andUncoveredIneresRaeariy國(guó)際金融香港3

CoveredandUncovered

InterestRateParityWONGKaFu26thJanuary2000ComparingLocalandForeignPricesPriceswithinacountryPricesacrosscountriesP(inhomecurrency)P*(inforeigncurrency)1HD=xFD=1/eFD,i.e.,eHD=1FDPvs.eP*tt+1Time

Forexample,t=January,t+1=FebruaryBuyAsset:payPtReturnonhomeassetSellasset:getPt+1MayreceivedividendDt+1betweentimetandtimet+1Return=Pt+1+Dt+1-PtRateofReturn=(Pt+1+Dt+1-Pt)/PtReturnonahomeassetPt+1-PtdividendsoranyinterestpaymentstotheassetholderDt+1

Pt+1-Pt+Dt+1RateofReturnonahomeassetReturn/costofassetattimeofpurchase/yearHomeassetinhomecurrency(Pt+1+Dt+1

-Pt

)/Pt=[(Pt+1+Dt+1

)/Pt

]-1tt+1Time

Forexample,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*ReturnonaforeignassetAforeigninvestorinvestsinaforeignassetPt+1*

-Pt*+Dt+1*=Pt+1*

+Dt+1*-Pt*Ahome

investorinvestsinaforeignassetet+1(Pt+1*

+Dt+1*)-etPt*

RateofReturnonaforeignassetForeignassetinhomecurrency[et+1(Pt+1*

+Dt+1*)-etPt*]/(etPt*)=[et+1(Pt+1*

+Dt+1*)/(etPt*)]-1=(et+1/et

)[(Pt+1*

+Dt+1*)/Pt*]-1ExpectationsLottery10.5probabilitytowin10000.5probabilitytowin0Expecttowin0.5×1000+0.5×0=500ExpectationsLottery20.2probabilitytowin10000.3probabilitytowin5000.5probabilitytowin0Expecttowin0.2×1000+0.3×500+0.5×0=350ExpectationsLottery3Pi=f(yi)probabilitytowinyiExpecttowin Et(y)=iPiyi=if(yi)yiExpectationsLottery4f(y)probabilitytowinyExpecttowin Et(y)=E(y|informationavailableattimet)

=y

f(y)ydyReplacingassetswithdepositsgreatlysimplifiesthealgebra:Someunknownquantitiesbecomeknown:Pt+1=1Pt=1Dt+1=Rt=homeinterestratePt+1*=1Pt*=1Dt+1*=Rt*=foreigninterestrateTheonlyunknownattimetiset+1ExpectedreturnandexpectedrateofreturnExpectedreturnonahomeasset:Et(Pt+1+Dt+1-Pt)=Et(Pt+1+Dt+1)-PtExpectedrateofreturnonahomeasset:Et[(Pt+1+Dt+1)/Pt-1]=Et(Pt+1+Dt+1)/Pt-1RateofreturnofhomedepositEt(Pt+1+Dt+1)/Pt-1Pt+1=1Pt=1Dt+1=Rt=homeinterestrateEt(1

+Rt)/1-1=RtExpectedreturnandexpectedrateofreturnExpectedreturnonaforeignasset:Et[et+1(Pt+1*

+Dt+1*)-etPt*]=Et[et+1(Pt+1*

+Dt+1*)]-etPt*

ExpectedrateofreturnonaforeignassetEt{[(et+1/et)(Pt+1*

+Dt+1*)/Pt*]-1}=Et[(et+1/et

)(Pt+1*

+Dt+1*)]/Pt*-1RateofreturnonforeigndepositEt[(et+1/et)(Pt+1*

+Dt+1*)]/Pt*-1Pt+1*=1Pt*=1Dt+1*=Rt*=foreigninterestrateEt[(et+1/et)(1

+Rt*)]/1-1=[Et(et+1)/et](1

+Rt*)-1Rateofreturnonforeigndeposit[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*RHS=[Et(et+1)-et]/et+Rt*SupposeEt(et+1)andRt*fixed,largeret

impliessmallerRHSSupposeetandRt*fixed,largerEt(et+1)implieslargerRHS

RHS=[Et(et+1)-et]/et+Rt*SupposeEt(et+1)andet

fixed,largerRt*implieslargerRHS

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