FRM一級(jí)強(qiáng)化段金融市場(chǎng)（打印版）

Financial

Marketsand

Products

FRMа?????-???

TopicWeightingsinFRMPart?

SessionNO.

Content

Weightings

StudySession1FoundationsofRiskManagement

StudySession2QuantitativeAnalysis

20

20

30

30

StudySession3FinancialMarketsandProducts

StudySession4ValuationandRiskModels

2-123

Framework

?BondMarket

?

?

?

InterestRates

TreasuryMarket

CorporateBond

?

DerivativesMarket

?

?

?

?

IntroductionofDerivativesMarket

ForwardandFutures

Swaps

OptionsMarkets

?

?

MBS

FinancialInstitutions

Banks

?

?

?

InsuranceCompanies

FundManagement

3-123

BondMarket

Topic1:InterestRates

1

2

3

.MarketRate

.Compounding

.SpotRateandForwardRate

4-123

MarketRate

?

CommonMarketRate

zTreasuryRates

9

9

TheratesaninvestorearnsonTreasurybillsandTreasurybonds.

Treasuryratesarerisk-freeratesinthesensethatitisconsideredhighly

unlikelythatthegovernmentofadevelopedcountrywilldefaultondebt

issuedinitsowncurrency.

9

?

TheTreasuryrateisusuallynotadoptedasrisk-freerate,becauseitis

usuallyartificiallylow,mainlyduetothefollowingtworeasons:

RegulationgenerallydoesnotrequireBankstoretaincapitalfortheir

Treasurypositions.

?

Insomecountries(suchastheUnitedStates),Treasuryyieldsget

preferentialtaxtreatment.

5-123

MarketRate

?

CommonMarketRate

z

9

LIBOR

LIBORarecompiledfromtheestimatedunsecuredborrowingcostsof18

highlyratedglobalbanks.

z

9

RepoRates

Inarepurchaseagreement,thedifferencebetweensellingprice(today)and

therepurchasedprice(tomorroworlater)iscalledthereporate.

SOFR

z

9

ThereareplanstobeginphasingoutLiborandreplaceitwitharatebased

onactualtransactions?U.S.hasproposedtheuseoftherepo-based

SecuredOvernightFinancingRate(SOFR)

?

Risk-FreeRate

z

Therisk-freerateatwhichderivativesarepricedisdeterminedfrom

overnightinterbankratesusingovernightindexedswaps.

6-123

Compounding

?

CompoundingFrequencies

zSupposewehaveanaccountwherethesimpleinterestisaddedineach

yearandthenthatmoneyalsoearnsinterest.

zAssuming持續(xù)更新通知微信

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R?istherateofinterestwithcontinuouscompounding.

R?istherateofinterestwithdiscretecompounding(mperannum)

Tisthenumberofyears.

??

R?

m

FV=PV1+

FV=PVe???

???

???

??

??

??

??

??

??

?

PV1+

=PV1+

PV1+

=PVe???

7-123

SpotRateandForwardRate

?

SpotRate

zAt-periodspotrate,orzerorate,istheinterestrateearnedwhencash

isreceivedatjustonefuturetime.

zForwardrates

Interestratescorrespondingtoafutureperiodimpliedbythespotcurve.

9

1

+R???1+F(?????)=1+R???

RT?RT

?

?

?

?

e????×e??????=e?????F=

T??T

?

8-123

BondMarket

Topic2:TreasuryMarket

1

.TreasuryInstruments

9-123

TreasuryInstruments

?

?

TreasuryBills

zAshort-termdebtobligationwithamaturityofoneyearorless.

zInterestrateisexpressedonadiscountbasis.

TreasuryNotesandTreasuryBonds

zBondwithamaturityofmorethanoneyear.Bondswhichtypicallyhave

maturitiesbetweenonetotenyearsarecalledTreasuryNotes.Butto

keeptheterminologysimple,wewillrefertoallcoupon-bearingTreasury

instrumentsasTreasuryBonds.

zBothmakeinterestpaymentssemi-annually.

zQuotedPrice?

9

Dollarsandthirty-secondsofadollarwithfacevalueof$100

?

TreasurySTRIPS

zC-StripsandP-Strips

10-123

TreasuryInstruments

?

?

CleanPrice

zThepriceofacouponbondnotincludinganyaccruedinterest.

Immediatelyfollowingeachcouponpayment,thecleanpricewillequal

thedirtyprice.

DirtyPrice

zAbondpricingquotereferringtothepriceofacouponbondthat

includesthepresentvalueofallfuturecashflows,includinginterest

accruingonthenextcouponpayment.

dirtyprice=cleanprice+accruedinterest

?

AccruedInterestandDayCountConventions

zTreasurybonds:actual/actual

zCorporateandmunicipalbonds:30/360

zMoneymarketinstruments(Treasurybills):actual/360

11-123

TreasuryInstruments

?

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

?

?

BondIndenture

zContractcontainscorporatebondissuerpromisesandinvestors’rights.

zMadeouttocorporatetrustee,whorepresentsbondholders’interests.

CorporateTrustee

zAfinancialinstitutionthatlooksaftertheinterestsofthebondholders

andensuresthattheissuercomplieswiththeindentures.

zItsdutiesarespecifiedintheindenturesandthetrusteeisunderno

obligationtoexceedthoseduties.

zForexample,sometimestheindenturespecifiedthattrusteecanrelyon

theissuerforinformation,sothat,itisnotrequiredtoconductitsown

investigations.

14-123

ClassificationofBonds

?

?

InterestRate

zFixed-RateBonds

zFloating-RateBonds

zZero-CouponBonds

Collateral

zMortgageBonds

zCollateralTrustBonds

zEquipmentTrustCertificates

zDebentureBonds(includingSubordinatedDebentures)

zGuaranteedBonds

?

High-YieldBond

15-123

BondRisk

?

?

EventRisk

zTherearemanyeventsinthemarketthatcanadverselyaffectbonds,

suchasnaturaldisasters.Thistypeofriskiscalledeventrisk.One

importanttypeofeventriskistheriskofalargeincreaseinleverage.

CreditRisk

zCreditDefaultRisk:Riskthatabondissuerwillbeunabletomeetits

financialobligations.

zCreditSpreadRisk:Riskoffinanciallossresultingfromchangesinthe

levelofcreditspreads.

16-123

Exercise1

?

Eachofthefollowingistrueaboutthecorporatetrusteeinacorporate

bondissuanceexcept:

A.Thetrusteeispaidbybondholders.

B.Thetrusteeactsinafiduciarycapacityforinvestorswhoownthebond

issue.

C.Thetrusteemust,atthetimeofissue,authenticatethebondsissued

(i.e.,keeptrackofallthebondssole)andmakesurethattheydonot

exceedtheprincipalamountauthorizedbytheindenture.

D.Ifacorporateissuerfailstopayinterestorprincipal,thetrusteemay

declareadefaultandtakesuchactionasmaybenecessarytoprotect

therightsofbondholders.

?

Answer:A

17-123

Derivatives

Market

Topic1:IntroductionofDerivativesMarket

1.IntroductionofDerivatives

2.OTCandExchangeMarket

3.CentralCounterparty

18-123

IntroductionofDerivatives

?

?

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

?

LinearandNon-LinearDerivatives

zDerivativescanbedividedintolinearandnonlinearcategories.

zThepayoffoflinearderivativesislinearlyrelatedtothevalueofthe

underlyingassets.Forexample,forwardcontractsarelinearderivatives.

zOptions,ontheotherhand,arenonlinearderivatives,thatis,thereisa

non-linearrelationshipbetweenthepayoffoftheoptionandthevalueof

theunderlyingasset.

20-123

OTCandExchangeMarket

?

Over-the-CounterandExchangeTraded

Over-the-Counter

Exchange-Traded

Customized

Standardized

Tradewithcounterparty(DefaultRisk)Backedbyaclearinghouse

Nottradeinacentrallocation

Unregulated

Tradeinaphysicalexchange

Regulated

Tradingvolume:large

Tradingvolume:small

21-123

OTCandExchangeMarket

?

?

?

ExchangeMarket

zAnexchangemarketisamarketwhereinvestorstradestandardized

contractsmadebyexchanges.

zToday,exchangesclearalltradesbetweenmembersthroughso-called

centralcounterparties(CCPs).

9

9

Exchanges(throughtheirCCPS)actascounterpartiestoallmembers.

AnotheradvantageofusingaCCPisthatitiseasierforexchange

memberstocloseoutpositions.

zAnothermeasuretoprotectmembersfromlossesisnetnetting.Netting

isanoperationinwhichshortandlongpositionsinaparticularcontract

canoffseteachother.持續(xù)更新通知微信

：xuebajun888s

2

2-123

OTCandExchangeMarket

ExchangeMarket

zTheexchangerequiresmemberstoprotectthemselvesbyproviding

margin.Marginreferstothecashorassetstransferredfromonetrader

toanotherforprotectionagainstcounterpartydefault.

9

9

VariationMargin

InitialMargin

zInaddition,membersarerequiredtosubmitadefaultfundasaloss

protection.持續(xù)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

?

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

?

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

?

?

?

ForwardRateAgreement

zAforwardrateagreement(FRA)isanagreementthatacertainratewill

applytoacertainprincipalduringacertainfuturetimeperiod.

zThebuyerlocksinaborrowingrate,andthesellerlocksinalendingrate.

zSettlement:TheinterestpaymentofFRAisnormallypaidattheendof

theperiod.However,anFRAisusuallysettledatthebeginningofthe

periodcoveredbytheFRAbyconvention.Thepayoffforthepartywho

paysfixedandreceivesfloatingortheothersideofthetransactionis:

R?R???

+??

R??R??

1+??

or

1

WhereRistherealizedfloatingrate,R?isthefixedrate,Listhe

principaland?isthelengthofthetimehorizon.

2

8-123

ForwardRateAgreement

Valuation

zThevaluationforthepartywhopaysfixedandreceivesfloatingorthe

othersideofthetransactionis:

R??R???

PV

PV

1

+R??

Or

R??R???

+R??

1

WhereR?istheforwardrateandPVdenotesthepresentvaluefromthe

beginningoftheperiodtotoday.

2

9-123

FuturesMarket

OperationofExchanges

zThenumberofcontractsthatexistatanytimeiscalledopeninterest.

Thisisthenumberofnetlongcontractsheldbymembers,whichisequal

tothenumberofnetshortcontractsheldbymembers.

zThenumberofcontractstradedinadayiscalledtradingvolume.If

manytradersclosetheirpositions,thevolumeofthedaymaybegreater

thantheopeninterest.Itcanalsohappenifthereisalargeamountof

intradaytrading.

30-123

FuturesMarket

?

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

?

NormalandInvertedFuturesMarket

FuturesPrice

SpotPrice

SpotPrice

Time

FuturesPrice

Time

zIfthefuturespriceincreasesastimetomaturityincreases,thefutures

curveissaidtobenormal,orinContango.

zIfthefuturepricedeclinesasmaturityincreases,thefuturescurveissaid

tobeinverted,orinBackwardation.

zSomeassetshavepatternsthatarepartlynormalandpartlyinverted.

32-123

FuturesMarket

?

TradingOrderTypes

zMarketOrder

9

Arequestthatatradebecarriedoutimmediatelyatthebestprice

availableinthemarket.

zLimitOrder

9

Thisorderspecifiesaparticularprice,theordercanbeexecutedonlyat

thispriceoratonemorefavorabletotheinvestor.

zStopOrder/Stop-LossOrder

9

Alsospecifiesaparticularprice.Theorderisexecutedatthebest

availablepriceonceabidorofferismadeatthatparticularpriceora

less-favorableprice.

33-123

FuturesMarket

?

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

?

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?

?

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

F?S1+R?

S1+R??F

336-01-2832

ForwardandFuturesPrices

?

ForwardPriceforaFinancialAssetthatProvidesnoIncome

F=S1+R?

zExample:Consideraforwardcontracttosellanon-dividend-paying

stockin3months.Thecurrentstockpriceis$40andthe3-monthrisk-

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

F=401+0.025?.??=40.25

?

ForwardPriceforaFinancialAssetthatPayingaKnownCashIncome

F=S?I1+R?

zExample:Considera10-monthforwardcontractonabondpayinga

USD2couponin3monthsandin9months.Assumether?forall

maturitiesis6%peryearandthecashpriceofthebondisUSD107.

2

2

??

+

=3.8856

F=107?3.8856×1.06??=108.2450

1

.06?.??1.06?.??

37-123

ForwardandFuturesPrices

?

ForwardPriceforaFinancialAssetthatProvidesaKnownYield

?

1

1

+R

+Q

F=S

zExample:Consideranassetexpectedtoprovidea2.5%yieldperyear

overthenextthreeyears.Therisk-freerateis3%peryearandthe

currentspotpriceoftheassetisUSD30.Theforwardprice(USD)is

?

1

+3%

F=30

=30.44

1

+2.5%

?

ForwardPriceforStockIndex

zExample:Consideranindexof2,000,ther?is4%peryearandthe

dividendyieldis2%peryear.Thefuturespricewithamaturityofsix

monthsis

?

.?

1

1

.04

.02

F=2,000×

=2019.5127

38-123

ForwardandFuturesPrices

?

ForeignExchangeForward/Futures

zInterestRateParity

?

1

1

+R?

+R?

F=S

WhereB/ArepresentstheexchangerateasthenumberofAperB.

0

??

t??

???????R?

1

????

1+R?

????

?

??????а??

????????

??????

???????R?

1

+R??/S

????

F1+R??/S

????

1/S????

39-123

ForwardandFuturesPrices

?

ForwardPriceforaCommodityAssetwithaLeaseRate

?

1

1

+R

+l

F=S

zExample:Assumethatthespotpriceofgoldis$1,250,theleaserateis

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

The6-monthfuturespriceisgivenby:

2

?

.?

1

.04

1

,250×

=1,259.1131

1

.025

?

ForwardPriceforaCommoditywithStorageCost&ConvenienceYield

?

1

1

+R

+Y

F=S+U

40-123

ForwardandFuturesPrices

?

ForwardPriceforaCommoditywithStorageCost&ConvenienceYield

zExample:ThespotpriceofoilisUSD65perbarrel,andtheconvenience

yieldis15%.ThestoragecostforsixmonthshasapresentvalueofUSD

3

perbarrel,andtherisk-freerateis2%peryear.the6-monthfutures

pricesatisfies

?

.?

1

1

.02

.15

65+3×

=64.0413

41-123

ForwardandFuturesPrices

?

ForwardPricevs.ValueofaForwardContract

zThevalueofaforwardcontractisquitedifferentfromtheforwardprice.

Whenforwardcontractsforfinancialassetsarefirstentered,thevalueof

theforwardcontractsthemselvesiszero.Overtime,however,asset

priceschangeandthevalueofforwardcontractscanbecomepositiveor

negative.

zWhilethevalueofthecontractchanges,thepriceatwhichtheassetwill

eventuallybeboughtorsoldremainsthesameastheoriginalforward

price.

F?K

Valueof????Forward????????=

1

+R?

42-123

InterestRateFutures

?

?

?

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

?

?

?

EurodollarFutures

zEurodollarFuturesvs.FRA

9

Withthesameunderlyingandthesamematurity,Theyshouldbethe

sameifinterestratesareperfectlypredictable.

9

9

ǐ?6?r)<0,Futurespriceislowerthanforwardprice.

Forshortmaturities,thedifferencesaresmallenoughtobeignored.

zConvexityAdjustment

1

2

Forward????=??????????????T(T+0.25)

9

?isthestandarddeviationofthechangeintheshort-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

48-123

HedgingStrategiesusingFutures

?

?

?

ShortHedgeandLongHedge

zAshorthedgeinvolvesashortpositioninfuturescontracts.Ashort

hedgeisappropriatewhenthehedgeralreadyownsanassetand

expectstosellitatsometimeinthefuture.

zAlonghedgeinvolvesalongpositioninafuturescontract.Along

hedgeisappropriatewhenacompanyknowsitwillhavetopurchasea

certainassetinthefutureandwantstolockinapricenow.

4

9-123

HedgingStrategiesusingFutures

HedgingwithFuturesContract

zMinimumVarianceHedgeRatio

9

Theminimumvariancehedgeratiodependsontherelationshipbetween

changesinthespotpriceandchangesinthefuturesprice.Byusingit,

wecanformahedgedpositionwithminimumvariance.

??

??

h?=??,?

50-123

HedgingStrategiesusingFutures

HedgingwithFuturesContract

zOptimalNumberofFuturesContracts

h?Q?

Q?

N?=

9

9

9

Q?:Sizeofpositionbeinghedged(units)

Q?:Sizeofonefuturescontract(units)

N?:Optimalnumberoffuturescontractsforhedging

zTailingtheHedge

9

Whenfuturescontractsareusedforhedging,thereisdailysettlement

andseriesofone-dayhedges.Tailingthehedgecandealwiththiscase

whenmakinghedgingdecision.

?????SQ?h?×V?

N?=

=

???FQ?

V?

9

??,??isthestandarddeviationoftheone-dayreturn,??isthecorrelation

?

?

betweentheone-dayspotreturnandthefuturesreturn.

51-123

HedgingStrategiesusingFutures

?

?

?

HedgingwithFuturesContract

zExample:Anairlineexpectstopurchase2milliongallonsofjetfuelin1

monthanddecidestouseheatingoilfuturesforhedging.Eachheating

oilcontracttradedbytheCMEGroupison42,000gallonsofheatingoil.

?

F

?6

Std.0.0310.026

Correlation0.928

??

?

HR=??,?

?

?

.???

=

0.928×

=0.778

=37.03

?

.???

???????

?????

N=0.778×

5

2-123

HedgingStrategiesusingFutures

HedgingwithFuturesContract

zHedgingwithStockIndexFutures

?

????????value

valueof???????????????

?

?????of?????????=??????????

×

?

????????value

=

??????????

×

?

???????????×??????????????????

?????????value

?

?????of?????????=(????)×

valueof???????????????

zHedgingwithInterestRateFutures

9

Thenumberofcontractsrequiredtohedgeagainstanuncertainchange

intheyieldgivenby?\?isgivenby:

PD?DV01?

FD?DV01?

N?=

=

53-123

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

?????1.4×

?97?????????

54-123

HedgingStrategiesusingFutures

?

?

?

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

?

?????of?????????=0?1.2×

=?444.44

5

5-123

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=?