Exercise-05-solution

ExerciseFive-Solution1.Supposeyousawthatthefollowingexchangeratesquotedintheforeignexchangemarket:1US$1US$1US$1US$1€1£1£=======7.7465ChineseRenminbi0.5143UKPoundSterling(£)0.7599Euros(€)11.1697MexicanPesos14.7121MexicanPesos22.7166Mexicanpesos15.0612ChineseRenminbia)Thehypotheticalexchangeratesabovecontainanarbitrageopportunity.Explainhowtoexploitit,usingnomorethanthreeofthecurrencieslistedabove.Answer:Assumethatyouhave1US$tobeginwith.Pickcurrencypairsandtrytoexchangeonecurrencyforanother.Ifyouendupwithmorethanonethenthatisyourarbitrageprofits.Otherwiseyoucouldworkbackwards.Let’sstartwith1US$,sellitforChineseRenminbi,thensellChineseRenminbiforUKPoundsandthensellitforUSdollaragain.USDGBPUSDCNYGBPUSDCNYUSDUSD==00007.15143.010612.1517465.71=×××Thedifferencebetween1.00007and1issosmallthattriangulararbitragehardlyexistshere.Nowtryadifferentthreecurrencies–US$,Peso,Pound.Sell1US$forPeso,sellPesoforPoundandfinallysellPoundforUSD.USDGBPUSDMXNGBPUSDMXNUSDUSD==956052.05143.017166.2211697.111=×××Thefinalamountyougetissmallerthanoriginalone.Soyoumustreverseyourtradingsequenceforaprofitablearbitrageopportunity:BuyPoundwiththeUSD,buyPesoswiththePoundandthenbuyUSDwithPesos.USDMXNUSDGBPMXNUSDGBPUSDUSD==046.11697.1117166.225143.01=×××So4.6%willbeyourarbitrageprofitoneachdollar.b)Youcanremovethearbitrageopportunitybychangingjustoneoftheexchangeratesgiven.(“Themarket”shoulditselfaccomplishthis,viaarbitrage.)Whichexchangerateisit,andwhatwouldthenewcorrectvaluebe?Answer:Ifyoucheckothercurrencypairsintriangulararbitragetrading,youwillseethatitisthePeso/￡ratethatisoutofline,ratherthanoneofthedollarexchangerates.Forexample,verifythefollowingarbitragetradingorder:9992.0==EURUSDMXNEURUSDMXNGBPUSDCNYGBPUSDCNYUSDUSDApartfromtheroundingerror,allcurrenciesalongthisorderarepricedcorrectly,whichleavesonlythethePeso/￡ratetobeincorrect.ThePoundisovervaluedrelativetothePeso.ThisiswhybuyingPesoforPoundearnedaprofit.ThecorrectPeso/￡rateis:7183.225143.011697.11=×==GBPUSDUSDMXNGBPMXN[notes:Ifonewantstobepreciseto4decimalpoints,then0.7599shouldhavebeen0.7592.ButtheseCalculationsarenotintendedtoapplytothefourthdecimalpoint,whichisthesizeoftransactioncostsAndthereforenotexploitablebyarbitrage.]2.Supposeyouareamanagerofabookstore.YoucansellcopiesofWorldTradeandPaymentsbyCaves,Frankel&Jones,at$135percopy.Thebook’sU.S.publisherwillsellittoyoufor$110acopy.AtthesametimethebookWorldTradeandPaymentsisalsowholesaledbytwoforeignfirms:AChinesefirmsellsitforCNY700,andaBritishfirmfor£50(exchangeratesaregivenaboveinProblem1).a)Explainverybrieflyhowyouwouldmaximizeyourprofitsfromtextbookpurchasesandsales.Answer:Giventhefollowingexchangerates,1US$=7.7465ChineseRenminbi1US$=0.5143UKPoundSterling(£)TheUS$priceofbuyingfromChinawouldbe$90.36,andtheUS$pricefromtheBritishfirmis$97.22.Hereisanapparentopportunityforarbitrageofgoods–amismatchofpricesatthedifferentgeographicallocations.Thestrategy“Buylow,sellhigh”againgoverns:buyingbooksfromtheChineseFirmandsellingthemintheUSwillmaximizeprofits.Aslongastheoriginalpriceplustransportationislessthan110$,youdobetterbuyingfromChina.b)Yourskepticalwork-studyassistantmakessomeinternationalphonecalls,andlearnsthatthecopiesfromtheBritishpublisherareofthepreviousedition,andthecopiesfromtheChinesepublisherareactuallyXeroxes(影印版,itisillegaltosellitinUSA).Nowwhatwillyoudo?Answer:YoucannotsellXeroxcopiesintheUSwithoutproperpublisherpermission.Evenifthestorewerewillingtotakechancesbyviolatingcopyrightlaws,studentswillcertainlynotpaythesame$135foraXeroxone;thus,theChinesealternativenolongeroffersapurearbitrageopportunity.Similarly,thepreviouseditionofferedbytheBritishfirmisnotaperfectsubstituteforthecurrentedition.Consequently,thereisnorealarbitragesituationanymore,evenifthedifferenceinpriceexceedstransportationcosts.c)Givethemainreason(s)whyitishardertotakeadvantageofanapparentarbitrageopportunityinagoodsmarketthaninafinancialmarket.Answer:Theimmediatereasonisthetransportationcost.Arbitragewillstarttooperateonlyifthepriceinonecountryexceedsthepriceintheotherbymorethantheshippingcosts.Otherwiseitisnotworthbothtobeartheshipmentcostandwaitfordaysorweekstogettheproduct.Inthisrespect,geographicdistanceandbordereffectsplayimportantroles.Tariffsandothertradebarriersarethesecondreasonwhyitishardertotakeadvantageofanapparentarbitrageopportunityinagoodsmarket.Thirdly,asaresultofimperfectinformation,consumers/retailersmaynotawareofthepricedifferenceindifferentlocations,orofthequalityoftheproductthattheyareimporting.Currenciesorsecuritiestradedinfinancialmarkets,bycontrast,havelowertransactionscoststhangoods,andareoftenstandardized.