FRM一级强化段金融市场（打印版）

Financial

Marketsand

Products

FRMа㓗ษ䇝䇢ѹ-ᕪॆ⨝

TopicWeightingsinFRMPartĉ

SessionNO.

Content

Weightings

StudySession1FoundationsofRiskManagement

StudySession2QuantitativeAnalysis

20

20

30

30

StudySession3FinancialMarketsandProducts

StudySession4ValuationandRiskModels

2-123

Framework

¾BondMarket

•

•

•

InterestRates

TreasuryMarket

CorporateBond

¾

DerivativesMarket

•

•

•

•

IntroductionofDerivativesMarket

ForwardandFutures

Swaps

OptionsMarkets

¾

¾

MBS

FinancialInstitutions

Banks

•

•

•

InsuranceCompanies

FundManagement

3-123

BondMarket

Topic1:InterestRates

1

2

3

.MarketRate

.Compounding

.SpotRateandForwardRate

4-123

MarketRate

¾

CommonMarketRate

zTreasuryRates

9

9

TheratesaninvestorearnsonTreasurybillsandTreasurybonds.

Treasuryratesarerisk-freeratesinthesensethatitisconsideredhighly

unlikelythatthegovernmentofadevelopedcountrywilldefaultondebt

issuedinitsowncurrency.

9

•

TheTreasuryrateisusuallynotadoptedasrisk-freerate,becauseitis

usuallyartificiallylow,mainlyduetothefollowingtworeasons:

RegulationgenerallydoesnotrequireBankstoretaincapitalfortheir

Treasurypositions.

•

Insomecountries(suchastheUnitedStates),Treasuryyieldsget

preferentialtaxtreatment.

5-123

MarketRate

¾

CommonMarketRate

z

9

LIBOR

LIBORarecompiledfromtheestimatedunsecuredborrowingcostsof18

highlyratedglobalbanks.

z

9

RepoRates

Inarepurchaseagreement,thedifferencebetweensellingprice(today)and

therepurchasedprice(tomorroworlater)iscalledthereporate.

SOFR

z

9

ThereareplanstobeginphasingoutLiborandreplaceitwitharatebased

onactualtransactionsDŽU.S.hasproposedtheuseoftherepo-based

SecuredOvernightFinancingRate(SOFR)

¾

Risk-FreeRate

z

Therisk-freerateatwhichderivativesarepricedisdeterminedfrom

overnightinterbankratesusingovernightindexedswaps.

6-123

Compounding

¾

CompoundingFrequencies

zSupposewehaveanaccountwherethesimpleinterestisaddedineach

yearandthenthatmoneyalsoearnsinterest.

zAssuming持续更新通知微信

：xuebajun888s

Rେistherateofinterestwithcontinuouscompounding.

R୫istherateofinterestwithdiscretecompounding(mperannum)

Tisthenumberofyears.

୫୘

R୫

m

FV=PV1+

FV=PVeୖి୘

୫భ୘

୫మ୘

୫୘

ୖభ

୫భ

ୖమ

୫మ

ୖౣ

୫

PV1+

=PV1+

PV1+

=PVeୖి୘

7-123

SpotRateandForwardRate

¾

SpotRate

zAt-periodspotrate,orzerorate,istheinterestrateearnedwhencash

isreceivedatjustonefuturetime.

zForwardrates

Interestratescorrespondingtoafutureperiodimpliedbythespotcurve.

9

1

+Rଵ୘భ1+F(୘మି୘భ)=1+Rଶ୘మ

RTെRT

ଶ

ଶ

ଵ

ଵ

eୖభ୘భ×e୊୘మି୘భ=eୖమ୘మ՜F=

TଶെT

ଵ

8-123

BondMarket

Topic2:TreasuryMarket

1

.TreasuryInstruments

9-123

TreasuryInstruments

¾

¾

TreasuryBills

zAshort-termdebtobligationwithamaturityofoneyearorless.

zInterestrateisexpressedonadiscountbasis.

TreasuryNotesandTreasuryBonds

zBondwithamaturityofmorethanoneyear.Bondswhichtypicallyhave

maturitiesbetweenonetotenyearsarecalledTreasuryNotes.Butto

keeptheterminologysimple,wewillrefertoallcoupon-bearingTreasury

instrumentsasTreasuryBonds.

zBothmakeinterestpaymentssemi-annually.

zQuotedPrice˖

9

Dollarsandthirty-secondsofadollarwithfacevalueof$100

¾

TreasurySTRIPS

zC-StripsandP-Strips

10-123

TreasuryInstruments

¾

¾

CleanPrice

zThepriceofacouponbondnotincludinganyaccruedinterest.

Immediatelyfollowingeachcouponpayment,thecleanpricewillequal

thedirtyprice.

DirtyPrice

zAbondpricingquotereferringtothepriceofacouponbondthat

includesthepresentvalueofallfuturecashflows,includinginterest

accruingonthenextcouponpayment.

dirtyprice=cleanprice+accruedinterest

¾

AccruedInterestandDayCountConventions

zTreasurybonds:actual/actual

zCorporateandmunicipalbonds:30/360

zMoneymarketinstruments(Treasurybills):actual/360

11-123

TreasuryInstruments

¾

Example

Supposea1000parvalueUScorporatebondpaysasemi-annual10

percentcoupononJanuary1andJuly1.AssumethatitisnowApril1,2005,

andthebondmaturesonJuly1,2015.Computetheinvoice(full)priceof

thisbondiftherequiredannualyieldis8percent.Computetheflat(clean)

priceoftheabovebond.

Time

Mar1stApr1stMay1stJune1stJuly1st

dirtyprice1155.301162.871170.501178.181185.90

cleanprice1138.631137.871137.171136.511135.90

12-123

BondMarket

Topic3:CorporateBond

1.BondIndentures

2.ClassificationofBonds

3.BondRisk

13-123

BondIndentures

¾

¾

BondIndenture

zContractcontainscorporatebondissuerpromisesandinvestors’rights.

zMadeouttocorporatetrustee,whorepresentsbondholders’interests.

CorporateTrustee

zAfinancialinstitutionthatlooksaftertheinterestsofthebondholders

andensuresthattheissuercomplieswiththeindentures.

zItsdutiesarespecifiedintheindenturesandthetrusteeisunderno

obligationtoexceedthoseduties.

zForexample,sometimestheindenturespecifiedthattrusteecanrelyon

theissuerforinformation,sothat,itisnotrequiredtoconductitsown

investigations.

14-123

ClassificationofBonds

¾

¾

InterestRate

zFixed-RateBonds

zFloating-RateBonds

zZero-CouponBonds

Collateral

zMortgageBonds

zCollateralTrustBonds

zEquipmentTrustCertificates

zDebentureBonds(includingSubordinatedDebentures)

zGuaranteedBonds

¾

High-YieldBond

15-123

BondRisk

¾

¾

EventRisk

zTherearemanyeventsinthemarketthatcanadverselyaffectbonds,

suchasnaturaldisasters.Thistypeofriskiscalledeventrisk.One

importanttypeofeventriskistheriskofalargeincreaseinleverage.

CreditRisk

zCreditDefaultRisk:Riskthatabondissuerwillbeunabletomeetits

financialobligations.

zCreditSpreadRisk:Riskoffinanciallossresultingfromchangesinthe

levelofcreditspreads.

16-123

Exercise1

¾

Eachofthefollowingistrueaboutthecorporatetrusteeinacorporate

bondissuanceexcept:

A.Thetrusteeispaidbybondholders.

B.Thetrusteeactsinafiduciarycapacityforinvestorswhoownthebond

issue.

C.Thetrusteemust,atthetimeofissue,authenticatethebondsissued

(i.e.,keeptrackofallthebondssole)andmakesurethattheydonot

exceedtheprincipalamountauthorizedbytheindenture.

D.Ifacorporateissuerfailstopayinterestorprincipal,thetrusteemay

declareadefaultandtakesuchactionasmaybenecessarytoprotect

therightsofbondholders.

¾

Answer:A

17-123

Derivatives

Market

Topic1:IntroductionofDerivativesMarket

1.IntroductionofDerivatives

2.OTCandExchangeMarket

3.CentralCounterparty

18-123

IntroductionofDerivatives

¾

¾

Derivatives

zAninstrumentwhosevaluedependsonthevaluesofothermorebasic

underlyingassets.

BasicTypesofDerivatives

zForwardandFutures

9

9

9

Agreementtobuy/sellassetatfuturetimeforcertainprice.

Forward:tradedintheover-the-counter(OTC)market.

Futures:Standardizedandtradesonanexchange.

zSwap

9

9

Aseriesofforwardcontracts.

Exchangecashflowsonperiodsettlementdates.

zOption

Givesholdertheright(butnotobligation)tobuy/sellatacertainprice.

9

19-123

IntroductionofDerivatives

¾

LinearandNon-LinearDerivatives

zDerivativescanbedividedintolinearandnonlinearcategories.

zThepayoffoflinearderivativesislinearlyrelatedtothevalueofthe

underlyingassets.Forexample,forwardcontractsarelinearderivatives.

zOptions,ontheotherhand,arenonlinearderivatives,thatis,thereisa

non-linearrelationshipbetweenthepayoffoftheoptionandthevalueof

theunderlyingasset.

20-123

OTCandExchangeMarket

¾

Over-the-CounterandExchangeTraded

Over-the-Counter

Exchange-Traded

Customized

Standardized

Tradewithcounterparty(DefaultRisk)Backedbyaclearinghouse

Nottradeinacentrallocation

Unregulated

Tradeinaphysicalexchange

Regulated

Tradingvolume:large

Tradingvolume:small

21-123

OTCandExchangeMarket

¾

¾

¾

ExchangeMarket

zAnexchangemarketisamarketwhereinvestorstradestandardized

contractsmadebyexchanges.

zToday,exchangesclearalltradesbetweenmembersthroughso-called

centralcounterparties(CCPs).

9

9

Exchanges(throughtheirCCPS)actascounterpartiestoallmembers.

AnotheradvantageofusingaCCPisthatitiseasierforexchange

memberstocloseoutpositions.

zAnothermeasuretoprotectmembersfromlossesisnetnetting.Netting

isanoperationinwhichshortandlongpositionsinaparticularcontract

canoffseteachother.持续更新通知微信

：xuebajun888s

2

2-123

OTCandExchangeMarket

ExchangeMarket

zTheexchangerequiresmemberstoprotectthemselvesbyproviding

margin.Marginreferstothecashorassetstransferredfromonetrader

toanotherforprotectionagainstcounterpartydefault.

9

9

VariationMargin

InitialMargin

zInaddition,membersarerequiredtosubmitadefaultfundasaloss

protection.持续更新通知微信：xuebajun888s

9

Iftheinitialmarginisnotsufficienttocoveramember'slossesduringa

default,themember'sdefaultfundcontributionswillbeusedtocover

thedifference.Ifthesefundsremaininsufficient,theyarereplenishedby

thedefaultfundsofothermembers.

23-123

OTCandExchangeMarket

ExchangeMarket

zMaintenanceMargin

9

9

Sofar,we'vebeentalkingaboutmarginaccountsbetweenCCPsand

theirmembers.However,ifaretailtradercontactsabrokertotrade,that

traderwillberequiredtoprovidemargintothebroker.

Marginaccountsbetweenretailtradersandbrokersdifferfromthose

betweenCCPsandtheirmembers.Itgenerallycontainsprovisionsfor

maintenancemargin.Inaccordancewiththegeneralrulesof

maintenancemargin,ifthebalanceofthemarginaccountfallsbelowthe

maintenancemarginlevel,thetradermustprovideadditionalmarginto

restoretheaccounttotheinitialmarginlevel.Ifthetraderdoesnot

provideadditionalmargin,thebrokerentersareversetradeonbehalfof

thetradertocloseouttheposition.

24-123

CentralCounterparty

¾

OperationofCCPs

zVariablemarginpaymentsaremadedailytoreflectchangesinthevalue

ofeachmember'sportfolio.

zWhenamemberdefaults,theexchangeusuallyholdsanauction,inviting

othermemberstobidforthetransaction.

zCCPsmaychoosetotearupdeals.Thisinvolvestheimmediatecloseout

oftransactionsbetweenamemberandthedefaultingpartyataprice

thatcausessomelosstothenon-defaultingparty.

zTheinitialmargintobepaidbyeachmemberiscalculatedusing

historicaldata.However,ifthedefaultmember'sinitialmarginis

insufficienttocovertheloss,thedefaultfundofthedefaultmember

needstobeusedtoreplenish.Ifthatisnotenough,thecontributions

fromothermembersareused.

25-123

CentralCounterparty

¾

AdvantagesandDisadvantagesofCCPs

zAdvantagesofOTCCentralClearing

9

9

9

Easyexit

Lossmutualization

Standardlossmanagementmechanism(margin,netting,default

resolution)

9

9

Increasedliquidity

FormulationofstandarddocumentsforOTCderivativestransactions.

zDisadvantagesofOTCCentralClearing

9

9

9

9

Moralhazard

Adverseselection

Procyclicality

Creditriskfacedbymembersbasedondefaultfundscontribution

26-123

Derivatives

Market

Topic2:ForwardandFutures

1.

2.

3.

4.

5.

6.

ForwardRateAgreement

FuturesMarket

ForwardandFuturesPrices

InterestRateFutures

HedgingStrategiesusingFutures

ForeignExchangeMarkets

27-123

ForwardRateAgreement

¾

¾

¾

ForwardRateAgreement

zAforwardrateagreement(FRA)isanagreementthatacertainratewill

applytoacertainprincipalduringacertainfuturetimeperiod.

zThebuyerlocksinaborrowingrate,andthesellerlocksinalendingrate.

zSettlement:TheinterestpaymentofFRAisnormallypaidattheendof

theperiod.However,anFRAisusuallysettledatthebeginningofthe

periodcoveredbytheFRAbyconvention.Thepayoffforthepartywho

paysfixedandreceivesfloatingortheothersideofthetransactionis:

RെR୏ɒꢀ

+ꢁɒ

R୏െRɒꢀ

1+ꢁɒ

or

1

WhereRistherealizedfloatingrate,R୏isthefixedrate,Listhe

principalandɒisthelengthofthetimehorizon.

2

8-123

ForwardRateAgreement

Valuation

zThevaluationforthepartywhopaysfixedandreceivesfloatingorthe

othersideofthetransactionis:

R୊െR୏ɒꢀ

PV

PV

1

+R୊ɒ

Or

R୏െR୊ɒꢀ

+R୊ɒ

1

WhereR୊istheforwardrateandPVdenotesthepresentvaluefromthe

beginningoftheperiodtotoday.

2

9-123

FuturesMarket

OperationofExchanges

zThenumberofcontractsthatexistatanytimeiscalledopeninterest.

Thisisthenumberofnetlongcontractsheldbymembers,whichisequal

tothenumberofnetshortcontractsheldbymembers.

zThenumberofcontractstradedinadayiscalledtradingvolume.If

manytradersclosetheirpositions,thevolumeofthedaymaybegreater

thantheopeninterest.Itcanalsohappenifthereisalargeamountof

intradaytrading.

30-123

FuturesMarket

¾

ConvergenceofFuturesandSpotPrices

zAsthedeliveryperiodapproaches,thefuturespriceconvergestothe

spotprice.Ifthefuturespriceishigherthanthespotpriceduringthe

deliveryperiod,thetraderhasanobviousarbitrageopportunity,which

canberealizedby:

9

9

9

Shortingfutures,

Buyingtheasset,and

Makingthedelivery.

zSucharbitrageopportunitiesdonotlastlongbecausetraderstake

advantageofthem.Inaddition,ifthefuturespriceislowerthanthespot

priceduringdelivery,thosewhowantaccesstotheunderlyingassetswill

finditprofitabletotakelongfuturespositionsandwaitfordelivery.

Whentheydoso,futurespriceswillrisetowardspotprices.

31-123

FuturesMarket

¾

NormalandInvertedFuturesMarket

FuturesPrice

SpotPrice

SpotPrice

Time

FuturesPrice

Time

zIfthefuturespriceincreasesastimetomaturityincreases,thefutures

curveissaidtobenormal,orinContango.

zIfthefuturepricedeclinesasmaturityincreases,thefuturescurveissaid

tobeinverted,orinBackwardation.

zSomeassetshavepatternsthatarepartlynormalandpartlyinverted.

32-123

FuturesMarket

¾

TradingOrderTypes

zMarketOrder

9

Arequestthatatradebecarriedoutimmediatelyatthebestprice

availableinthemarket.

zLimitOrder

9

Thisorderspecifiesaparticularprice,theordercanbeexecutedonlyat

thispriceoratonemorefavorabletotheinvestor.

zStopOrder/Stop-LossOrder

9

Alsospecifiesaparticularprice.Theorderisexecutedatthebest

availablepriceonceabidorofferismadeatthatparticularpriceora

less-favorableprice.

33-123

FuturesMarket

¾

TradingOrderTypes

zStop-LimitOrder

9

Combinationofstop&limitorder.Orderbecomeslimitorderassoonas

abid/offerismadeatapriceequalto/lessfavorablethanthestopprice.

zMarket-if-TouchOrder/BoardOrder

9

Executedatthebestavailablepriceafteratradeoccursataspecified

price/atapricemorefavorablethanthespecifiedprice.Itisdesignedto

ensureprofitsaretakenifsufficientlyfavorablepricemovementsoccur.

zDiscretionaryOrder/Market-not-HeldOrder

9

Istradedasamarketorderexceptthatexecutionmaybedelayedatthe

broker’sdiscretioninanattempttogetabetterprice.

zFill-or-KillOrder

Mustbeexecutedimmediatelyonreceiptornotatall.

9

34-123

FuturesMarket

¾

Futuresvs.Forward

Forward

Futures

Tradeover-the-counter(OTC)

Notstandardized

Tradeonanexchange

Standardizedcontracts

Rangeofdeliverydates

Settleddaily

Onespecifieddeliverydate

Settledatcontract’send

Deliveryorfinalcashsettlement

usuallyoccurs

Contractusuallyclosedoutpriorto

maturity

Reducesbasisriskduetotailored

specificationsbutlessliquid

Highliquidityduetostandardized

specificationsbutmorebasisrisk

Defaultriskispresent

Guaranteedbyclearinghouse

Marginrequiredandadjusted

Nomargindepositrequired

35-123

ForwardandFuturesPrices

F=S1+R୘

¾

AssumptionsofPricing:NoArbitragePrinciple

F>S1+R୘

F<S1+R୘

Now:

Now:

BorrowStobuyaunitofasset,enterintoShortsaleSandinvestinabank,enter

aforwardcontracttoshorttheassetforFintoaforwardcontracttobuytheasset

intimeT;

forFintimeT;

Tlater:

Tlater:

„

SellassetatFandrepaytheloanfor

S1+R୘

„

GetS1+R୘fromthebankandbuy

theassetatFtocloseshortposition.

„

Gainaprofitof

„

Gainaprofitof

FെS1+R୘

S1+R୘െF

336-01-2832

ForwardandFuturesPrices

¾

ForwardPriceforaFinancialAssetthatProvidesnoIncome

F=S1+R୘

zExample:Consideraforwardcontracttosellanon-dividend-paying

stockin3months.Thecurrentstockpriceis$40andthe3-monthrisk-

freerate(annuallycompounded)is2.5%peryear.Theforwardprice:

F=401+0.025଴.ଶହ=40.25

¾

ForwardPriceforaFinancialAssetthatPayingaKnownCashIncome

F=SെI1+R୘

zExample:Considera10-monthforwardcontractonabondpayinga

USD2couponin3monthsandin9months.Assumether୤forall

maturitiesis6%peryearandthecashpriceofthebondisUSD107.

2

2

ଵ଴

+

=3.8856

F=107െ3.8856×1.06ଵଶ=108.2450

1

.06଴.ଶହ1.06଴.଻ହ

37-123

ForwardandFuturesPrices

¾

ForwardPriceforaFinancialAssetthatProvidesaKnownYield

୘

1

1

+R

+Q

F=S

zExample:Consideranassetexpectedtoprovidea2.5%yieldperyear

overthenextthreeyears.Therisk-freerateis3%peryearandthe

currentspotpriceoftheassetisUSD30.Theforwardprice(USD)is

ଷ

1

+3%

F=30

=30.44

1

+2.5%

¾

ForwardPriceforStockIndex

zExample:Consideranindexof2,000,ther୤is4%peryearandthe

dividendyieldis2%peryear.Thefuturespricewithamaturityofsix

monthsis

଴

.ହ

1

1

.04

.02

F=2,000×

=2019.5127

38-123

ForwardandFuturesPrices

¾

ForeignExchangeForward/Futures

zInterestRateParity

୘

1

1

+R୅

+R୆

F=S

WhereB/ArepresentstheexchangerateasthenumberofAperB.

0

ᰦ࡫

tᰦ࡫

ᆈޕᵜഭ䬦㹼ˈR୅

1

অսᵜᐱ

1+R୅

অսᵜᐱ

୘

ށᦒˈᒦ䘋ޕаԭআ

ࠪཆᐱⲴ䘌ᵏਸ㓖

ᢗ㹼䘌ᵏਸ㓖

ᆈޕཆഭ䬦㹼ˈR୆

1

+R୆୘/S

অսཆᐱ

F1+R୆୘/S

অսᵜᐱ

1/Sঅսཆᐱ

39-123

ForwardandFuturesPrices

¾

ForwardPriceforaCommodityAssetwithaLeaseRate

୘

1

1

+R

+l

F=S

zExample:Assumethatthespotpriceofgoldis$1,250,theleaserateis

.5%,andthe6-monthrisk-freerateis4%(withannualcompounding).

The6-monthfuturespriceisgivenby:

2

଴

.ହ

1

.04

1

,250×

=1,259.1131

1

.025

¾

ForwardPriceforaCommoditywithStorageCost&ConvenienceYield

୘

1

1

+R

+Y

F=S+U

40-123

ForwardandFuturesPrices

¾

ForwardPriceforaCommoditywithStorageCost&ConvenienceYield

zExample:ThespotpriceofoilisUSD65perbarrel,andtheconvenience

yieldis15%.ThestoragecostforsixmonthshasapresentvalueofUSD

3

perbarrel,andtherisk-freerateis2%peryear.the6-monthfutures

pricesatisfies

଴

.ହ

1

1

.02

.15

65+3×

=64.0413

41-123

ForwardandFuturesPrices

¾

ForwardPricevs.ValueofaForwardContract

zThevalueofaforwardcontractisquitedifferentfromtheforwardprice.

Whenforwardcontractsforfinancialassetsarefirstentered,thevalueof

theforwardcontractsthemselvesiszero.Overtime,however,asset

priceschangeandthevalueofforwardcontractscanbecomepositiveor

negative.

zWhilethevalueofthecontractchanges,thepriceatwhichtheassetwill

eventuallybeboughtorsoldremainsthesameastheoriginalforward

price.

FെK

Valueofꢀ‘‰Forwardꢂ‘–”ƒꢃ–=

1

+R୘

42-123

InterestRateFutures

¾

¾

¾

T-BondFutures

zTheTreasurybondfuturescontractallowsthepartywiththeshort

positiontochoosewhichparticularbondwithamaturitymorethan15

yearsonthefirstdayofthedeliverymonthandisnotcallablewithin15

yearsfromthatdaytodeliver.

zWhenaparticularbondisdelivered,aparameterknownasconversion

factordefinesthepricereceivedforthebondbythepartywiththeshort

position.

zSpecially,thecashreceivedbytheshortpositionis:

Cashreceived=(QFP×CF)+AI

zCheapest-to-DeliverBond

Cost=quotedbondprice–(QFPhCF)

43-123

InterestRateFutures

T-BondFutures

zExample:Assumeaninvestorwithashortpositionisabouttodelivera

bondandhasfourbondstochoosefromwhicharelistedinthe

followingtable.Thelastsettlementpriceis$95.75(thisisthequoted

futuresprice).Determinewhichbondisthecheapest-to-deliver.

BondQuotedBondPriceConversionFactorCost

1

2

3

4

99

1.01

1.24

1.06

1.14

2.29

6.27

1.51

5.85

125

103

115

44-123

InterestRateFutures

EurodollarFutures

zOneofthemostpopularinterestratefuturesintheUnitedStatesisthe

three-monthEurodollarfuturescontracttradedbytheCMEGroup.

zAthree-monthEurodollarfuturescontractisafuturescontractonthe

interestthatwillbepaid(bysomeonewhoborrowsattheEurodollar

interestrate)on$1millionforafuturethree-monthperiod.

zAfinalsettlementpriceisusedtodeterminefinaltransfersbetween

thosewithlongandshortpositions.ItisUSD100-R,whereRisthe

Liborfixingfor90-dayUSDborrowings.Forexample,iftheUSD90-day

Liborfixingis2.5%,thefinalsettlementpriceofthecorresponding

EurodollarfuturescontractwouldbeUSD97.50(=100-2.5).

z1basispointmoveinthefuturesquotecorrespondstoagain/lossof

$25percontract.

45-123

InterestRateFutures

¾

¾

¾

EurodollarFutures

zEurodollarFuturesvs.FRA

9

Withthesameunderlyingandthesamematurity,Theyshouldbethe

sameifinterestratesareperfectlypredictable.

9

9

ǐꢀ6ꢁr)<0,Futurespriceislowerthanforwardprice.

Forshortmaturities,thedifferencesaresmallenoughtobeignored.

zConvexityAdjustment

1

2

Forwardꢁƒ–‡=ꢄ—–—”‡•”ƒ–‡െɐଶT(T+0.25)

9

IJisthestandarddeviationofthechangeintheshort-terminterestrate

inoneyear.

9

9

Tistimetomaturityoffuturescontract.

T+0.25istimetomaturityoftherateunderlyingthefuturescontract.

4

6-123

HedgingStrategiesusingFutures

BasisRisk

zThebasisisthedifferencebetweenthepriceofthefuturescontractand

thespotpriceoftheunderlyingasset.

Basis=spotprice–futuresprice

zLongthebasisreferstoasetofpositionsthatconsistsofashortfutures

positionandalongcashposition.Positionthatarelongthebasisbenefit

whenthebasisisstrengthening.

zShortthebasisreferstoasetofpositionsthatconsistsofalongfutures

positionandashortcashposition.Positionsthatareshortthebasis

benefitwhenthebasisisweakening.

47-123

HedgingStrategiesusingFutures

BasisRisk

zFuturescontractoftendoesnottrackexactlywiththeunderlying

commodity.Basisriskistherisk(tothehedger)createdbythe

uncertaintyinthebasis.

zThehedgingriskistheuncertainty

associatedwithb2:

Differentasset

S1

F1

Spotprice

S2

9

9

Differentmaturity

FuturespriceF2

t2

zCrosshedgingoccurswhenthe

assetsunderlyingthefuturescontract

andtheassetwhosepriceisbeing

hedgedaredifferent.

t1

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HedgingStrategiesusingFutures

¾

¾

¾

ShortHedgeandLongHedge

zAshorthedgeinvolvesashortpositioninfuturescontracts.Ashort

hedgeisappropriatewhenthehedgeralreadyownsanassetand

expectstosellitatsometimeinthefuture.

zAlonghedgeinvolvesalongpositioninafuturescontract.Along

hedgeisappropriatewhenacompanyknowsitwillhavetopurchasea

certainassetinthefutureandwantstolockinapricenow.

4

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HedgingStrategiesusingFutures

HedgingwithFuturesContract

zMinimumVarianceHedgeRatio

9

Theminimumvariancehedgeratiodependsontherelationshipbetween

changesinthespotpriceandchangesinthefuturesprice.Byusingit,

wecanformahedgedpositionwithminimumvariance.

ɐୗ

ɐ୊

hכ=ɏୗ,୊

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HedgingStrategiesusingFutures

HedgingwithFuturesContract

zOptimalNumberofFuturesContracts

hכQ୅

Q୊

Nכ=

9

9

9

Q୅:Sizeofpositionbeinghedged(units)

Q୊:Sizeofonefuturescontract(units)

Nכ:Optimalnumberoffuturescontractsforhedging

zTailingtheHedge

9

Whenfuturescontractsareusedforhedging,thereisdailysettlement

andseriesofone-dayhedges.Tailingthehedgecandealwiththiscase

whenmakinghedgingdecision.

ɏොɐෝୗSQ୅hכ×V୅

Nכ=

=

ɐෝ୊FQ୊

V୊

9

ɐෝ,ɐෝisthestandarddeviationoftheone-dayreturn,ɏොisthecorrelation

ୗ

୊

betweentheone-dayspotreturnandthefuturesreturn.

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HedgingStrategiesusingFutures

¾

¾

¾

HedgingwithFuturesContract

zExample:Anairlineexpectstopurchase2milliongallonsofjetfuelin1

monthanddecidestouseheatingoilfuturesforhedging.Eachheating

oilcontracttradedbytheCMEGroupison42,000gallonsofheatingoil.

©

F

©6

Std.0.0310.026

Correlation0.928

ɐୗ

ɐ

HR=ɏୗ,୊

୊

଴

.଴ଶ଺

=

0.928×

=0.778

=37.03

଴

.଴ଷଵ

ଶ଴଴଴଴଴଴

ସଶ଴଴଴

N=0.778×

5

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HedgingStrategiesusingFutures

HedgingwithFuturesContract

zHedgingwithStockIndexFutures

’

‘”–ˆ‘Ž‹‘value

valueofˆ—–—”‡•ꢃ‘–”ƒꢃ–



—„‡”ofꢃ‘–”ƒꢃ–•=Ⱦ୮୭୰୲୤୭୪୧୭

×

’

‘”–ˆ‘Ž‹‘value

=

Ⱦ୮୭୰୲୤୭୪୧୭

×

ˆ

—–—”‡•’”‹ꢃ‡×ꢃ‘–”ƒꢃ–—Ž–‹’Ž‹‡”

’‘”–ˆ‘Ž‹‘value



—„‡”ofꢃ‘–”ƒꢃ–•=(ȾכെȾ)×

valueofˆ—–—”‡•ꢃ‘–”ƒꢃ–

zHedgingwithInterestRateFutures

9

Thenumberofcontractsrequiredtohedgeagainstanuncertainchange

intheyieldgivenby଱\ꢁisgivenby:

PD୮DV01୔

FD୊DV01୊

Nכ=

=

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HedgingStrategiesusingFutures

HedgingwithFuturesContract

zExample1

9

Youareaportfoliomanagerwitha$20milliongrowthportfoliothathas

abetaof1.4,relativetotheS&P500.TheS&P500futuresaretradingat

1,150,andthemultiplieris250.Youwouldliketohedgeyourexposure

tomarketriskoverthenextfewmonths.Identifywhetheralongorshort

hedgeisappropriate,anddeterminethenumberofS&P500contracts

youneedtoimplementthehedge.

$

1

20,000,000

,150×250

ꢅŠ‘”–1.4×

ൎ97ꢃ‘–”ƒꢃ–•

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HedgingStrategiesusingFutures

¾

¾

¾

HedgingwithFuturesContract

zExample2

9

Supposewehaveawell-diversified$100millionequityportfolio.The

portfoliobetarelativetotheS&P500is1.2.Thecurrentvalueofthe3-

monthS&P500Indexis1,080.Theportfoliomanagerwantsto

completelyhedgethesystematicriskoftheportfoliooverthenextthree

monthsusingS&P500Indexfutures.Demonstratehowtoadjustthe

portfolio’sbeta:

1

1

00,000,000

,080×250



—„‡”ofꢃ‘–”ƒꢃ–•=0െ1.2×

=െ444.44

5

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HedgingStrategiesusingFutures

HedgingwithFuturesContract

zExample3

9

Thereisaportfolioof$100millionwitha6-monthhedginghorizon.And

the6-monthT-bondcontractisquotedat105-09,andthecontractsize

is$100,000.Thedurationoftheportfoliois15,andthedurationofthe

futurescontractis17.Outlinetheappropriatehedgeforsmallchanges

inyield.

P×D୔

F×D୊

100,000,000×15

105,281.25×17

N=െ