CFA二级基础班-衍生-标准版

CFA二级培训项目

讲师：TOM

m鱼艺栉MM6aPr中血吗

TopicWeightingsinCFALevelII

SessionNO.ContentWeightings

StudySession1Ethical&ProfessionalStandards10-15

StudySession2-3QuantitativeMethods5-10

StudySession4Economics5-10

StudySession5-6FinancialReportingandAnalysis10-15

StudySession7-8CorporateFinance5-10

StudySession9-11Equity10-15

StudySession12-13FixedIncome10-15

StudySession14Derivatives5-10

StudySession15AlternativeInvestments5-10

StudySession16-17PortfolioManagement10-15

行业•创新•憎值

(S)FrameworkSS14Derivatives

•R37PricingandValuationof

ForwardCommitments

Derivatives•R38ValuationofContingent

Claims

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PricingandValuationofForwardCommitments

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1.Forward

■PrincipleofArbitrage-freePricing

Framework■EquityForwardandFuturesContracts

■InterestRateForwardandFutures

Contracts(FRA)

■Fixed-IncomeForwardandFuturesContracts

■CurrencyForwardContracts

2.T-bondFutures

3.Swap

■InterestRateSwapContracts

■CurrencySwapContracts

■EquitySw叩Contracts

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♦ForwardContracts

“Aforwardcontractisanagreementbetweentwopartiesinwhichone

party,thebuyer,agreestobuyfromtheotherparty,theseller;anunderlying

assetorotherderivative,atafuturedateatapriceestablishedatthestartof

thecontract.最新资料领取微信xiiebajun888s

“Longposition:apositioninanassetorcontractinwhichoneownstheasset

orhasanexercisablerightunderthecontract.

jShortposition:apositioninanassetorcontractinwhichonehassoldan

assetordoesnotown,orinwhicharightunderacontractcanbeexercised

againstoneself.

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PriceandValue

Thepriceisthepredeterminedpriceinthecontractthatthelongshould

paytotheshorttobuytheunderlyingassetatthesettlementdate.

Thecontractvalueiszerotobothpartiesatinitiation.

Theno-arbitrageprinciple:tradablesecuritieswithidenticalcashflow

paymentsmusthavethesameprice.Otherwise,traderswouldbeableto

generaterisk-freearbitrageprofits.

•Twoassetsorportfolioswithidenticalfuturecashflows,regardlessof

futureevents,shouldhavesameprice;

•Theportfolioshouldyieldtherisk-freerateofreturn,ifitgenerates

certainpayoffs.

T

•Generalformula:FP=S0X(l+Rf)

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♦ForwardsArbitrage

>Cash・and・CarryArbitragewithforwardcontractmarketpriceto。high

relativetocarryarbitragemodel.

•IfFP>S0X(1+Rff

AtinitiationAtsettlementdate

•Shortaforwardcontract•Delivertheunderlyingtothelong

•BorrowSoattherisk-free•GetFPfromthelong

rate•Repaytheloanamountof

•UsethemoneytobuytheSoX(l+Rf)T

underlyingbond

Profit=FP-S0X(l+Rf)T

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♦ForwardsArbitrage

>ReverseCasivsnd-CarryArbitragewithforwardcontractmarketpriceto。

lowrelativetocarryarbitragemodel.

•IfFP<S0X(l+Rff

AtinitiationAtsettlementdate

•Longaforwardcontract•PaytheshortFPtogetthe

underlyingbond

•Shortselltheunderlying

•Closeouttheshortpositionby

bondtogetSodeliveringthebond

•InvestSoattherisk-freerate•Receiveinvestmentproceeds

S0X(URf)T

Profit=S°X(l+Rf)「FP

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专业•创新•憎值

♦GenericPricing:No-ArbitragePrinciple

>Pricingaforwardcontractistheprocessofdeterminingtheno-arbitrage

pricethatwillmakethevalueofthecontractbezerotobothsidesatthe

initiationofthecontract.

•Forwardprice=pricethatwouldnotpermitprofitablerisklessarbitrage

infrictionlessmarkets

・)

FP=Sox(l+rfT+CarryingCosts-CarryingBenefits

>Va山ationofaforwardcontractmeansdeterminingthevalueofthe

contracttothelong(ortheshort)atsometimeduringthelifeofthe

contract.

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行业•创新•憎值

Forwardcontractvalue

T-bill(zero-couponbond)forwards

•buyaT-billtodayatthespotprice(So)andshortaT-monthT-bill

forwardcontractattheforwardprice(FP);

-x(l趣.

理)------

•Forwardvalueoflongpositionatinitiation(t=0)zduringthecontract

life(t=t)zandatexpiration(t=T).

TimeForwardContractValuation

Zero,becausethecontractispricedtoprevent

t=0arbitrage

t=t

芟（1+

B、理一浅

或

t=T明

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专业•创新•憎值

♦EquityForwardContracts

>Forwardcontractsonadividend-payingstock

•Price:理瑕=6母一瑞fl演）x（争羊

百）./

•Value:品在斫冕-啜真＞（1+7—

袋■粮更）.桂

「到/圜钊、函慧型一。卷）

图=伙,M哦矍一0可）用吟¥1、一一技

=+晋q

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♦Example

圜>Assumingaforwardcontractwith100daysuntilmaturityonastock,

thestockpriceis$45andexpectedtopaydividendof$0.3in20days,

and$0.5in75days.Theriskfreerateis4%.Calculatetheno-arbitrage

forwardprice.

>CorrectAnswer:

So=$45

Di=$0.3D2=$0.5FP=?

I▲IAk

02075100days

$0.3,$0.5

10420/365+10475/365$0.795343

旬果=($45-$0,795343)x1.O4100/365=$44,68

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♦Example

圜>After40days,thestockpricechangedto$48.Calculatethevaluationof

theforwardcontract.

>CorrectAnswer:

•There'sonlyonedividendremaining(in35days)beforethe

contractmatures(in60days)asshownbelow；so:

So=$45Di=$0,3S40二$48D=$0.5FP=$44.68

I2

2040y75100days

35daysJ

x，_60days

—o

$0.5

]0435/365=$0.498123

契40$44.68

田。（碧衽哥强吾衽茎=($48—]0460/365=$3,11

$0.498123）-

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行业•创新•憎值

♦Example

>Onemonthago,Todpurchasedaforwardcontractwiththreemonths

toexpirationataquotedpriceof100.20(quotedasaper100par

Bvalue).Thecontractnotionalamountis¥100,000,000.Thecurrent

forwardpriceis100.05.Theriskfreerateis0.3%.Thevalueofthe

positionisclosestto:

A.-¥149,925.

B.-¥150,000.

C.-¥150,075.

“CorrectAnswer:A.最新资料领取微信xuebajun888s

•ThevalueofTod'sforwardpositioniscalculatedas

馥翌=母葭到名(一)]

咫碧

黑(里专100.05-100^0(/1+产12=-0.149925(吾强芸100年利表

0.0030普器理法很)

•Therefore,thevalueoftheTod'sforwardpositionis

r「0.149925

留《毛—(¥100,000,000)=-¥149,925

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专业•创新•憎值

♦EquityIndexForwardContracts

>Forwardcontractsonanequityindex

c-In1+Kf

•Continuouslycompoundedrisk-freerate:Rf^^

•Continuouslycompoundeddividendyield:6C

•Price:即装=图0避

•Value：誓铲(jpM)一(点心)

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♦Example

圜>AssumingaforwardcontractontheDowJonesIndexwith100days.

Currently,thevalueofDowJonesIndexis21,000andthecontinuous

dividendyieldis2%.Thecontinuouslycompoundedriskfreerateis

3.2%.Calculatetheno-arbitragepriceoftheforwardcontract.

)

FP=21,000X^(0.032-0.02)x(100/365=21069.1547

>After75days,thevalueofDowJonesIndexis20,050.Keeptherisk

freerateanddividendyieldsameasbefore.Calculatethevaluationof

theforwardcontract.

20,05021,069.1547

Vr(longposition)=------强»亡-一~强c=-1,000.481

7畜0.02x(25/365)<10.032x(25/365)

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♦ForwardContractsonCouponBonds

>Couponbonds

•Similartodividend-payingstocks,butthecashflowsarecoupons

•Price:利果=金一福留裸）x@吗

+®)

•Value:矗衽铲（春演一7TTT--------

艰氯等】鞅技）一%决）蛋.我

用段胤豆干敢割罡嚏）汜Z田

留的理］

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♦Example

圜>Assumingaforwardcontractwith150daysonaUStreasurybill.The

UStreasurybillhasa5%couponrate,thepriceis$1,100andwillmake

couponpaymentin90days.Theriskfreerateis4%.Calculatethe

forwardprice.

>CorrectAnswer:

”$1000x0.05

段=-----z--------=$25

—】$25.00

营利段01.049。/365=$2生7594

•Theforwardpriceofthecontractistherefore:

旬累(onaincuniesecurity)=($1,100—S24.7594)x

1.04150/365=1,092.7122.

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♦CurrencyForwardContracts

Price:coveredInterestRateParity(IRP)

一］(1+雪奥)

理歆=若。(1+-2沼

x

FPandSoarequotedincurrencyDperunitofcurrencyF(i.e.fD/F)

Value:

斗.

己1-

（1+整金尸-丁一^:

用决）-一

Ifyouaregiventhecontinuousinterestrates

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♦Example

圜>Considerthefollowing:TheU.S.risk-freerateis6percent,theSwiss

risk-freerateis4percent,andthespotexchangeratebetweenthe

UnitedStatesandSwitzerlandis$0.6667.

•CalculatethecontinuouslycompoundedU.S.andSwissrisk-free

rates;

•Calculatethepriceatwhichyoucouldenterintoaforwardcontract

thatexpiresin90days;

•Calculatethevalueoftheforwardposition25daysintothe

contract.Assumethatthespotrateis$0.65.

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♦CurrencyForwardContracts

>CorrectAnswer:

1.rCHF=ln(1.04)=0.0392;r$=ln(1.06)=0.0583

2

.阅珏g.666腔各9爆晒392("U/36b))⑶o.o583(W/36b))=

$0.6698

3.St=$0.65;T=90/365;t=25/365;T-t=65/365

Thevalueofthecontractis-$0.0174perSwissfranc

第t(0,T)=($0.65x毁一。。392(65/365))_($06698x

程-0.0583(6勺/365))

=-$0.0174

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行业•创新•憎值

♦ForwardRateAgreements(FRAs)

>AForwardRateAgreement(FRA)isaforwardcontractonaninterest

rate(LIBOR).

■Thelongpositioncanbeviewedastherightandtheobligationto

borrowattheforwardrateiathefuture;

•Theshortpositioncanbeviewedastherightandtheobligationtolend

attheforwardrateinthefuture;

•Noloanisactuallymade,andFRAsarealwayssettledincashatcontract

expiration.

>Let'stakea1X4FRAforexample.A1X4FRAis

•aforwardcontractexpiresin1month,

•andtheunderlyingloanissettledin4months,

•witha3-monthnotionalloanperiod.

•Theunderlyinginterestrateis90-dayLIBORin30daysfromnow.

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行业•创新•憎值

♦ForwardRateAgreements(FRAs)

>LIBOR(LondonInterbankOfferedRate):Collectivenameformultiple

ratesatwhichaselectsetofbanksbelievetheycouldborrowunsecured

fundsfromotherbneksintheLondoninterbankmarketfordifferent

currenciesanddifferentborrowingperiodsrangingfromovernighttoone

year.

•anannualizedratebasedona360-dayyear

•anadd-onrate

•thereferencerateformanyfloating-ratebonds

•USDinterestrate

•publisheddailybytheBritishBanker'sAssociation

>Euribor(EuropeInterbankOfferedRate):establishedinFrankfurt,and

publishedbyEuropeanCentralBank.

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行业•创新•憎值

♦ForwardPricingandValuation-FRA

>LIBOR,Euribor,andFRAs(Con't)

Settlement:settleincash,butnoactualloanismadeatthesettlementdate.

•Payoffqualitativeanalysis:

/Ifthereferencerateattheexpirationdateisabovethespecified

contractrate,thelongwillreceivecashpaymentfromtheshort;

/Ifthereferencerateattheexpirationdateisbelowthecontractrate,

theshortwillreceivecashpaymentfromthelong.

•Payoffquantitativeanalysis

days

(Floatingrateatsettlement-forwardrate)

(Notionalprincipal)

1+Floatingrateatsettlement

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行业•创新•憎值

♦Example

圜>In30days,aUKcompanyexpectstomakeabankdepositof

£10,000,000foraperiodof90daysat90-dayLiborset30daysfrom

today.Thecompanyisconcernedaboutapossibledecreaseininterest

rates.Thecompanyentersintoa£10,000,000notionalamount1X4

receive-fixedFRA.TheappropriatediscountrrtcfortheFRAsettlement

cashflowsis0.40%.After30days,90-dayLiborinBritishpoundsis

0.55%.最新资料领取微信xuebajun888s

IftheFRAwasinitiallypricedat0.60%,thepaymentreceivedtosettleit

willbeclosestto:

A.-£2,448.75.

B.£1,248.75.

C.£1,250.00.

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行业•创新•憎值

♦Example

昌j>CorrectAnswer:B.

•Thesettlementamountofthe1X4FRAathforreceive-fixedis

•NA{[FRA(0hm)-Lh(m)]tm}/[1+Dh(m)tm]

二[10,000,000(0.0060-0.0055)(0.25)]/[l+0.0040(0.25)]

=£1,248.75.

•BecausetheFRAinvolvespayingfloating,itsvaluebenefitedfroma

declineinrates.

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♦FRAPricing

>TheforwardpriceinanFRAistheno-arbitrageforwardrate(FR)

•Ifspotratesareknown,TheFRisjusttheunbiasedestimateofthe

forwardinterestrate:

-------►L(m)/m-------1-------►FR/n------

--------------►L(m+n)/m+n◄----------------

(1+堂理x鎏/360)(1+理mx噂/360)=(1+琛加嗯x(翌+

善)/360)

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行业•创新•憎值

♦Example

>Calculatethepriceofa1X4FRA.Thecurrent30-dayLIBORis3%and

120-dayLIBORis3.9%.

>CorrectAnswer:

(1+3%x30/360)[1+FRAox(120-30)/360]=(1+3.9%x120/360)

•TheannualizedforwardrateisFRAo=4.2%.

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行业•创新•憎值

♦Example

圜>Supposeweenteredareceive-floating6X9FRAatarateof0.86%,

withnotionalamountofC$10,000,000atTime0.Thesix-monthspot

Canadiandollar(C$)Liborwas0.628%,andthenine-monthC$Libor

was0.712%.After90dayshavepassed,thethree-monthC$Liboris

1.25%andthesix-monthC$Liboris1.35%.

AssumingtheappropriatediscountrateisC$Libor,thevalueofthe

originalreceive-floating6X9FRAwillbeclosestto:

A,C$14,125.

B.C$14,350.

C.C$14,651.

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行业•创新•憎值

♦Example

>CorrectAnswer:C.

•First,calculatethequotedFRAatt=90

(1+1.25%x90/360)[1+FRA90x(180-90)/3601(1+1.35%x180/360)

/TheannualizedforwardrateisFRA90=1.4455%.

•Second,calculatethevalueofFRAatt=90

ViOng=10z000z000[(0.014455-0.0086)(90/360)]/[l+0.0135(180/360)]

=14,539.35

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行业•创新•憎值

1.Forward

■PrincipleofArbitrage-freePricing

Framework■EquityForwardandFuturesContracts

■InterestRateForwardandFutures

Contracts(FRA)

■Fixed-IncomeForwardandFuturesContracts

■CurrencyForwardContracts

2.T-bondFutures

3.Swap

■InterestRateSwapContracts

■CurrencySwapContracts

■EquitySw叩Contracts

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专业•创新•憎值

FuturesContractValue

Thevalueofafuturescontractiszeroatcontractinception.

Futurescontractsaremarkedtomarketdaily,thevaluejustaftermarking

tomarketisresettozero.

Betweenthetimesatwhichthecontractismarkedtomarket,thevaluecan

becHfferentfromzero.

•V(long)=currentfuturesprice-futurespriceatthelastmark-to-

markettime.

Anotherviewoffutures:settlepreviousfutures,andthenopenanother

newfutureswithsamedateofmaturity.

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行业•创新•憎值

T-bondFuturesContracts

Underlying:Hypothetical30yeartreasurybondwith6%couponrate.

Bondcanbedeliverable:$100,000parvalueT-bondswithanycouponbut

withamaturityofatleast15years.

Thequotesareinpointsand32nds:Apricequoteof95-18isequalto

95.5625andadollarquoteof$95,562.50.

Theshorthasadeliveryoptiontochoosewhichbondtodeliver.Eachbond

isgivenaconversionfactor(CF),whichmeansaspecificbondis

equivalenttoCFstandardbondunderlyinginfuturescontract.

•ForaspecificBondA:

现毁标准=即数咽£—

X歆噌

Theshortdesignateswhichbondhewilldriver(cheapest-to-deliverbond).

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行业•创新•憎值

♦ArbitragefromT-Bondfutures

>TherearemethodstobuytheunderlyingbondA

•BuybondAthroughT-bondfutures

/Theadjustedpriceofthefuturescontractisequaltotheconversion

factormultipliedbythequotedfuturesprice:

理零理=即歌根sx•现

/AddingtheaccruedinterestofAhatexpiration,theadjustedprice

ofthefuturescontractgivesatotalpriceof:

第1=现嗷标准x型现理+

制理理

•Buybondthroughholdingthebondatthebeginningoftheperiod

/theno-arbitragefuturespriceatexpirationisequaltothefollowing:

组-$京22档）“（1也建）—

>Theavailablearbitrage而扁1is补金presentvalueofthisdifference

噌装型i技装/勇哥旁晴笠迎i卷|

=致留型2—留

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行业•创新•憎值

♦Example-Arbitrage

>Troubadouridentifiesanarbitrageopportunityrelatingtoafixed-

圜incomefuturescontractanditsunderlyingbond.Currentdataonthe

futurescontractandunderlyingbondarepresentedinExhibit.The

currentannualcompoundedrisk-freerateis0.30%.

Exhibit1CurrentDataforFuturesandUnderlyingBond

FuturesContractUnderlyingBond

Quotedfuturesprice125.00Quotedbondprice112.00

Conversionfactor0.90Accruedinterestsincelastcoupon0.08

payment

TimeremainingtocontractexpirationThreeAccruedinterestatfuturescontract0.20

monthsexpiration

Accruedinterestoverlifeoffutures0.00

contract

BasedonExhibitandassumingannualcompounding,thearbitrage

profitonthebondfuturescontractisclosestto:

A.0.4158.

B.0.5356.

C.0.6195.

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行业•创新•憎值

♦Example

圜>CorrectAnswer:B.

Therearemethodstobuytheunderlyingbond:

•BuybondthroughT-bondfutures

/Theadjustedpriceofthefuturescontractisequaltothe

conversionfactormultipliedbythequotedfuturesprice:

F0(T)=CF(T)QF0(T)=(0.90)(125)=112.50

/Addingtheaccruedinterestof0.20atexpiration,theadjusted

priceofthefuturescontractgivesatotalpriceof112.70.

•Buybondthroughholdingthebondatthebeginningoftheperiod

/theno-arbitragefuturespriceatexpirationisequaltothe

following:用(矍=他制)］聿明+■虱目

=(1(112.00+0.08-0)=112.1640

•Theavailablearbitrageprofitisthepresentvalueofthis

difference:(112.70-112.1640)/(1.003)0.25=0.5356.

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♦Quotedfuturespriceandforwardprice

>Thequotedfuturespriceisadjustedwithconversionfactor

现利果招歆=（=+嘲^x（i^）—理者-］。

学朝母祖思黑刑者救X之

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♦Example

圜>Euro-bondfutureshaveacontractvalueof€100,000,andthe

underlyingconsistsoflong-termGermandebtinstrumentswith8.5to

10.5yearstomaturity.TheyaretradedontheEurex.Supposethe

underlying2%Germanbondisquotedat€108andhasaccrued

interestof€0.083(one-halfofamonthsincelastcouponwhichpays

annually).Theeuro-bondfuturescontractmaturesinonemonth.At

contractexpiration,theunderlyingbondwillhaveaccruedinterestof

€0.25,therearenocouponpaymentsdueuntilafterthefutures

contractexpires,andthecurrentone-monthrisk-freerateis0.1%,The

conversionfactoris0.729535.Theequilibriumeuro-bondfuturesprice

basedonthecarryarbitragemodelwillbeclosestto:

A.€147.57.

B.€147.82.

C.€148.15.

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♦Example

>CorrectAnswer:B.

Inthiscase,wehaveT=1/12,CF(T)=0.729535,B0(T+Y)=108z

FVCI0J=0,AI0=0.5(2/12)=€0.083,AIT=1.5(2/12)=0.25,r=0.1%.

QF0(T)=[1/CF(T)]{FVOJ[BO(T+Y