投资学课后习题答案 Chap022

CHAPTER22:FUTURESMARKETS

PROBLEMSETS

1.Thereislittlehedgingorspeculativedemandforcementfutures,sincecementprices

arefairlystableandpredictable.Thetradingactivitynecessarytosupportthefutures

marketwouldnotmaterialize.

2.Theabilitytobuyonmarginisoneadvantageoffutures.Anotheristheeasewithwhich

onecanalterone'sholdingsoftheasset.Thisisespeciallyimportantifoneisdealingin

commodities,forwhichthefuturesmarketisfarmoreliquidthanthespotmarket.

3.Shortsellingresultsinanimmediatecashinflow,whereastheshortfutures

positiondoesnot:

ActionInitialCFFinalCF

ShortSale+Po-PT

ShortFutures0Fo-PT

4.a.False.Foranygivenlevelofthestockindex,thefuturespricewillbelower

whenthedividendyieldishigher.Thisfollowsfromspot-futuresparity:

T

Fo=So(l+rf-d)

b.False.Theparityrelationshiptellsusthatthefuturespriceisdeterminedbythe

stockprice,theinterestrate,andthedividendyield;itisnotafunctionofbeta.

c.True.Theshortfuturespositionwillprofitwhenthemarketfalls.Thisisa

negativebetaposition.

5.Thefuturespriceistheagreed-uponpricefordeferreddeliveryoftheasset.Ifthat

priceisfair,thenthevalueoftheagreementoughttobezero;thatis,thecontract

willbeazero-NPVagreementforeachtrader.

6.Becauselongpositionsequalshortpositions,futurestradingmustentaila

"cancelingout“ofbetsontheasset.Moreover,nocashisexchangedatthe

inceptionoffuturestrading.Thus,thereshouldbeminimalimpactonthespot

marketfortheasset,andfuturestradingshouldnotbeexpectedtoreducecapital

availablefbrotheruses.

7.a.TheclosingfuturespricefortheMarchcontractwas1,108.60,whichhasa

dollarvalueof:

$250x1,108.60=$277,150

Therefore,therequiredmargindepositis:$27,715

b.Thefuturespriceincreasesby:$1,150.00-1,108.60=$41.40

Thecredittoyourmarginaccountwouldbe:41.40x$250=$10,350

Thisisapercentgainof:$10,350/$27,715=0.3734=37.34%

Notethatthefuturespriceitselfincreasedbyonly3.73%.

c.Followingthereasoninginpart(b),anychangeinFismagnifiedbyaratioof

(1/marginrequirement).Thisistheleverageeffect.Thereturnwillbe-10%.

8.a.Fo=So(l+rf)=$150x1.03=$154.50

b.Fo=So(l+rf)3=$150x1.033=$163.91

c.Fo=15()x1.063=$178.65

9.a.TakeashortpositioninT-bondfutures,tooffsetinterestraterisk.Ifrates

increase,thelossonthebondwillbeoffsettosomeextentbygainsonthe

futures.

b.Again,ashortpositioninT-bondfutureswilloffsettheinterestraterisk.

c.Youwanttoprotectyourcashoutlaywhenthebondispurchased.Ifbond

pricesincrease,youwillneedextracashtopurchasethebond.Thus,you

shouldtakealongfuturespositionthatwillgenerateaprofitifpricesincrease.

10.Fo=Sox(l4-rf-d)=1,100x(1+0.03-0.02)=1,111

IftheT-billrateislessthanthedividendyield,thenthefuturespriceshouldbeless

thanthespotprice.

11.Theput-callparityrelationstatesthat:Butspot-futuresparitytellsusthat:

c=—+._(]/.F=Sox(\+rfy

Substituting,wefindthat:

r

|Sox(l+r..)]

p=c-so+-(]+r=c-s0+s0=c

12.Accordingtotheparityrelation,theproperpriceforDecemberfuturesis:

1/21/2

FDec=Fjune(l+ff)=946.30x1.05=969.67

TheactualfuturespricefbrDecemberislowrelativetotheJuneprice.Youshould

takealongpositionintheDecembercontractandshorttheJunecontract.

13.a.120x1.06=$127.20

b.Thestockpricefallsto:120x(1-0.03)=$116.40

Thefuturespricefallsto:116.4x1.06=$123,384

Theinvestorloses:(127.20-123.384)x1,000=$3,816

c.Thepercentagelossis:$3,816/$12,000=0.318=31.8%

14.a.TheinitialfuturespriceisFo=1300x(1+0.005-0.002)12=$1,347.58

Inonemonth,thefuturespricewillbe:

11

Fo=1320x(1+0.005-0.002)=$1,364.22

Theincreaseinthefuturespriceis16.64,sothecashflowwillbe:

16.64x$250=$4,160.00

b.Theholdingperiodreturnis:$4,160,00/$13,000=0.3200=32.00%

15.Thetreasurerwouldliketobuythebondstoday,butcannot.Asaproxyforthis

purchase,T-bondfuturescontractscanbepurchased.Ifratesdoinfactfall,the

treasurerwillhavetobuybackthebondsforthesinkingfundatpriceshigherthan

thepricesatwhichtheycouldbepurchasedtoday.However,thegainsonthe

futurescontractswilloffsetthishighercosttosomeextent.

16.TheparityvalueofFis:1,300x(1+0.04-0.01)=1,339

Theactualfuturespriceis1,330,toolowby9.

ArbitragePortfolioCFnowCFin1year

ShortIndex1,300-ST-(0.01x1,300)

BuyFutures0ST-1,330

Lend-1,3001,300x1.04

Total09

17.a.Futurespricesaredeterminedfromthespreadsheetasfollows:

SpotFuturesParityandTimeSpreads

Spotprice1,500

Incomeyield(%)1.5Futurespricesversusmaturity

Interestrate(%)3.0

Today'sdate1/1/2011Spotprice1,500.00

Maturitydate12/14/2011Futures11,502.67

Maturitydate25/21/2011Futures21,508.71

Maturitydate311/18/2011Futures31,519.79

Timetomaturity10.12

Timetomaturity20.39

Timetomaturity30.88

LEGEND:

Enterdata

Valuecalculated

Seecomment

b.Thespreadsheetdemonstratesthatthefuturespricesnowdecreasewith

increasedincomeyield:

SpotFuturesParityandTimeSpreads

Spotprice1,500

Incomeyield(%)4.0Futurespricesversusmaturity

Interestrate(%)3.0

Today'sdate1/1/2011Spotprice1,500.00

Maturitydate12/14/2011Futures11,498.20

Maturitydate25/21/2011Futures21,494.15

Maturitydate311/18/2011Futures31,486.78

Timetomaturity10.12

Timetomaturity20.39

Timetomaturity30.88

LEGEND:

Enterdata

Valuecalculated

Seecomment

18.a.ThecurrentyieldforTreasurybonds(coupondividedbyprice)playstheroleof

thedividendyield.

b.Whentheyieldcurveisupwardsloping,thecurrentyieldexceedstheshort

rate.Hence,T-bondfuturespricesonmoredistantcontractsarelowerthan

thoseonnear-termcontracts.

19.a.

CashFlows

ActionNowTiT2

LongfutureswithmaturityT10Pl-F(Ti)0

ShortfutureswithmaturityT200F(T2)-P2

BuyassetatT1,sellatT20-PlP2

(T2-T1)

AtTj,borrowF(Ti)0F(T,)

-F(TI)x(l+rf)

(T2-TI)

Total00F(T2)-F(Ti)x(l+rf)

b.SincetheT2cashflowisrisklessandthenetinvestmentwaszero,thenany

profitsrepresentanarbitrageopportunity.

c.Thezero-profitno-arbitragerestrictionimpliesthat

T

F(T2)=F(Ti)x(14-rf)(2-Ti)

CFAPROBLEMS

1.a.Thestrategythatwouldtakeadvantageofthearbitrageopportunityisa"reverse

cashandcarry.^^Areversecashandcarryopportunityresultswhenthefollowing

relationshipdoesnotholdtrue:

Fo>So(l+C)

Ifthefuturespriceislessthanthespotpriceplusthecostofcarryingthegoodsto

thefuturesdeliverydate,thenanarbitrageopportunityexists.Atraderwouldbe

abletoselltheassetshort,usetheproceedstolendattheprevailinginterestrate,

andthenbuytheassetforfuturedelivery.Atthefuturedelivery,thetraderwould

thencollecttheproceedsoftheloanwithinterest,acceptdeliveryoftheasset,and

covertheshortpositioninthecommodity.

b.

CashFlows

ActionNowOneyearfromnow

Sellthespotcommodityshort+$120.00-$125.00

Buythecommodityfuturesexpiringin1year$0.00$0.00

Contracttolend$120at8%for1year-$120.(1)+$129.60

Totalcashflow$0.00+$4.60

2.a.Thecalloptionisdistinguishedbyitsasymmetricpayoff.IftheSwissfranc

risesinvalue,thenthecompanycanbuyfrancsforagivennumberofdollars

toserviceitsdebt,andtherebyputacaponthedollarcostofitsfinancing.If

thefrancfalls,thecompanywillbenefitfromthechangeintheexchangerate.

Thefuturesandforwardcontractshavesymmetricpayoffs.Thedollarcostofthe

financingislockedinregardlessofwhetherthefrancappreciatesordepreciates.

Themajordifferencefromthefirm'sperspectivebetweenfuturesandforwardsis

inthemark-to-marketfeatureoffutures.Theconsequenceofthisisthatthefirm

mustbereadyforthecashmanagementissuessurroundingcashinflowsor

outflowsasthecurrencyvaluesandfuturespricesfluctuate.

b.Thecalloptiongivesthecompanytheabilitytobenefitfromdepreciationinthe

franc,butatacostequaltotheoptionpremium.Unlessthefirmhassomespecial

expertiseincurrencyspeculation,itseemsthatthefuturesorforwardstrategy,

whichlocksinadollarcostoffinancingwithoutanoptionpremium,maybethe

betterstrategy.

3.Theimportantdistinctionbetweenafuturescontractandanoptionscontractisthatthe

futurescontractisanobligation.Whenaninvestorpurchasesorsellsafuturescontract,

theinvestorhasanobligationtoeitheracceptordeliver,respectively,theunderlying

commodityontheexpirationdate.Incontrast,thebuyerofanoptioncontractisnot

obligatedtoacceptordelivertheunderlyingcommoditybutinsteadhastheright,or

choice,toacceptdelivery(forcallholders)ormakedelivery(fbrputholders)ofthe

underlyingcommodityanytimeduringthelifeofthecontract.

Futuresandoptionsmodifyaportfolio^riskindifferentways.Buyingorsellinga

futurescontractaffectsaportfolio^upsideriskanddownsideriskbyasimilar

magnitude.Thisiscommonlyreferredtoassymmetricalimpact.Ontheotherhand,the

additionofacallorputoptiontoaportfoliodoesnotaffectaportfolio'supsideriskand

downsiderisktoasimilarmagnitude.Unlikefuturescontracts,theimpactofoptionson

theriskprofileofaportfolioisasymmetric.

4.a.Theinvestorshouldselltheforwardcontracttoprotectthevalueofthebond

againstrisinginterestratesduringtheholdingperiod.Becausetheinvestorintends

totakealongpositionintheunderlyingasset,thehedgerequiresashortposition

inthederivativeinstrument.

b.Thevalueoftheforwardcontractonexpirationdateisequaltothespotpriceof

theunderlyingassetonexpirationdateminustheforwardpriceofthecontract:

$978.40-$1,024.70=-$46.30

Thecontracthasanegativevalue.Thisisthevaluetotheholderofalongposition

intheforwardcontract.Inthisexample,theinvestorshouldbeshorttheforward

contract,sothatthevaluetothisinvestorwouldbe+$46.30sincethisisthecash

flowtheinvestorexpectstoreceive.

c.Thevalueofthecombinedportfolioattheendofthesix-monthholdingperiodis:

$978.40+$46.30=$1,024.70

Thechangeinthevalueofthecombinedportfolioduringthissix-month

periodis:$24.70

Thevalueofthecombinedportfolioisthesumofthemarketvalueofthe

bondandthevalueoftheshortpositionintheforwardcontract.Atthestart

ofthesix-monthholdingperiod,thebondisworth$1,000andtheforward

contracthasavalueofzero(becausethisisnotanoff-marketforward

contract,nomoneychangeshandsatinitiation).Sixmonthslater,thebond

valueis$978.40andthevalueoftheshortpositionintheforwardcontractis

$46.30,ascalculatedinpart(b).

Thefactthatthecombinedvalueofthelongpositioninthebondandtheshort

positionintheforwardcontractattheforwardcontracfsmaturitydateisequal

totheforwardpriceontheforwardcontractatitsinitiationdateisnota

coincidence.Bytakingalongpositionintheunderlyingassetandashort

positionintheforwardcontract,theinvestorhascreatedafullyhedged(and

hencerisk-free)position,andshouldearntherisk-freerateofreturn.Thesix­

monthrisk-freerateofreturnis5.00%(annualized),whichproducesareturn

of$24.70overasix-monthperiod:

($1,000x1.05(1/2))-$1,00