第一章汇率的决定与国际平价条件S培训教材

第一章

汇率决定与国际平价条件

基本内容有关外汇与汇率的基本知识（referencetochapterfour)汇率变化幅度的测定汇率变化的影响因素购买力平价利率平价国际费雪效应汇率预测Foreignexchange(fx)marketsAnexchangeratemeasuresthevalueofonecurrencyinunitsofanothercurrency.MarketsSpotmarketTradeincashwithdeliveryintwobusinessdaysForwardmarketTradeatapre-specifiedpriceandonapre-specifiedfuturedateVolume$1.2trillionaveragedailyvolumeduring200175%oftradeisintheinterbankmarket（75%的交易是银行之间的外汇交易，其日均交易额达1.2trillion美元）ParticipantsinthefxmarketWholesalemarketDealers(ormarketmakers) BuyandsellatquotedbidandofferpricesBrokers Serveasmatchmakers,withoutputtingtheirownmoneyatriskRetailmarketGovernmentsCorporationsSmallerfinancialinstitutionsIndividualsTworulesformultinationalfinanceRule#1

Keeptrackofyourunits

（注意货币单位）Rule#2

Alwaysbuyorsellthecurrencyinthedenominatorofaforeignexchangequote（买卖的货币是指外汇标价中处于分母的货币）Rule#1

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

Û 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/€

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

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

Thinkofbuyingorselling

theassetinthedenominator先从商品买卖说起，Buyingandsellingabottleofwine Buyabottleat€40/btlandsellat€50/btl

Þ€10/btlprofit。在这里买卖的对象是分母中的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$sat€1.00/$

Þ$0.20/€profit Þ€0.25/$profitAnexampleofwhatcangowrong如果买卖价格弄错了，即如果Buy$sat$0.80/€andsell$sat$1.00/€，结果会如何呢？ Buy$sat$0.80/€

º Sell€sat€1.25/$

Sell$sat$1.00/€

º

Buy€sat€1.00/$

Þ$0.20/€

loss

Þ€0.25/$

loss So,Alwaysthinkofbuyingorselling thecurrencyinthedenominator!FXquotationconventions

(汇率报价惯例）European/Americanquotesforthe$EuropeanquotesareconvenientforaEuropeanbecausetheyplacetheforeigncurrency(the$)inthedenominator（银行间报价多为欧式报价，即单位美元的外国货币汇率，因为美元是最经常交易的货币。）欧式标价法对当地人很方便。 e.g.€1.25/$AmericanquotesareconvenientforanAmericanbecausetheyplacetheforeigncurrency(the€)inthedenominator美式标价法对美国人很方便。 e.g.$0.80/€FXquotationconventions(汇率报价惯例）Direct/indirectquotesforforeigncurrencyfDirectquotesareconvenientforadomesticresidentbecausetheyplacetheforeigncurrencyinthedenominator(d/f); e.g.¥110.95/€foraresidentofJapanIndirectquotesareinconvenientforadomesticresidentbecausetheyplacetheforeigncurrencyinthenumerator(f/d); e.g.¥110.95/€foraresidentofEurope

汇率变动幅度的测定Whenacurrencydeclinesinvalue,itissaidtodepreciate.Whenitincreasesinvalue,itissaidtoappreciate.外国货币相对于本国货币的变动百分比Thepercentagechange(%D)inthevalueofaforeigncurrencyiscomputedas:Apositive%Drepresentsappreciationoftheforeigncurrency,whileanegative%Drepresentsdepreciation.本国货币相对于外国货币汇率的变动百分比人民币兑美元汇率变动例如：人民币兑美元汇率:2005年7月21日:$1=8.1100RMB2010年3月4日:$1=6.8265RMB请计算美元相对于人民币的变化率和人民币相对于美元的变化率？美元相对于人民币的汇率变动率=（6.8265-8.1100）/8.1100=-15.8%人民币相对于美元的汇率变动率=（8.1100-6.8265)/6.8265=18.8%人民币兑欧元汇率变动例如：人民币兑欧元汇率:2005年7月21日:€

1=10.0641RMB2010年3月4日:€1=9.3482RMB欧元相对于人民币的汇率变动率=（9.3482-10.0641）/10.0641=-7.1%人民币相对于欧元的汇率变动率=（10.0641-9.3482)/9.3482=7.7%RMB/$Quantityof$S0D0r0

RMB.inflation

中国对美国商品的需求增加,因而外汇需求也增加美国对中国商品的需求减少,因而美元外汇供应减少D1r1S1影响汇率变化的因素1.RelativeInflationRatesRMB/$Quantityof$r0S0D0S1D1r1

RMB.interestrates

人民币对美元存款的需求减少,因而外汇需求下降美元对人民币存款的需求增加,因而外汇供给增加影响汇率变化的因素2.RelativeInterestRatesRMB/$Quantityof$S0D0r0

RMB.incomelevel

人民币对美国商品需求增加,因而外汇需求上升对外汇供给的影响不无法预测D1r1影响汇率变化的因素3.RelativeIncomeLevels,S14.GovernmentControlsimposingforeignexchangebarriers（设置外汇交易障碍）,imposingforeigntradebarriers（设置贸易障碍）,interveningintheforeignexchangemarket（干预外汇市场）,affectingmacrovariablessuchasinflation,interestrates,andincomelevels.（影响宏观变量）影响汇率变化的因素5.ExpectationsForeignexchangemarketsreacttoanynewsthatmayhaveafutureeffect.当市场预计某种货币趋跌时，交易者会大量抛售该货币，造成该货币汇率下浮的事实；反之，当人们预计某种货币趋于坚挺时，又会大量买进该种货币，使其汇率上扬。由于公众预期具有投机性和分散性的特点，加剧了汇率短期波动的振荡。

影响汇率变化的因素ExpectationsFedchairmansuggestsFedis StrengthenedunlikelytocutU.S.interestratesApossibledeclineinGerman StrengthenedinterestratesCentralbanksexpectedto Weakenedintervenetoboosttheeuro

Signal Impacton$PoorU.S.economicindicators Weakened影响汇率变化的因素6.Speculating自1973年实行浮动汇率制以来，外汇市场的投机活动越演越烈，投机者往往拥有雄厚的实力，可以在外汇市场上推波助澜，使汇率的变动远远偏离其均衡水平。投机的关键内容是低价买入、高价卖出，或者是高价卖出、低价买入。PurchasingPowerParity,

orPPP1.绝对购买力平价的基本内容TheabsoluteformofPPP,orthe“lawofoneprice”（Equivalentassetssellforthesameprice.）suggeststhatsimilarproductsindifferentcountriesshouldbeequallypricedwhenmeasuredinthesamecurrency.这就是绝对购买力的基本公式即，汇率取决于以不同货币衡量的可贸易商品的价格水平之比，也就是不同货币对可贸易商品的购买力之比。TheLawofOnePriceEquivalentassetssellforthesameprice(alsocalledpurchasingpowerparity,orPPP)SeldomholdsfornontradedassetsCan’tcompareassetsthatvaryinqualityMaynotholdpreciselywhentherearemarketfrictionsAnexample:TheworldpriceofgoldSuppose P£=£250/ozinLondon P€=€400/ozinBerlinThelawofonepricerequires:

Pt£

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

or1/(£0.6250/€)=€1.6000/£PurchasingPowerParity,

orPPP2.相对购买力平价的基本内容TherelativeformofPPP

认为，即期汇率应根据两国预期的通货膨胀率进行调整。即E[Std/f]=S0d/f[(1+E[pd]/(1+E(pf)]t即RPPP将汇率的涨落归因于物价或货币购买力的变动。RPPPstatesthattheexpectedappreciationordepreciationofthespotrateisdeterminedbytheexpectedinflationdifferential.Ifinflationisaknownconstantineachcurrency,thenRPPPcanbestatedasE[Std/f]=S0d/f[(1+pd/(1+pf]tArbitrageIfPPPdoesnothold,thenthereisanopportunitytolockinarisklessarbitrageprofit.有些书上将arbitrage指为speculativepositions，但是，arbitrageismorestrictlydefinedasaprofitablepositionobtainedwith:Nonetinvestmentand

Norisk因此，套利利润是指无净投资和无风险情况下的利润。考虑交易成本，在不存在市场摩擦的情况下，如果一价定律不成立，则存在无风险套利机会。Eg,X银行：Bid

A$0.5838/€;OfferA$0.5841/€Y银行：Bid

A$0.5842/€;OfferA$0.5845/€套利者可以从X银行买进欧元，与此同时，再卖给Y银行，即可赚取无风险利润。因为汇率比为：(Y银行)0.5842/(X银行)0.5841=1.0001712>1，套利收益率为0.01712%TheNo-ArbitrageConditionPPP意味着：即期汇率由本国货币资产价格与相同资产的外国货币价格之比决定。如果PPP不成立，则价格差异会使套利有利可图。Pd/Pf=Sd/fPd=Pf×Sd/fTheNo-ArbitrageCondition非套利条件，即PPP成立。双边套汇的汇率均衡条件SXd/f/SYd/f=1即SXd/f=SYd/f交叉三角套汇情况下的均衡汇率：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（说明分母货币相对于分子货币价格较低，有上升的可能）Þ Foreachspotrate,buythecurrencyinthedenominator（分母）

withthecurrencyinthenumerator（即出售分子货币，购买分母货币）

IfSd/eSe/fSf/d>1,theneither

Sd/e,Se/forSf/dmustfall（说明分母货币相对于分子货币价格较高，有下降的可能）Foreachspotrate,sellthecurrencyinthedenominator（分母）forthecurrencyinthenumerator：即出售分母货币，购买分子货币CrossexchangeratesandtriangulararbitrageSupposeSRbl/$ = Rbl5.000/$ Û S$/Rbl=$0.2000/RblS$/¥ = $0.01000/¥ Û S¥/$=¥100.0/$S¥/Rbl = ¥20.20/Rbl Û 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）,（出售分母货币以购买分子货币）：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(利润率为1%）

Anexampleoftriangulararbitrage反之也成立。检验过程：根据汇率折算方式，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）,（出售分子货币以购买分母货币）：仍以$1million出发

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(利润率为1%）Anexampleoftriangulararbitragewhatcangowrong？如果将方向反了，就会带来亏损。例如，当SRbl/$S$/¥S¥/Rbl

=(Rbl5/$)($.01/¥)(¥20.20/Rbl)=1.01>1却从买进分母货币入手，这样的套利结果是：仍以100万美元出发，就是卖出美元买进日元、然后卖出日元买进卢布，最后卖出卢布买进美元，则有：$100万×1/0.01×1/20.20×1/5=99.01亏损：99.01－100＝0.99万美元。PPP的图示:Whichwaydoyougo?InflationRateDifferential(%)homeinflationrate–foreigninflationrate%

Dintheforeigncurrency’sspotrate-

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3PPPline外国商品的购买力上升外国商品的购买力下降CDPPP的图示:Whichwaydoyougo?例如,D点,表示国内通货膨胀比国外低3%,但是,外币只贬值了2%,因此,出现了购买力差别,外国商品的购买力低于本国商品的购买力.PPP理论表明在这个例子中外币应该贬值3%,以便完全抵销3%的通货膨胀差额.由于外币没有疲软到这种程度,本国消费者不再继续购买外国的商品,外币需求下降,使外币疲软到PPP理论所预计的水平,因此,D点应移向PPP线PPP线右边或下面的所有点表示对本国商品的购买力大于对外国商品的购买力PPP的图示：Whichwaydoyougo?例如,C点,表示国内通货膨胀比国外高4%,但是,外币只升值了1%,因此,出现了购买力差别,外国商品的购买力高于本国商品的购买力.PPP理论表明在这个例子中外币应该升值4%,以便完全抵销4%的通货膨胀差额.由于外币没有坚挺到这种程度,本国消费者不再继续购买本国的商品,而是转而购买外国商品,外币需求上升,使外币坚挺到PPP理论所预计的水平,因此,C点应移向PPP线PPP线左边或上面的所有点表示对外国商品的购买力大于对本国商品的购买力.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.(远期升贴水几乎完全由利率差异所决定)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:

Þ$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的图示：Whichwaydoyougo?InterestRateDifferential(%)homeinterestrate–foreigninterestrateForwardPremium(%)ForwardDiscount(%)-

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3IRPlineABXY4ZWiH-iF=2%P=4%本国投资者到外国投资有利iH-iF=-3%P=-1%本国投资者到外国投资有利iH-iF=3%P=-2%外国投资者到本国投资有利iH-iF=-1%P=-3%外国投资者到本国投资有利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的图示：Whichwaydoyougo?InterestRateDifferential(%)homeinterestrate–foreigninterestrate-

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3IFEline%

Dintheforeigncurrency’sspotrateBA投资外国取得高的回报率投资外国取得较低的回报率亚洲金融危机期间IFE的运用根据IFE,在亚洲危机前夕,高利率将不会吸引外国投资,因为高利率意味着汇率的下降.但是,由于一些国家中央银行实行的是固定汇率度,仍然吸引了大量的外国投资.不幸的是,中央银行的这种努力被市场力量所淹没了.

结果,东南亚国家贬值

彻底消灭了高利率的收益.

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.基于市场的预测法看起来很美！Unfortunately,一方面，它在短期预测上效果差。

theseforecastsdonotworkwellintheshortterm.Theinternationalparityconditionsprovideasignalastowhichdirectionacurrencyshouldchangeinequilibrium.相对于每天汇率的波动而言，thissignalisweak。因此，它可用于一年以上的汇率预测。Market-BasedForecasting另一方面，国际平价条件对于长期名义汇率的预测也许有是用的，但对于实际汇率的预测却是少有帮助的。Althoughtheinternationalparityconditionsareusefulforforecastinglong-termtrendsinnominalexchangerate,theyarelesshelpfulinforecastingrealexchangeratesbecauserealexchangeratesa