HedgingwithForwardsandFutures

FNCE30007DerivativeSecurities/Lecture8

Schedule

2

IntroductiontoOptions

PropertiesofStockOptions

TheBinomialModel

TheBlackScholes MertonModel

DividendsandOptionsonOther

InstrumentsTheGreeksFuturesMarkets

HedgingwithFuturesandForwards

ForwardandFuturesPrices FuturesOptions Swaps

Outlineandreadings

3

Outline Issuesinhedging Basisrisk Optimalhedgeratio Portfoliohedging Rollingthehedgeforward

Readings Hull,7th/8th ed.,chapter3

IssuesinHedging

4

Shortandlonghedges

5

Ashorthedgeisengagedtoprotectagainst: anexistinglongpositionintheunderlyingasset anintentiontomakeasaleinthefuture

Alonghedgeismatchedagainst: anexistingshortpositionintheunderlyingasset anintentiontomakeapurchaseinthefuture

Whatisthemainobjective?

Mainobjectiveofahedge

6

Tolockincurrentprices,andindoingsoreducepriceexposure/risk.

Theprincipalobjectiveistoreducethevarianceofoutcomes

Ishedgingdonetoachievezeroexposure?

Hedgingisgood

7

Afirmshouldfocusonthemainstreambusinessesthatitdoesbest.

Itshouldnthavetorejectprojectsthatconsequentlyincreaseitsexposuretointerestrates,exchangerates,theweatheretc.

Hencehedgingallowsafirmtotakeinallgoodbusiness,andthenworryabouthowtotakestepstominimizerisks.

Hedgingisbad

8

Ultimatelyifallriskisremovedwehaveariskfreeinvestment. Shareholdersmaynotthankmanagersforthat whynot?

Shareholdersareusuallywelldiversifiedandcanmaketheirownhedgingdecisions.

Itmayincreaserisktohedgewhencompetitorsdonot. Explainingasituationwherethereisalossonthehedgeandagainontheunderlyingcanbedifficult.

Hedging example

9

ItisJune15.Afarmerhasnegotiatedtosell40,000bushelsofwheat.

Quotesaregivenas: Spotpriceofwheat:$1.50perbushel. Septemberwheatfuturesprice:$1.20perbushel(eachcontractisfor5,000bushels)

Hedging example

10

Thefarmercanhedgewiththefollowingtransactions: June15:ShorteightSeptemberfuturescontracts September15:Closeoutfuturesposition

Aftergainsandlossesonthefuturescontractsareconsidered,thepricereceivedbythefarmershouldbecloseto$1.20perbushel.

Hedging example

11

WhatifthespotpriceonSeptember15is$1.00perbushel? Thefarmersellsthewheatat($1.00)(40,000)=$40,000. Thefarmergains($1.20 $1.00)(40,000)=$8,000fromthefuturescontracts.

Thetotalamountrealizedbythefarmer:$40,000+$8,000=$48,000. Perbushelpricerealized=$48,000/40,000=$1.20.

Hedging example

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Mostofthetimehedgerswithlongpositionsdonottakethedeliveryastheycloseouttheirpositionsbeforethedeliveryandbuyinthespotmarket.Thisispartlybecausedeliveryarrangementscanbeveryexpensive.

BasisRisk

13

Basisrisk

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Aperfecthedgeistheonethatcompletelyeliminatestherisk.Perfecthedgesareveryrare.

Mosthedgesareimperfectbecause: Theassettobehedgedisnotidenticaltotheassetthatthecontractiswrittenon(jetfuelvs.regularoilfuturescontract)

Thehedgermaynotbesureabouttheexactdatetheassetwillbeboughtorsold.

Thehedgemayrequirethefuturestobeclosedoutpriortocontractmaturity.

Theprecedingissuesgiverisetowhatiscommonlytermedbasisrisk.

Basisrisk

15

Basisisthedifferencebetweenspotandfutures.

Basis=spotpriceofassettobehedged futurespriceofcontractused

Thebasiscanbenegative,zeroorpositive. Basisriskarisesbecauseoftheuncertaintyaboutthebasiswhenthehedgeisclosedout.

Basisrisk

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Ahedgeisnotfullyeffectiveifthebasisisnotconstantovertime.

t1 t2

Futuresprice

Spotprice

Longhedge

17

Supposethat F1:InitialFuturesPrice F2 :FinalFuturesPrice S2 :FinalAssetPrice

Youhedgethefuturepurchaseofanassetbyenteringintoalongfuturescontract.

CostofAsset=S2 (F2 F1)=F1+Basis

Shorthedge

18

Supposethat F1:InitialFuturesPrice F2 :FinalFuturesPrice S2 :FinalAssetPrice

Youhedgethefuturesaleofanassetbyenteringintoashortfuturescontract.

PriceRealized=S2+(F1 F2)=F1+Basis

Basisrisk example

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Hedgergoesshortfuturesatt1 whenS(t1)=2.50andF(t1)=2.20.

Thehedgeisthenclosedatt2

Basisrisk example

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IfthehedgeisclosedatT:S(T)=2.30,F(T)=2.30 Futuresprofit=0.10 PhysicalsaleatTgivesnetproceedsof2.20

Hedgingeffectiveness

21

Thepresenceofbasisriskdilutestheeffectivenessofahedgingstrategy.

Whatarethedecisionsthatahedgerhastomakeinformingahedgingstrategy? Chooseamongsimilarcontracts. Numberofcontracts. Choiceof(Tt).

Choiceofcontract

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Thechoiceofcontractaffectsbasisrisk. Ahedgertriestoseekoutthecontractwhosefuturespriceishighlycorrelatedwiththepriceoftheassetbeinghedged.

Insomecases,thechoiceisobvious. Inothercases,crosshedgingisinvolved.Forexample:

Differentgradesofwool,wheat,coffeebean Crudeoil,petroleum,heatingoil,LPGetc Governmentbondfuturestohedgeacorporatebond

Choiceofcontract

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Ifthereisnofuturescontractforanasset,thenbasisriskmightincrease.

F1 +(S*2 F2)+(S2 S*2)

(S*2 F2)isthebasisthatwouldexistiftheassetbeinghedgedwerethesameastheassetunderlyingthefuturescontract

(S2 S*2)isthebasisthatarisesfromthedifferencebetweenthetwoassets.

Hedgingperiod

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Thechoiceof(Tt)alsoaffectsbasisrisk. Basisriskincreasesasthetimegapbetweenhedgeexpirationanddeliverymonthincreases.

Chooseadeliverymonththatisascloseaspossibleto,butlaterthan,theendofthelifeofthehedge SupposethatdeliverymonthsareMarch,June,September,andDecember.IfaparticularhedgeexpiresinJanuary,theMarchcontractshouldbechosen.

Hedgingperiod

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SPI200December2008Futuresvs.S&P/ASX200

SPI200Futures S&P/ASX200

Hedgingperiod example

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ItisJuly25.Acompanyknowsthatitwillneedtopurchase40,000bushelsofcornsometimeinSeptemberorOctober,ThecurrentDecembercornfuturespriceis$2.55perbushel.(Assumethateachcornfuturescontractisfor5,000bushels).

Hedgingstrategy: Takealongpositionin40,000/5,000=8DecembercornfuturescontractsonJuly25atafuturespriceof$2.55.

Closeoutthecontractwhenreadytopurchasethecorn.

Choiceofcontract example

27

LetsassumethatthecompanyisreadytopurchasecornonOctober15.

SpotpriceonOctober15=$2.90 DecemberfuturespriceonOctober15=$2.80 BasisonOctober15:$2.90 $2.80=$0.10 Netcostofcorn:

SpotpriceonOctober15 gainonfutures=2.90 (2.802.55)=$2.65

FuturespriceonJuly25+basisonOctober15=2.55+(2.902.80)=$2.65.

OptimalHedgeRatio

28

Crosshedging

29

Hedgingoneinstrumentsriskwithadifferentonebytakingapositioninarelatedderivativescontract.

Thisisoftendonewhenthereisnoderivativescontractfortheinstrumentbeinghedged,orasuitablederivativescontractexistsbutthemarketishighlyilliquid.

Thesuccessofcrosshedgingdependsonhowstronglycorrelatedtheinstrumentbeinghedgediswiththepriceoftheinstrumentwhichunderliesthederivativescontract.

Optimalhedgeratio

30

Hedgeratioistheratioofsizeofthepositiontakeninfuturescontractstothesizeoftheexposure.

Hedgeratiois1.0whentheassetunderlyingthefuturescontractisthesameastheassetbeinghedged.

Whencrosshedgingisused,itissometimesnotoptimalsettingthehedgeratioequalto1.0.

Proportionoftheexposurethatshouldoptimallybehedgedis

F

Sh *

Optimalhedgeratio

31

S isthestandarddeviationofS,thechangeinthespotpriceduringthehedgingperiod,

F isthestandarddeviationofF,thechangeinthefuturespriceduringthehedgingperiod

isthecoefficientofcorrelationbetweenS andF.

Optimalnumberofcontracts

32

QA isthesizeofthepositionbeinghedged(units). QF isthesizeofonefuturescontract. Nistheoptimalnumberoffuturescontractsforhedging.

** AF

h QNQ

Optimalnumberofcontracts

33

GenerallyN*willnotbeawholenumber. h*andN*areestimatesinvolvingsamplingerror. Ifvolatilityetc istimevarying,optimalhedgeratioisalsotime varying.

Ifvalueofunderlyingpositionchanges(independentofchangeinfuturesvalue)optimalhedgemaychange.

Tailingthehedge

34

Anadjustmentisneededinmostcaseswhenfuturesareusedforhedging.

Thisadjustmentiscalledtailingthehedgeandbecauseofdailysettlement.

Optimalnumberofcontractsformulaismodifiedasfollows:

whereVA isthedollarvalueofthepositionbeinghedgedandVF isthedollarvalueofonefuturescontract(=futurespricexsizeofonefuturescontract).

*

* A

F

h VNV

Tailingthehedge example

35

OptimalnumberofcontractsinthepreviousExcelexampleismodifiedasfollows: Assumespotandfuturespricesofoil/literis$1.68and$1.74.

So,insteadof80contracts,78contractsshouldbepurchased.

(0.844)[(4,000,000)(1.68)] 77.6 ~ 78(42,000)(1.74)

PortfolioHedging

36

Reasonsforhedginganequityportfolio

37

Desiretobeoutofthemarketforashortperiodoftime.(hedgingmaybecheaperthansellingtheportfolioandbuyingitback.)

Desiretohedgesystematicrisk(appropriatewhenyoufeelthatyouhavepickedstocksthatwilloutperformthemarket.)

Hedgingusingindexfutures

38

Tohedgetheriskinaportfoliothenumberofcontractsthatshouldbeshortedis

whereP isthevalueoftheportfolio,isitsbeta(theweightedaverageofbetaofthecomponentpartsoftheportfolio),andF isthecurrentvalueofonefutures(=futurespricetimescontractsize).

PF

Hedgingusingindexfutures

39

Whenbeta=1,thereturnontheportfoliotendstomirrorthereturnonthemarket.

Whenbeta=2,thereturnontheportfoliotendstobetwiceasgreatasthereturnonthemarket.

Whenbeta=0.5,thereturnontheportfoliotendstobehalfasgreatasthereturnonthemarket.

h*=(S/F) =

Hedgingusingindexfutures example1

40

ValueofASX200is5,500 Futurespriceis5,600 Sizeoftheportfoliois$10million Betaoftheportfoliois1.2 Riskfreerate=8%perannum Dividendyieldontheindex=1%perannum Onecontractison$25timestheindex

Hedgingusingindexfutures example1

41

WhatpositioninfuturescontractsontheASX200isnecessarytohedgetheportfolio(forthreemonths)? (1.2)($10million/($25*5,600))=85.71~86contractsneedtobeshorted.

Supposetheindexturnsouttobe5,300inthreemonthsandthefuturespriceis5,350.

Thegainfromtheshortfuturespositionis(86)(5,6005,350)($25)=$537,500.

Thelossontheindexis(5,500 5,300)/5,500=3.64%.

Hedgingusingindexfutures example1

42

Theindexpaysadividendof1%perannum(0.25%perthreemonths).

Afterwetakedividendsintoaccount,thelossreducesto3.64 0.25=3.39%.

CapitalAssetPricingModel(CAPM):ri =rf +Beta(rm rf) Wefindtheexpected(%)lossontheportfolioduringthethreemonths. rp =0.02+1.2(0.0339 0.02)=4.46%

Hedgingusingindexfutures example1

43

Theexpectedvalueoftheportfoliois$10,000,000(10.0446)=$9,554,000.

Theexpectedvalueofthehedgerspositionis$9,554,000+$537,500=$10,091,500.

Changingbeta

44

Whatpositionisnecessarytoreducethebetaoftheportfolioto0.90?

Short22contracts Whatpositionisnecessarytoincreasethebetaoftheportfolioto2.5?

Buy97contracts

22~43.22)25)($350,5(

000,000,10$)9.02.1()( * FP

97~20.97)25)($350,5(

000,000,10$)2.15.2()( * FP

RollingtheHedgeForward

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Rollingthehedge

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Atdate0,expectedphysicalsaleatdate2,futurescontracttradedonlyhasexpirydate1.

Atdate1newcontractwithexpirydate2willbegin. Hedgeoverperiod(0,2)byrolloveroffuturescontract Date0:shortfuturesforexpirydate1atF0. Date1:settleexpiringfuturescontractandenternewshortfuturesforexpirydate2atF1. Assumenostoragecostsnordividendyield

Rollingthehedge

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ImportantImplications. Wecanhedgeverylongdatedtransactionsbysequenceoffuturescontracts,butsubjecttobasisriskfromeachrollover.

Cashflowswilloccurduringlifeofhedgeduetoprofitsorlossesonclosingoutcontracts(orascontractsaremarkedtomarketandmargincallsetc.made).