andUncoveredInterestRateParity(国际金融(香港

1CoveredandUncoveredInterestRateParityWONGKaFu26thJanuary20002ComparingLocalandForeignPricesPriceswithinacountryPricesacrosscountriesP(inhomecurrency)P*(inforeigncurrency)1HD=xFD=1/eFD,i.e.,eHD=1FDPvs.eP*3tt+1TimeForexample,t=January,t+1=FebruaryBuyAsset:payPtReturnonhomeassetSellasset:getPt+1MayreceivedividendDt+1betweentimetandtimet+1Return=Pt+1+Dt+1-PtRateofReturn=(Pt+1+Dt+1-Pt)/Pt4ReturnonahomeassetPt+1-PtdividendsoranyinterestpaymentstotheassetholderDt+1Pt+1-Pt+Dt+15RateofReturnonahomeassetReturn/costofassetattimeofpurchase/yearHomeassetinhomecurrency(Pt+1+Dt+1-Pt)/Pt=[(Pt+1+Dt+1)/Pt]-16tt+1TimeForexample,t=January,t+1=FebruaryBuyAsset:payetPt*ReturnonforeignassetSellasset:getet+1Pt+1*MayreceivedividendDt+1*betweentimetandtimet+1Return=et+1(Pt+1*+Dt+1*)/-etPt*RateofReturn=[et+1(Pt+1*+Dt+1*)/-etPt*]/etPt*7ReturnonaforeignassetAforeigninvestorinvestsinaforeignassetPt+1*-Pt*+Dt+1*=Pt+1*+Dt+1*-Pt*Ahomeinvestorinvestsinaforeignassetet+1(Pt+1*+Dt+1*)-etPt*8RateofReturnonaforeignassetForeignassetinhomecurrency[et+1(Pt+1*+Dt+1*)-etPt*]/(etPt*)=[et+1(Pt+1*+Dt+1*)/(etPt*)]-1=(et+1/et)[(Pt+1*+Dt+1*)/Pt*]-19ExpectationsLottery10.5probabilitytowin10000.5probabilitytowin0Expecttowin0.5×1000+0.5×0=50010ExpectationsLottery20.2probabilitytowin10000.3probabilitytowin5000.5probabilitytowin0Expecttowin0.2×1000+0.3×500+0.5×0=35011ExpectationsLottery3Pi=f(yi)probabilitytowinyiExpecttowinEt(y)=iPiyi=if(yi)yi12ExpectationsLottery4f(y)probabilitytowinyExpecttowinEt(y)=E(y|informationavailableattimet)=yf(y)ydy13Replacingassetswithdepositsgreatlysimplifiesthealgebra:Someunknownquantitiesbecomeknown:Pt+1=1Pt=1Dt+1=Rt=homeinterestratePt+1*=1Pt*=1Dt+1*=Rt*=foreigninterestrateTheonlyunknownattimetiset+114ExpectedreturnandexpectedrateofreturnExpectedreturnonahomeasset:Et(Pt+1+Dt+1-Pt)=Et(Pt+1+Dt+1)-PtExpectedrateofreturnonahomeasset:Et[(Pt+1+Dt+1)/Pt-1]=Et(Pt+1+Dt+1)/Pt-115RateofreturnofhomedepositEt(Pt+1+Dt+1)/Pt-1Pt+1=1Pt=1Dt+1=Rt=homeinterestrateEt(1+Rt)/1-1=Rt16ExpectedreturnandexpectedrateofreturnExpectedreturnonaforeignasset:Et[et+1(Pt+1*+Dt+1*)-etPt*]=Et[et+1(Pt+1*+Dt+1*)]-etPt*ExpectedrateofreturnonaforeignassetEt{[(et+1/et)(Pt+1*+Dt+1*)/Pt*]-1}=Et[(et+1/et)(Pt+1*+Dt+1*)]/Pt*-117RateofreturnonforeigndepositEt[(et+1/et)(Pt+1*+Dt+1*)]/Pt*-1Pt+1*=1Pt*=1Dt+1*=Rt*=foreigninterestrateEt[(et+1/et)(1+Rt*)]/1-1=[Et(et+1)/et](1+Rt*)-118Rateofreturnonforeigndeposit[Et(et+1)/et](1+Rt*)-1=(1+Rt*){[Et(et+1)-et]+et]}/et-1=[Et(et+1)-et]/et+1+Rt*[Et(et+1)-et]/et+Rt*-1[Et(et+1)-et]/et+Rt*19RHS=[Et(et+1)-et]/et+Rt*SupposeEt(et+1)andRt*fixed,largeretimpliessmallerRHSSupposeetandRt*fixed,largerEt(et+1)implieslargerRHS20RHS=[Et(et+1)-et]/et+Rt*SupposeEt(et+1)andetfixed,largerRt*implieslargerRHS21UncoveredInterestParitySupposewecareonlyaboutexpectedreturn(say,weareriskneutral)DepositinhomecurrencyifandonlyiftherateofreturnonthedepositinhomecurrencyisnotlessthanthedepositinforeigncurrencyRt[Et(et+1)-et]/et+Rt*EquilibriumifRt=[Et(et+1)-et]/et+Rt*22UncoveredInterestParityfloatingexchangerateregimeIfRt[Et(et+1)-et]/et+Rt*bothhomeandforeigninvestorswilldepositinhomecurrencyimpliessupplyforeigncurrencyanddemandhomecurrencyinitially,e=yHD=1FDnow,e=zHD=1FD,zyhencelargerRHS,i.e.,towardsequality23UncoveredInterestParityfloatingexchangerateregimeAlsobecausebothhomeandforeigninvestorswilldepositinhomecurrencyI.e.,largersupplyofhomedepositandsmallersupplyofforeigndeposithence,homeinterestrateRtdecreases,i.e.towardsequalityRt*increases,i.e.towardsequality24UncoveredInterestParityfloatingexchangerateregimeIngeneral,bothinterestratesandexchangeratewilladjusttorestoretheequality.CantheCBsfixtheinterestratesatsomedesiredlevel?Yes.Ifso,theexchangeratealonewilldothejob.25UncoveredInterestParityfloatingexchangerateregimeRt=[Et(et+1)-et]/et+Rt*Hence,theUncoveredInterestParitycanbeusedtodeterminetheexchangerate.And,givenanythreeofthevariableswecancomputetheremainingone.E.g.,givenEt(et+1),et,andRt*,wecancomputeRt=[Et(et+1)-et]/et+Rt*.26RecallrateofreturnonforeigndepositdecreaseswithetetRHSRHS=[Et(et+1)-et]/et+Rt*27RecallrateofreturnonforeigndepositincreaseswithRt*etRHS28RecallrateofreturnonforeigndepositincreaseswithEt(et+1*)etRHS29DeterminationofetgivenRt,Et(et+1)andRt*etRHSReturnonhomedeposit30EffectofanincreaseinthehomedepositinterestrateetRHSReturnonhomedeposit31EffectofanincreaseintheforeigndepositinterestrateetRHSReturnonhomedeposit32FixedexchangerateregimeTomaintaintheexchangerateatafixedlevel,CBhastocommittobuyingwhateverthemarketsupplyofhomecurrencyandsellingwhateverthemarketdemandforhomecurrency33UncoveredInterestParityfixedexchangerateregimeIfRt[Et(et+1)-et]/et+Rt*=Rt*bothhomeandforeigninvestorswilldepositinhomecurrencyandsupplyforeigncurrencyanddemandhomecurrencyCBiscommittedtoafixedexchangerateandhencehastosellhomecurrencyandbuyforeigncurrencyofficialforeignreservesincrease34UncoveredInterestParityfixedexchangerateregimeBothhomeandforeignin