International FinanceWord格式.docx
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International FinanceWord格式.docx
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Coveredinterestrateparity(CIRP)isakindofInterestrateparitieswhichreferstotheexpectedchangesofexchangerateandtheinterestratedifferentialbetweentwocurrenciesduringaperiodoftime.
“Theexpectedexchangeratechangecanbecoveredbyenteringaforwardcontractfortheforeignexchangetransactionatafuturetime.Subsequently,itiscalledcoveredinterestrateparity(CIRP),whichidentifiestherelationshipsbetweenthespotexchangerate,theforwardexchangerate,andtheinterestratesinthetwocountriesinatimeperiod.”(Wang,2005,45)
UnderthetheoryofCIRP,theforwardpremiummustbeequaltothetwocountries’interestratedifferentialsoastoeliminateanyarbitrageopportunities.Theformulaisasfollows:
Inwhich,F0,1isforwardexchangerate.S0isspotexchangerate.rhisinterestrateinhomecountry.rfisinterestrateinforeigncountry.Ifthisrelationshipholds,profitablearbitrageopportunitieswillnotexistanditissametoinvestinhomecountryortheforeigncountry.Iftheforwardpremiumisgreaterthantheinterestratedifferentialbetweenthehomecountryandtheforeigncountry,itwillbeprofitabletoinvestintheforeigncountry.Inthiscase,investorneedstoconverthomecurrencyintoforeigncurrencyatthespotexchangerate,investinforeigncountryandearninterestrateinacertainperiod,thenconverttheforeigncurrencybacktohomecurrencythroughaforwardcontractenteredatthebeginning.Iftheforwardpremiumissmallerthantheinterestratedifferential,itwillbeprofitabletoinvestinhomecountry.
LetusexaminetheCIRPbycomparingandanalyzing€and$intwoperiods,and€and¥(ChinaYuan)inonecertainperiods.
ExchangerateandinterestrateinformationofeuroandUSdollaron23December,2005isasfollows(€ishomecurrency):
€/$spotrate
0.8428
Oneyear€/$forwardrate
0.8263
Eurolandinterestrate
1.25%pa
USinterestrate
4.64%pa
(Sourcefrom
http:
//www.ecb.int/stats/monetary/rates/html/index.en.html
//research.stlouisfed.org/fred2/series/WCD6M?
cid=121)
InordertoexaminewhetherCIRPholds,weneedtocalculateifforwardpremiumisequaltotheinterestratedifferential.
Theforwardpremium=(F0,1-S0)/S0=(0.8263-0.8428)/0.8428=-0.01958
Theinterestratedifferential=(rh-rf)/1+rf=(0.0125-0.0464)/1+0.0464=-0.03240
Accordingtotheresult,theforwardpremiumisnotequaltotheinterestratedifferential,soarbitrageopportunityexists.Alsobecausetheforwardpremium>
interestratedifferential,itwouldbemoreprofitabletoinvestin$,whichmeans:
A.ifsomeonehave$toinvest,justinvestinthe$toearninterest.
B.ifsomeonehave€toinvest,heorsheneedstoconvert€to$atthebeginningoftheperiod,atthesametimeenterintoaforwardcontracttosell$attheendoftheperiod,investin$toearninterest,thenconvert$backto€throughtheforwardcontractattheendoftheperiod.
LetusexamineandanalyzetheinvestmentprocessBindetail.TherearetwosituationsinB,thatis,B1:
theinvestorhashisorherownmoneytoinvest;
B2:
theinvestorborrowsmoneyfrombanktoinvest.
B1:
assumetheinvestorhas€5,000,000toinvest,theprocessofinvestmentwouldbe:
First,Convertthe€5,000,000to$atthespotexchangerate€0.8428/$,whichgives€5,000,000/€0.8428/$=$5,932,605.6.
Second,Enterintoaforwardcontracttosell$attheforwardexchangerate€0.8263/$,thesizeofthecontractwillbedecidedbelow.
Third,investthe$5,932,605.6foroneyearattherateof4.64%intheUS.Afteroneyear,theinvestmentreturnis$5,932,605.6×
(1+0.0464)=$6,207,878.5,whichisthesizeoftheforwardcontractabove.
Finally,Convert$6,207,878.5to€throughtheforwardcontract,whichis$6,207,878.5×
€0.8263/$=€5,129,570
Sotheprofitfromthisinvestmentis€5,129,570-€5,000,000=€129,570.Iftheinvestorjustinvestthe€5,000,000ineurolandforoneyearattheinterestrateof1.25%,theinvestmentreturnwillbe€5,000,000×
(1+0.0125)=€5,062,500,whichgivestheprofitof€62,500.Thearbitrageprofitis€129,570-€62,500=€67,070.Obviously,itismoreprofitabletoinvestintheUS.
B2:
assumetheinvestorborrows€5,000,000frombanktoinvest.Thentransactioncostmustbeconsidered.Thatis,borrowingrateisdifferentfromlendingrate.ThelendingratesintheUSandineurolandareasfollow:
Eurolandborrowingrate
Eurolandlendingrate
3.25%pa
USborrowingrate
USlendingrate
7.25%pa
cid=121
//research.stlouisfed.org/fred2/series/DPRIME/downloaddata?
cid=117)
Thentheinvestmentprocesswouldbe:
First,borrow€5,000,000atthelendingrateof3.25%.
Second,Convertthe€5,000,000to$atthespotexchangerate€0.8428/$,whichgives€5,000,000/€0.8428/$=$5932605.6.
Third,Enterintoaforwardcontracttosell$attheforwardexchangerate€0.8263/$,thesizeofthecontractwillbedecidedbelow.
Fourth,investthe$5,932,605.6foroneyearattheborrowingrateof4.64%intheUS.Afteroneyear,theinvestmentreturnis$5,932,605.6×
(1+0.0464)=$6207878.5,whichisthesizeoftheforwardcontractabove.
Then,Convert$6207878.5to€throughtheforwardcontract,whichis$6,207,878.5×
Finally,repaythebankatthelendingrateof3.25%,whichis€5,000,000×
(1+0.0325)=€5,162,500.
Obviously,theinvestorneedstorepaymoremoney(€5,162,500)thantheamountofprofit(€5,129,570).Sothereisnoarbitrageopportunityexistsincethelendingrateishigherthanborrowingrate.
Besidestheborrowingrateandlendingrate,otherkindsoftransactioncosts,suchasbid-askspreads,wouldreducearbitrageopportunitiesaswell.
LetusanalyzeanothercasetoexaminetheCIRP.ExchangerateandinterestrateinformationofeuroandUSdollaron26December,2008isasfollowsand€isstillthehomecurrency:
0.7116
0.7155
2%pa
3%pa
1.8%pa
(Sourcefrom:
Theprocessisthesameasthatinthepreviousexamplethatweneedtocalculateifforwardpremiumisequaltotheinterestratedifferential:
Theforwardpremium=(F0,1-S0)/S0=(0.7155-0.7116)/0.7116=0.0059
Theinterestratedifferential=(rh-rf)/1+rf=(0.02-0.018)/1+0.018=0.0020
Sincetheforwardpremium>
interestratedifferential,arbitrageopportunityexistsanditwouldbemoreprofitabletoinvestin$.Supposeaninvestorhas$2,000,000toinvest,heorsheshouldsimplychoosetoinvestin$.
Iftheinvestordoesnothavemoneyandborrows€2,000,000frombanktoinvest,thenthelendingrateshouldbeincluded:
First,borrow€2,000,000atthelendingrateof3%.
Second,convertthe€2,000,000to$atthespotexchangerate€0.7116/$,whichgives€2,000,000/€0.7116/$=$2,810,567.7
Third,enterintoaforwardcontracttosell$afteroneyearattheforwardexchangerate€0.7155/$,thesizeofthecontractwillbedecidedbelow.
Fourth,investthe$2,810,567.7foroneyearattherateof1.8%intheUS.Afteroneyear,theinvestmentreturnis$2,810,567.7×
(1+0.018)=$2,861,158,whichisthesizeoftheforwardcontractabove.
Then,Convert$2,861,158to€throughtheforwardcontract,whichis$2,861,158×
€0.7155/$=€2,047,158
Finally,repaythebankatthelendingrateof3%,whichis€2,000,000×
(1+0.03)=€2,060,000.
Itiscanbeseeneasilythattherepayfund(€2,060,000)ismorethantheamountofprofit(€2,047,158).Sothereisnoarbitrageopportunityexists.
However,iftheinvestoruseshisorherown€2,000,000toinvest,heorshestillcangainprofit.Theprocessisasfollow:
First,Convertthe€2,000,000to$atthespotexchangerate€0.7116/$,whichgives€2,000,000/€0.7116/$=$2,810,567.7
Second,Enterintoaforwardcontracttosell$afteroneyearattheforwardexchangerate€0.7155/$.
Third,investthe$2,810,567.7foroneyearattherateof1.8%intheUS.Afteroneyear,theinvestmentreturnis$2,810,567.7×
(1+0.018)=$2,861,158.
Finally,Convert$2,861,158to€throughtheforwardcontract,whichis$2,861,158×
Sotheprofitfromthisinvestmentis€2,047,158-€2,000,000=€47,158.Iftheinvestorjustinvestthe€2,000,000ineurolandforoneyearattheinterestrateof2%,theinvestmentreturnwillbe€2,000,000×
(1+0.02)=€2,040,000,whichgivestheprofitof€40,000.Thearbitrageprofitis€47,158-€40,000=€7,158.So,itismoreprofitabletoinvestintheUS.But,whenothertransactioncostsareconsidered,thearbitrageprofitwillbedifferentagain.
Now,letusmovetothe€and¥(ChinaYuan).Thistime,weassume¥ishomecurrency.TheExchangerateandinterestrateinformationof€and¥on8April,2009isasfollows:
¥/€spotrate
9.0446
Oneyear¥/€forwardrate
9.0300
0.25%pa
2.25%pa
Chinaborrowingrate
Chinalendingrate
5.31%pa
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