arbirage国际金融香港大学,WONGKaFu

AnIntroductionto

ExchangeRateDeterminationWONGKaFu10thJanuary2000AndArbitrageHowwouldyouexplainthemovementofJapaneseYen?(source:merce.ubc.ca/xr/plot.html)HowwouldyouexplainthemovementofJapaneseYen?(source:merce.ubc.ca/xr/plot.html)HowwouldyouexplainthemovementofEuropeanEuros?(source:merce.ubc.ca/xr/plot.html)HowwouldyouexplainthemovementofEuropeanEuros?(source:merce.ubc.ca/xr/plot.html)Howdoweexplainthemovementofforeignexchange?ArbitragePurchasingPowerParityHongKong’sCurrencyBoardmechanismUCMacDonaldNAMacDonaldPricesofBigMac7.8015.60Case1Whatwouldyoudo?Whatwouldyoudo?ChoosethecheaperMacDonaldforlunch.BuyBigMacfromUCandsellatNA.EffectofouractionOuraction:ChoosethecheaperMacDonaldforlunch.BuyBigMacfromUCandsellatNA.MoresupplyofBigMac,lessdemandforBigMacAtNAPriceofBigMacfalls.GreaterdemandforBigMac,lesssupplyforBigMacAtUCPriceofBigMacincreases.UCMacDonaldNAMacDonaldWhatwouldyoudointheabsenceoftransactioncosts?PUCPNACase2PUCPNACase3><Punchline:Arbitrageactivitiescontinueuntilpricesequalize.Arbitrageisastrongdrivingforcetoequalizeprices.HKMacDonaldUSMacDonaldPricesofBigMac(assume1USD=7.8HKD)HKD7.80USD1Case4HKD15.60USD1Case5HKMacDonaldUSMacDonaldPricesofBigMac(assume1USD=eHKD)PHKePUSCase7PHKePUSCase8><Arbitrageactivitiescontinueuntilpricesequalize.Thatis,PHK=ePUSande=PHK/PUSPricesatdifferentlocations,whenexpressedinthesamecurrency,havetoequalize.Thatis,PurchasingPowerParityExchangerateimpliedbyPPPe=PHK/PUSPHK=ePUS.Ifeisfixed,PUShastoadjustwhenthereisachangeinPHK.PurchasingPowerParityThreevariablesintherelation:Knowinganytwoofthem,wecancomputethethird.PHK=ePUS.ePHKPUSIfPUSisfixed,ehastoadjustwhenthereisachangeinPHK.OtherarbitrageopportunitiesacrossspaceInternationalphonecall:HKdirecttoBeijing(Price=P1)HKtoCantonprovince,fromwherethecallisredirectedtoBeijing(Price=P2)ArbitrageopportunitiesexistswhenP1P2,orP1-P20.Arbitrageactivities(thoughillegal)willdriveP1-P2towardszero.ArbitrageopportunitiesacrossspaceABXP2P1OtherarbitrageopportunitiesacrossspaceBuyingorsellingJapaneseYenHKDdirecttoJPY(Price=P1)HKDtoSwedishKronaandSwedishKronatoYen(Price=P2)ArbitrageopportunitiesexistswhenP1P2,orP1-P20.ArbitrageactivitieswilldriveP1-P2towardszero.ArbitrageacrosstimeTodayTomorrow189200StockpricesIfcostofinterestiszero,<onewouldliketobuystocktoday,holditforadayandsellittomorrow.Profit=11.ArbitrageacrosstimeinreallifeInreallife,interestrateisnonzeroandwedonotknowtomorrow’’sstockpriceforsure.Thus,economictheoryhastoadjustforthesefactorsbutstillusesthisideaofarbitrage.WhatdoesPPPtellusaboutexchangeratesBigMacIndexbyEconomists:“BigMacCurrencies””11April,1998.HK’’sBigMacJapan’’sBigMacHKD10.2Yen280e=PHK/PJP=10.2/280=HKD364.29per10000YenWhyisBigMacIndexsofarofffromtheactualexchangerates?Adjustmentofpricesslowingeneral(pricerigidity)NoiseneedtouseeconometricstotestthetheoryOtherfactors(andalsonoise)thatdeterminestheexchangerate.Transportationtakestime(somegoodsareperishable)TheIdeaofHongKong’’sCurrencyboardBankABankB10Exchangeratequotes(perUSD)<7.8Arbitragewilleliminatethedifference.TheIdeaofHongKong’’sCurrencyboardHKMABankB10Exchangeratequotes(perUSD)<7.8BecauseHKMAwillsupplyanddemandHKDat7.8,arbitragewillpushHK’’sexchangerateto7.8.WhywouldthesupplyofHKdollarfallintoashortagewhenspeculatorsattackHKD?SpeculatorsattackHKDbecausetheyexpectHKDtodevalue.E.g.,from1:7.8to1:15.6.IfyouknowthatHK’’sexchangeratewilldevaluefrom1:7.8to1:15.6,youcansellHKDandbuyUSDtodaybuyHKDandsellUSDafterdevaluationWhowouldtradewithyou?Whenyou(thepublic)sellHKDandbuyUSDtoday,HKMAbuysHKDandsellsUSD.Interestratehastogoupgivenmoneyandloandemandbythepublic.TheHKMApromisestobuyandsellHKDat1:7.8.Lessmoneyisinpublic’shand.Thatismoneysupplydecreases.WhywouldthesupplyofHKdollarfallintoashortagewhenspeculatorsattackHKD?Effectofhighinterestrate?InvestmentConsumptionWhenwillinterestratereturntoa““normal”level?WhatdoesPPPsay?Whatdoesinterestparitysay?Willinterestratebebacktothenormallevelifthegovernmentgofishingorgolfing?-End-Pricesatdifferentlocations,whenexpressedinthesamecurrency,havetoequalize.Thatis,PurchasingPowerParityExchangerateimpliedbyPPPe=PHK/PUSPHK=ePUS.SpeculatorsattackHKDbecausetheyexpectHKDtodevalue.E.g.