第一章匯率的決定與國際平價條件S培訓(xùn)教材

第一章

匯率決定與國際平價條件

基本內(nèi)容有關(guān)外匯與匯率的基本知識（referencetochapterfour)匯率變化幅度的測定匯率變化的影響因素購買力平價利率平價國際費雪效應(yīng)匯率預(yù)測Foreignexchange(fx)marketsAnexchangeratemeasuresthevalueofonecurrencyinunitsofanothercurrency.MarketsSpotmarketTradeincashwithdeliveryintwobusinessdaysForwardmarketTradeatapre-specifiedpriceandonapre-specifiedfuturedateVolume$1.2trillionaveragedailyvolumeduring200175%oftradeisintheinterbankmarket（75%的交易是銀行之間的外匯交易，其日均交易額達1.2trillion美元）ParticipantsinthefxmarketWholesalemarketDealers(ormarketmakers) BuyandsellatquotedbidandofferpricesBrokers Serveasmatchmakers,withoutputtingtheirownmoneyatriskRetailmarketGovernmentsCorporationsSmallerfinancialinstitutionsIndividualsTworulesformultinationalfinanceRule#1

Keeptrackofyourunits

（注意貨幣單位）Rule#2

Alwaysbuyorsellthecurrencyinthedenominatorofaforeignexchangequote（買賣的貨幣是指外匯標(biāo)價中處于分母的貨幣）Rule#1

KeeptrackofyourunitsAbottleofGeorgesdeBouefmerlot Buy1bottleofwine P€ =€40/btl Spotexchangerate S$/€ =$0.80/€

? S€/$ =1/S$/€ =€1.25/$Howmuchisthisindollars?P$

=P€S$/€ =(€40/btl)($0.80/€) =$32/btl

=P€/S€/$ =(€40/btl)/(€1.25/$) =$32/btlRule#1

KeeptrackofyourunitsAbottleofGeorgesdeBouefmerlot Buy1bottleofwine P€ =€40/btl Spotexchangerate S$/€ =$0.80/€

? S€/$ =1/S$/€ =€1.25/$Howmuchisthisindollars?P$

=P€S€/$ =(€40/btl)(€1.25/$) =€250/(btl×$)這是什么???因此，Keeptrackofyourcurrencyunits!Rule#2

Thinkofbuyingorselling

theassetinthedenominator先從商品買賣說起，Buyingandsellingabottleofwine Buyabottleat€40/btlandsellat€50/btl

T€10/btlprofit。在這里買賣的對象是分母中的wine。Buyingorsellingaforeigncurrencyislikebuyingorsellinganyotherasset.Buyingandselling

euros Buy€sat$0.80/€andsellat$1.00/€ Buy€sat$0.80/€

o Sell$sat€1.25/$

Sell€sat$1.00/€

o

Buy$sat€1.00/$

T$0.20/€profit T€0.25/$profitAnexampleofwhatcangowrong如果買賣價格弄錯了，即如果Buy$sat$0.80/€andsell$sat$1.00/€，結(jié)果會如何呢？ Buy$sat$0.80/€

o Sell€sat€1.25/$

Sell$sat$1.00/€

o

Buy€sat€1.00/$

T$0.20/€

loss

T€0.25/$

loss So,Alwaysthinkofbuyingorselling thecurrencyinthedenominator!FXquotationconventions

(匯率報價慣例）European/Americanquotesforthe$EuropeanquotesareconvenientforaEuropeanbecausetheyplacetheforeigncurrency(the$)inthedenominator（銀行間報價多為歐式報價，即單位美元的外國貨幣匯率，因為美元是最經(jīng)常交易的貨幣。）歐式標(biāo)價法對當(dāng)?shù)厝撕芊奖恪? e.g.€1.25/$AmericanquotesareconvenientforanAmericanbecausetheyplacetheforeigncurrency(the€)inthedenominator美式標(biāo)價法對美國人很方便。 e.g.$0.80/€FXquotationconventions(匯率報價慣例）Direct/indirectquotesforforeigncurrencyfDirectquotesareconvenientforadomesticresidentbecausetheyplacetheforeigncurrencyinthedenominator(d/f); e.g.￥110.95/€foraresidentofJapanIndirectquotesareinconvenientforadomesticresidentbecausetheyplacetheforeigncurrencyinthenumerator(f/d); e.g.￥110.95/€foraresidentofEurope

匯率變動幅度的測定Whenacurrencydeclinesinvalue,itissaidtodepreciate.Whenitincreasesinvalue,itissaidtoappreciate.外國貨幣相對于本國貨幣的變動百分比Thepercentagechange(%D)inthevalueofaforeigncurrencyiscomputedas:Apositive%Drepresentsappreciationoftheforeigncurrency,whileanegative%Drepresentsdepreciation.本國貨幣相對于外國貨幣匯率的變動百分比人民幣兌美元匯率變動例如：人民幣兌美元匯率:2005年7月21日:$1=8.1100RMB2010年3月4日:$1=6.8265RMB請計算美元相對于人民幣的變化率和人民幣相對于美元的變化率？美元相對于人民幣的匯率變動率=（6.8265-8.1100）/8.1100=-15.8%人民幣相對于美元的匯率變動率=（8.1100-6.8265)/6.8265=18.8%人民幣兌歐元匯率變動例如：人民幣兌歐元匯率:2005年7月21日:€

1=10.0641RMB2010年3月4日:€1=9.3482RMB歐元相對于人民幣的匯率變動率=（9.3482-10.0641）/10.0641=-7.1%人民幣相對于歐元的匯率變動率=（10.0641-9.3482)/9.3482=7.7%RMB/$Quantityof$S0D0r0

RMB.inflation

中國對美國商品的需求增加,因而外匯需求也增加美國對中國商品的需求減少,因而美元外匯供應(yīng)減少D1r1S1影響匯率變化的因素1.RelativeInflationRatesRMB/$Quantityof$r0S0D0S1D1r1

RMB.interestrates

人民幣對美元存款的需求減少,因而外匯需求下降美元對人民幣存款的需求增加,因而外匯供給增加影響匯率變化的因素2.RelativeInterestRatesRMB/$Quantityof$S0D0r0

RMB.incomelevel

人民幣對美國商品需求增加,因而外匯需求上升對外匯供給的影響不無法預(yù)測D1r1影響匯率變化的因素3.RelativeIncomeLevels,S14.GovernmentControlsimposingforeignexchangebarriers（設(shè)置外匯交易障礙）,imposingforeigntradebarriers（設(shè)置貿(mào)易障礙）,interveningintheforeignexchangemarket（干預(yù)外匯市場）,affectingmacrovariablessuchasinflation,interestrates,andincomelevels.（影響宏觀變量）影響匯率變化的因素5.ExpectationsForeignexchangemarketsreacttoanynewsthatmayhaveafutureeffect.當(dāng)市場預(yù)計某種貨幣趨跌時，交易者會大量拋售該貨幣，造成該貨幣匯率下浮的事實；反之，當(dāng)人們預(yù)計某種貨幣趨于堅挺時，又會大量買進該種貨幣，使其匯率上揚。由于公眾預(yù)期具有投機性和分散性的特點，加劇了匯率短期波動的振蕩。

影響匯率變化的因素ExpectationsFedchairmansuggestsFedis StrengthenedunlikelytocutU.S.interestratesApossibledeclineinGerman StrengthenedinterestratesCentralbanksexpectedto Weakenedintervenetoboosttheeuro

Signal Impacton$PoorU.S.economicindicators Weakened影響匯率變化的因素6.Speculating自1973年實行浮動匯率制以來，外匯市場的投機活動越演越烈，投機者往往擁有雄厚的實力，可以在外匯市場上推波助瀾，使匯率的變動遠遠偏離其均衡水平。投機的關(guān)鍵內(nèi)容是低價買入、高價賣出，或者是高價賣出、低價買入。PurchasingPowerParity,

orPPP1.絕對購買力平價的基本內(nèi)容TheabsoluteformofPPP,orthe“l(fā)awofoneprice”（Equivalentassetssellforthesameprice.）suggeststhatsimilarproductsindifferentcountriesshouldbeequallypricedwhenmeasuredinthesamecurrency.這就是絕對購買力的基本公式即，匯率取決于以不同貨幣衡量的可貿(mào)易商品的價格水平之比，也就是不同貨幣對可貿(mào)易商品的購買力之比。TheLawofOnePriceEquivalentassetssellforthesameprice(alsocalledpurchasingpowerparity,orPPP)SeldomholdsfornontradedassetsCan’tcompareassetsthatvaryinqualityMaynotholdpreciselywhentherearemarketfrictionsAnexample:TheworldpriceofgoldSuppose P￡=￡250/ozinLondon P€=€400/ozinBerlinThelawofonepricerequires:

Pt￡

=Pt€St￡/€ T￡250/oz=(€400/oz)St￡/€即St￡/€＝￡0.6250/€

or1/(￡0.6250/€)=€1.6000/￡P(guān)urchasingPowerParity,

orPPP2.相對購買力平價的基本內(nèi)容TherelativeformofPPP

認為，即期匯率應(yīng)根據(jù)兩國預(yù)期的通貨膨脹率進行調(diào)整。即E[Std/f]=S0d/f[(1+E[pd]/(1+E(pf)]t即RPPP將匯率的漲落歸因于物價或貨幣購買力的變動。RPPPstatesthattheexpectedappreciationordepreciationofthespotrateisdeterminedbytheexpectedinflationdifferential.Ifinflationisaknownconstantineachcurrency,thenRPPPcanbestatedasE[Std/f]=S0d/f[(1+pd/(1+pf]tArbitrageIfPPPdoesnothold,thenthereisanopportunitytolockinarisklessarbitrageprofit.有些書上將arbitrage指為speculativepositions，但是，arbitrageismorestrictlydefinedasaprofitablepositionobtainedwith:Nonetinvestmentand

Norisk因此，套利利潤是指無凈投資和無風(fēng)險情況下的利潤。考慮交易成本，在不存在市場摩擦的情況下，如果一價定律不成立，則存在無風(fēng)險套利機會。Eg,X銀行：Bid

A$0.5838/€;OfferA$0.5841/€Y銀行：Bid

A$0.5842/€;OfferA$0.5845/€套利者可以從X銀行買進歐元，與此同時，再賣給Y銀行，即可賺取無風(fēng)險利潤。因為匯率比為：(Y銀行)0.5842/(X銀行)0.5841=1.0001712>1，套利收益率為0.01712%TheNo-ArbitrageConditionPPP意味著：即期匯率由本國貨幣資產(chǎn)價格與相同資產(chǎn)的外國貨幣價格之比決定。如果PPP不成立，則價格差異會使套利有利可圖。Pd/Pf=Sd/fPd=Pf×Sd/fTheNo-ArbitrageCondition非套利條件，即PPP成立。雙邊套匯的匯率均衡條件SXd/f/SYd/f=1即SXd/f=SYd/f交叉三角套匯情況下的均衡匯率：Sd/eSe/fSf/d=1

Anexamplewithtransactionscosts

GolddealerA

GolddealerB€401.40/ozOffer€401.00/ozBid￡250.25/ozOffer￡250.00/ozBidBuylowfromASellhightoBFXdealer€1.599/￡bid€1.601/￡askArbitrageprofitCrossexchangeratesandtriangulararbitrageWhichwaydoyougo?IfSd/eSe/fSf/d<1,theneither

Sd/e,Se/forSf/dmustrise（說明分母貨幣相對于分子貨幣價格較低，有上升的可能）T Foreachspotrate,buythecurrencyinthedenominator（分母）

withthecurrencyinthenumerator（即出售分子貨幣，購買分母貨幣）

IfSd/eSe/fSf/d>1,theneither

Sd/e,Se/forSf/dmustfall（說明分母貨幣相對于分子貨幣價格較高，有下降的可能）Foreachspotrate,sellthecurrencyinthedenominator（分母）forthecurrencyinthenumerator：即出售分母貨幣，購買分子貨幣CrossexchangeratesandtriangulararbitrageSupposeSRbl/$ = Rbl5.000/$ ? S$/Rbl=$0.2000/RblS$/￥ = $0.01000/￥ ? S￥/$=￥100.0/$S￥/Rbl = ￥20.20/Rbl ? SRbl/￥

?Rbl0.04950/￥SRbl/$S$/￥S￥/Rbl

=(Rbl5/$)($.01/￥)(￥20.20/Rbl) =1.01>1CrossexchangeratesandtriangulararbitrageSRbl/$S$/￥S￥/Rbl=1.01>1Currenciesinthedenominators(分母)aretoohighrelativetothenumerators（分子）,（出售分母貨幣以購買分子貨幣）：selldollarsandbuyrubles：Sell$1millionandbuyRbl5millionsellrublesandbuyyen：SellRbl5millionandbuy￥101million（5×20.20）sellyenandbuydollars：Sell￥101millionyenandbuy$1.01million（101×0.01）Profitof$1million

=($1.01-$1)million

=0.01million

=10000$ or1%oftheinitialamount(利潤率為1%）

Anexampleoftriangulararbitrage反之也成立。檢驗過程：根據(jù)匯率折算方式，有下式成立：（SRbl/$S$/￥S￥/Rbl）-1＝S$/RblS￥/$SRbl/￥

由于S$/RblS￥/$SRbl/￥＝0.2×100×0.04950＝0.99<1Currenciesinthedenominators(分母)aretoolowrelativetothenumerators（分子）,（出售分子貨幣以購買分母貨幣）：仍以$1million出發(fā)

selldollarsandbuyrubles：1million/0.2=5million

rubles sellrublesandbuyyen:5million/0.0495=101million

yen sellyenandbuydollars:101million/100=1.01million

dollars

Profitof$1million

=($1.01-$1)million

=0.01million

or1%oftheinitialamount(利潤率為1%）Anexampleoftriangulararbitragewhatcangowrong？如果將方向反了，就會帶來虧損。例如，當(dāng)SRbl/$S$/￥S￥/Rbl

=(Rbl5/$)($.01/￥)(￥20.20/Rbl)=1.01>1卻從買進分母貨幣入手，這樣的套利結(jié)果是：仍以100萬美元出發(fā)，就是賣出美元買進日元、然后賣出日元買進盧布，最后賣出盧布買進美元，則有：$100萬×1/0.01×1/20.20×1/5=99.01虧損：99.01－100＝0.99萬美元。PPP的圖示:Whichwaydoyougo?InflationRateDifferential(%)homeinflationrate–foreigninflationrate%

Dintheforeigncurrency’sspotrate-

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3PPPline外國商品的購買力上升外國商品的購買力下降CDPPP的圖示:Whichwaydoyougo?例如,D點,表示國內(nèi)通貨膨脹比國外低3%,但是,外幣只貶值了2%,因此,出現(xiàn)了購買力差別,外國商品的購買力低于本國商品的購買力.PPP理論表明在這個例子中外幣應(yīng)該貶值3%,以便完全抵銷3%的通貨膨脹差額.由于外幣沒有疲軟到這種程度,本國消費者不再繼續(xù)購買外國的商品,外幣需求下降,使外幣疲軟到PPP理論所預(yù)計的水平,因此,D點應(yīng)移向PPP線PPP線右邊或下面的所有點表示對本國商品的購買力大于對外國商品的購買力PPP的圖示：Whichwaydoyougo?例如,C點,表示國內(nèi)通貨膨脹比國外高4%,但是,外幣只升值了1%,因此,出現(xiàn)了購買力差別,外國商品的購買力高于本國商品的購買力.PPP理論表明在這個例子中外幣應(yīng)該升值4%,以便完全抵銷4%的通貨膨脹差額.由于外幣沒有堅挺到這種程度,本國消費者不再繼續(xù)購買本國的商品,而是轉(zhuǎn)而購買外國商品,外幣需求上升,使外幣堅挺到PPP理論所預(yù)計的水平,因此,C點應(yīng)移向PPP線PPP線左邊或上面的所有點表示對外國商品的購買力大于對本國商品的購買力.四、InterestRateParity,orIRPCoveredInterestArbitrage

UnconeredInterestArbitrageFtd/f/S0d/f=[(1+id)/(1+if)]t=E[Std/f]/S0d/f

=[(1+pd)/(1+pf)]twhere S0d/f=today’sspotexchangerate E[Std/f]=expectedfuturespotrate Ftd/f=forwardratefortimetexchange i=acountry’snominalinterestrate p=acountry’sinflationrateForwardpremiumsanddiscountsareentirelydeterminedbyinterestratedifferentials.(遠期升貼水幾乎完全由利率差異所決定)Interestrateparity:

Whichwaydoyougo?

Whichcurrencydoweborrowandwhichcurrencydowelendinordertotakeadvantageofamarketdisequilibrium?

IfFtd/f/S0d/f>[(1+id)/(1+if)]t

then so...Ftd/fmustfall SellfatFtd/fS0d/fmustrise BuyfatS0d/fidmustrise Borrowatid

ifmustfall LendatifIfFtd/f/S0d/f<[(1+id)/(1+if)]t then so...Ftd/fmustrise BuyfatFtd/fS0d/fmustfall SellfatS0d/fidmustfall Lendatidifmustrise BorrowatifInterestrateparity:

Whichwaydoyougo?Interestrateparityisenforcedthrough“coveredinterestarbitrage”AnExample:Given: i$=7% S0$/￡=$1.20/￡ i￡=3% F1$/￡=$1.25/￡ F1$/￡/S0$/￡

>(1+i$)/(1+i￡) 1.041667

>1.038835ThefxandEurocurrencymarketsarenotinequilibrium.Coveredinterestarbitrage1. Borrow$1,000,000

ati$=7%2. Convert$sto￡s

atS0$/￡=$1.20/￡ 3. Invest￡s

ati￡=3% 4. Convert￡sto$s

atF1$/￡=$1.25/￡ 5. Takeyourprofit:

T$1,072,920-$1,070,000=$2,920+$1,000,000+￡833,333-$1,000,000-￡833,333-$1,070,000+￡858,333+$1,072,920-￡858,333RulesIfIfFtd/f/S0d/f>[(1+id)/(1+if)]t,thenborrowatid,buyS0d/f,lendatid,andsellFd/fIfIfFtd/f/S0d/f<[(1+id)/(1+if)]t,thenborrowatif,sellSd/f,lendatid,andbuyF0d/f.ForwardratesaspredictorsoffuturespotratesFtd/f=E[Std/f]thatis:Forwardratesareunbiasedestimatesoffuturespotrates.Ftd/f/S0d/f=E[Std/f]/S0d/fthatis:forwardpremiumsreflecttheexpectedchangeinthespotexchangerate.Forwardratesarenotgoodpredictorsoffuturespotratesovershortforecastinghorizons.Attheveryleast,thelongtimeholds.ExchangerateTimet2t3t4t1S1S2S3S4F1F2F3ErrorErrorErrort2t3t4t1

Theforwardrateavailabletoday(Ft,t+1),timet,fordeliveryatfuturetimet+1,isusedasa“predictor”ofthespotratethatwillexistatthatdayinthefuture.Therefore,theforecastspotratefortimeSt2isF1;theactualspotrateturnsouttobeS2.Theverticaldistancebetweenthepredictionandtheactualspotrateistheforecasterror.Whentheforwardrateistermedan“unbiasedpredictorofthefuturespotrate,”itmeansthattheforwardrateoverorunderestimatesthefuturespotratewithrelativelyequalfrequencyandamount.Ittherefore“missesthemark”inaregularandorderlymanner.Thesumoftheerrorsequalszero.ForwardRateasanUnbiasedPredictorforFutureSpotRateIRP的圖示：Whichwaydoyougo?InterestRateDifferential(%)homeinterestrate–foreigninterestrateForwardPremium(%)ForwardDiscount(%)-

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3IRPlineABXY4ZWiH-iF=2%P=4%本國投資者到外國投資有利iH-iF=-3%P=-1%本國投資者到外國投資有利iH-iF=3%P=-2%外國投資者到本國投資有利iH-iF=-1%P=-3%外國投資者到本國投資有利ManagingforValue:HowIRPAffectsIBM'sHedgeIBMhassomeforeignsubsidiariesbasedinBrazil.IBMconsidershedginganyfundsthatitsBraziliansubsidiariesplantoremittotheparent.ForwardcontractsconbeusedtohedgethefuturetransactionsinwhichtheBrazilianrealwillbeconvertedintodollars.DuetoIRP,however,theforwardrateoftheBrazilianrealisunfavorablerelativetoitsspotrate.SincetheBrazilianinterestrateishigherthantheU.S.interestrate,IRPforcestheforwardrateofBrazilianrealtoexhibitadiscount.Thisexchangeratemaynotbeasfavorableastheprevailingspotrateatthatfuturetime,eveniftoday'sspotratedeclinesovertime.InternationalFisherrelation

(FisherOpenhypothesis)RecalltheFisherrelation:(1+i)=(1+

)(1+p)Ifrealratesofinterestareequalacrosscurrencies,fromtheIRP,then[(1+id)/(1+if)]t =[(1+

d)(1+pd)]t/[(1+

f)(1+pf)]t

=[(1+pd)/(1+pf)]tThisrelationiscalledtheinternationalFisherrelation.InternationalFisherrelation

(FisherOpenhypothesis)[(1+id)/(1+if)]t=[(1+pd)/(1+pf)]t

SpeculatorswillforcethisrelationtoholdonaverageIfrealratesofinterestareequalacrosscountries(

d=

f),theninterestratedifferentialsmerelyreflectinflationdifferentialsThisrelationisunlikelytoholdatanypointintime,butshouldholdinthelongrunIFE的圖示：Whichwaydoyougo?InterestRateDifferential(%)homeinterestrate–foreigninterestrate-

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3IFEline%

Dintheforeigncurrency’sspotrateBA投資外國取得高的回報率投資外國取得較低的回報率亞洲金融危機期間IFE的運用根據(jù)IFE,在亞洲危機前夕,高利率將不會吸引外國投資,因為高利率意味著匯率的下降.但是,由于一些國家中央銀行實行的是固定匯率度,仍然吸引了大量的外國投資.不幸的是,中央銀行的這種努力被市場力量所淹沒了.

結(jié)果,東南亞國家貶值

徹底消滅了高利率的收益.

Summary:Int’lparityconditionsInterestrates[(1+id)/(1+if)]tInflationrates[(1+pd)/(1+pf)]tE[Std/f]/S0d/fExpectedchangeinthespotrateFtd/f/S0d/fForward-spotdifferentialInterestrateparityRelativePPPInternationalFisherrelationForwardratesaspredictorsoffuturespotratesExchangeRateForecastingNumerousforeignexchangeforecastingservicesexist,manyofwhichareprovidedbybanksandindependentconsultants.Somemultinationalfirmshavetheirownin-houseforecastingcapabilities.Predictionscanbebasedonelaborateeconometricmodels,technicalanalysisofchartsandtrends,intuition,andacertainmeasureofgall.ExchangeRateForecastingA.Market-BasedForecastingExchangerateforecastsareprovidebyseveraloftheinternationalparityconditions.E[Std/f]=Ftd/f

forwardparityE[Std/f]=S0d/f[(1+id)/(1+if)]t

acombinationofforwardandinterestrateparityE[Std/f]=S0d/f[(1+pd)/(1+pf)]trelativePPPMarket-BasedForecastingThebeautyofmarket-basedforecastsisthatanyonewithaccesstoafinancialnewspapercanmakethem.基于市場的預(yù)測法看起來很美！Unfortunately,一方面，它在短期預(yù)測上效果差。

theseforecastsdonotworkwellintheshortterm.Theinternationalparityconditionsprovideasignalastowhichdirectionacurrencyshouldchangeinequilibrium.相對于每天匯率的波動而言，thissignalisweak。因此，它可用于一年以上的匯率預(yù)測。Market-BasedForecasting另一方面，國際平價條件對于長期名義匯率的預(yù)測也許有是用的，但對于實際匯率的預(yù)測卻是少有幫助的。Althoughtheinternationalparityconditionsareusefulforforecastinglong-termtrendsinnominalexchangerate,theyarelesshelpfulinforecastingrealexchangeratesbecauserealexchangeratesa