E(CPI*/CPI)ThendR/R=dE/E+dCPI*/CPI*-dCPI/CPIPPPholdsmeansthatdR/R=0,so1)theCPIwillgrowat3percentperyear2)theCPIwillgrowat10percentperyear3)theCPIwillnotchange2.SupposeaU.S.exporterexpectstoreceiveapaymentofSingaporeDollars(SGD)1millionin12months.a)Theone-yearinterestrateonSGDdepositsis3percentperannum.Theone-yearinterestrateondollardepositsis6percentperannum.Thepresentspotexchangerateis$0.65469forSGD.Whatistheone-yearforwardexchangerate?Answer:Coveredinterestrateparityindicatesthat(1+iUS)=(1/e)(1+iSGD)e*,whereeisthespotratein$/SGDande*istheforwardrate.Thereforee*=(1.06/1.03)*0.65469=0.674Intuitively,whenyouinvestin$nowyoushouldgetexactlythesameamountwhenyouchangeyou$forSGDnowandinvestinSGDandthenchangeSGDfor$afterayear.b)Assumingtheexporterviewsdollarsashisorherbasecurrency(i.e.,ultimatelyneedsdollars),therearetwowaystocoverhimselfagainsttheexchangerateriskthatarisesfromnotknowingwhatwillbethevalueoftheSingaporeDollarin12months.Describethem(usingonlyinformationgivenhere)andshowtheirequivalencecomputationally.Answer:Youaregetting1millionSGDinoneyear.Youcaneither:i)sellthemforwardandget1*e*=1*0.673758millionUSdollarsayearfromnowon,orii)borrow1/((1+iSGD)=1/1.03=0.970874millionSGD,convertintoUS$toobtain0.970874*0.65469milliondollarintheUS,whichyields1.06timesUS$0.673758million,whichisexactlyequaltotheamountinthefirstoption.Finally,use1millionSGDyoureceivetopaybackyourborrowingobligation.c)NowsupposetheclaimonSGD1millionisdueinsixmonths.Theinterestrateonsix-monthSGDdepositsis2percentperannum.Theinterestrateonsix-monthdollardepositsis2.7percentperannum.Whatisthesix-monthforwardexchangerate?Answer:(1+iUS)=(1/e)(1+iSGD)e*Thene*=e(1+iUS)/(1+iSGD)=0.65469*(1+2.7%/2)/(1+2%/2)=0.65696d)Whatdoa)andc)implyabout“themarket’sexpectations”regardingthefuturepathoftheexchangerate?Answer:Partsa)andc)implythat,“themarketexpects”thattheexchangeratewillbehigherinthefuture–increasefrom0.65469todayto0.65696sixmonthsfromnow-andthatitwillrisefurtheroverthesubsequentsixmonths,to0.673758.ThedollarwilldepreciateagainstSGD.Thereasonisthat,sincethedollarinterestrateishigherthanthatofSGD,forinvestorstobeindifferentbetweenholdingdollarsandSGDthevalueofdollarshastodecreaseovertime.Butthismightnotbethetrueexpectationofmarketparticipants.Iftheyareuncertainaboutthefuturepath,andarerisk-averse,thentheywillnotnecessarilydrivetheforwardrateintoequalitywiththeirbestguess.Theremaybeariskpremium,inwhichcaseuncoveredinterestparitywillnothold.e)AssumethatthePolishZlotyisworth0.52SGPtodayandobeysone-yearcoveredinterestparityrelationship.Suppose,however,thattodayinvestorsknowwithcertaintythatinoneyear,1zlotywillbeworth$0.3285inthespotmarket.SupposethattheU.S.interestrateremainsthesame.(TheUnitedStatesisabigcountry.)Whatwillinvestorsdo?Towhatlevelwilltheydrivetheone-yearforwardexchangerate?Whatwillthatimplyfortheinterestrateonone-yeardepositsinzloty?Answer:Today’sspotexchangerateforthePolishZlotyis(0.65469$/SGP)(0.52SGP/PZL)=0.340439$/Zloty.Ifinvestorsknowwithcertaintythatinoneyear1PolishZlotywillbeworth$0.3285,thentheywilldrivetoday’sforwardratetothatlevel.Accordingtothecoveredinterestrateparity,thereshouldbe:(1+iUS)=(1/e)(1+izl)e*SotheZlotyinterestrateis(1+6%)*0.340439/0.3285-1=1.099–1=0.099.(annualrate)