Chapter14:

ForwardandFutures MarketsObjectiveHowtopriceforwardandfuturesStorageofcommoditiesCostofcarryUnderstandingfinancialfutures1Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallChapter14:Contents14.1DistinctionBetweenForward&FuturesContracts14.2TheEconomicFunctionofFuturesMarkets14.3TheRoleofSpeculators14.4RelationBetweenCommoditySpot&FuturesPrices14.5ExtractingInformationfromCommodityFuturesPrices14.6Forward-SpotPriceParityforGold14.7FinancialFutures14.8The“Implied”RisklessRate14.9TheForwardPriceisnotaForecastoftheSpotPrice14.10Forward-SpotPrice-ParitywithCashPayouts14.11“Implied”Dividends14.12TheForeign-ExchangeParityRelation14.13TheRoleofExpectationsinDeterminingExchangeRates2Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall14.1DistinctionBetweenForward&FuturesContractspartiesagreetoexchangesomeiteminthefutureatadeliverypricespecifiednowtheforwardpriceisdefinedasthedeliverypricewhichmakesthecurrentmarketvalueofthecontractzeronomoneyispaidinthepresentbyeitherpartytotheotherthefacevalueofthecontractisthequantityoftheitemspecifiedinthecontractmultipliedbytheforwardpricethepartywhoagreestobuythespecifiedtakesthelongposition,andthepartywhoagreestoselltheitemtakestheshortposition3Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallTermsOpen,High,Low,Settle,Change,Lifetimehigh,Lifetimelow,OpeninterestMark-to-marketMarginrequirementMargincall4Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallCharacteristicsofFuturesFuturesare:standardcontractsimmunefromthecreditworthinessofbuyerandsellerbecauseexchangestandsbetweentraderscontractsmarkedtomarketdailymarginrequirements5Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall14.2TheEconomicFunctionofFuturesMarketsThefuturesmarketsfacilitatethere-allocationofexposuretocommoditypriceriskamongmarketparticipantsBut:6Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallbyprovidingameanstohedgethepriceriskassociatedwithstoringacommodity,futurescontractsmakeitpossibletoseparatethedecisionofwhethertophysicallystoreacommodityfromthedecisiontohavefinancialexposuretopricechanges7Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallTheEconomicFunctionofFuturesMarkets(Continued)Adistributor,j,mayhedgebysellingthecommodityonthespotmarketnowatapriceSsellingshortafuturescontractatapriceFanddeliverthecommodityataspecifiedtimeinthefuturetherewillbeacarryingcostCjfordistributorj,andshewillstoreonlyifCj<F-S8Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallTheEconomicFunctionofFuturesMarkets(Continued)Thedifferencebetweenthefuturespriceandthespotprice,F-S,iscalledthespread,andgovernshowmuchwheatwillbestored,andbywhom9Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallTheEconomicFunctionofFuturesMarkets(Continued)Supposethecommodityiswheat,andnextyear’scropisexpectedtobemuchhigherthanaverage,thenfuturespricesmaybelowerthanthespot,(thespreadmaybenegative,)nobodywillstorewheat10Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallTheEconomicFunctionofFuturesMarkets(Continued)Theexistenceofthefuturesmarketforwheatconveysinformationtoallproducers,distributors,andconsumers;andthiseliminatesthenecessityformarketparticipantstogatherandprocessinformationinordertoforecastthefuturespotprice11Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall14.3TheRoleofSpeculatorsHedgeranyoneusingafuturesmarkettoreduceriskSpeculatoranyonewhotakesapositioninthemarket(increasinghisrisk)inordertoprofitfromhisforecastsoffuturespotprices(Aproducer,distributororconsumerwhochoosesnottohedgeherriskmaybeconsideredtobeaspeculator)12Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallTheRoleofSpeculators:ExampleSupposethatthecurrent1-monthfuturesinwheatis$1.5/bushel,andafarmingfamilywithstoredwheatbelievesthatthepricewillriseto$2.00Nothedgingthestoredwheatresultsinthefamilybeingexposedtothevagranciesofthewheatmarket,anditbecomes,ineffect,awheatspeculator(justliketheircobblercousinswhoarelongwheatfutures)13Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallTheRoleofSpeculators:GamblersandWastersCritic:“Speculatorshavenosocialvalue”Answer:Successfulspeculatorsmakethemarketmoreefficientasaninformationresourceprovideliquiditywhenitisneeded,whichiswhenproducers,distributors,andconsumerscan’torwon’thedgemoreefficientbycontributingtowardsrecoveringthefixedcostsofprovidingafuturesexchange14Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall14.4RelationshipBetweenCommoditySpotandFuturesPricesArbitrageursplaceanupperboundonfuturespricesbylockinginasureprofitonfuturespricesifthespreadbetweenthefuturespriceandspotpricebecomesgreaterthanthecostofcarry,F-S￡Cthecostofcarryvariesasafunctionoftimeandwarehousingorganization15Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall14.5ExtractingInformationfromCommodityFuturesPricesCase1If(FuturesPrice<CurrentSpot)ThenthefuturespriceisanindicatoroftheexpectedfuturespotpriceThefuturespriceisabiasedestimatebecausethereareriskpremiumsanddiscountsassociatedwithholdingthecommodity16Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallExtractingInformationfromCommodityFuturesPricesCase2If(FuturesPrice>CurrentSpot)ThenthefuturespriceisnotanindicatoroftheexpectedfuturespotpriceThespreadcannotexceedthecostofcarry17Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall14.6Spot-FuturesPriceParityforGoldInthecaseofgoldfutures,arbitrageestablishesanupper-andlower-boundonthespreadbetweenthefuturesandspotprices,resultinginthespot-futuresprice-parityrelationship18Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallSpot-FuturesPriceParityforGoldTherearetwowaystoinvestingoldbuyanounceofgoldatS0,storeitforayearatastoragecostof$h/$S0,andsellitforS1investS0ina1-yearT-billwithreturnrf,andpurchasea1-ounceofgoldforward,F,fordeliveryin1-year19Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallSpot-FuturesPriceParityforGoldAcontractwithlifeT:Thisisnotacausalrelationship,buttheforwardandcurrentspotjointlydeterminethemarketIfweknowone,thentheruleofonemarketdeterminesthatweknowtheother20Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallSpot-FuturesPriceParityforGoldThefollowingdiagramshowshowtocreatesyntheticgold,T-bills,orgoldforwardcontractfromtheothertwoAllpricesarepredetermined,exceptthepriceoftheoneyearoftheforwardandthepriceinoneyearofthegold,butthedifferencebetweenthemisequaltotheknownfinancingandstoragecosts21Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallRuleofOnePrice:NoArbitrageProfitsPurchaseActualAuSellT-BillSellAuForwardSellActualAuSettleT-BillSettleAuForwardAu=Gold22Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallImpliedCostofCarryAsaconsequenceoftheforward-spotpriceparityrelationship,youcan’textractinformationabouttheexpectedfuturespotpriceofgold(unlikeonewheatcase)fromfuturespricesTheimpliedcostofcarry(per$spot)is h=(F-S0)/S0-rf23Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall14.7FinancialFuturesWenowfocusonfinancialfuturesstandardizedcontractsforfuturedeliveryofstocks,bonds,indices,andforeigncurrencytheyhavenointrinsicvalue,butrepresentclaimsonfuturecashflowstheyhaveverylowstoragecostssettlementisusuallyincash24Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallFinancialFuturesWithnostoragecost,therelationshipbetweentheforwardandthespotisAnydeviationfromthiswillresultinanarbitrageopportunity25Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallFinancialFutures:ExampleConsidersharesinBablonics,Inc,tradingat$50each,($5,000foraroundlot);assume6-monthT-billsyield6%(compoundedsemiannually)26Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallBablonics,Inc(Continued)1PurchaseoneroundlotofstockatspotThisresultsinanegativecashflowtodayof$5,000(out),andwillgenerateacashflowof100*Spot6m(in)

insixmonths27Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallBablonics,Inc(Continued)2Covertoday’snegativecashflowbysellingshort$5,000worthof6-monthT-billswithafacevalueof5000(1+0.06/2)^0.5=$5,150Thecashflowtodayis$5,000(in),andthecashflowinsixmonthstimewillbe$5,150(out)28Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallBablonics,Inc(Continued)3Covertheriskexposurebyselling100sharesforwardattheequilibriumpriceof5000*(1+0.06/2)^0.5=$5,150Thereisnocashflowtoday,butthevalueofthisforwardcontractinsixmonthstimewillbe$(Spot6m-5,150)29Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallBablonics,Inc(Continued)-$5,000(longstock)+$5,000(shortbond)+$0(shortforward)=$030Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallBablonics,Inc(Continued)CashFlowin6-Months+$Spot6m(settlelongstock)-$5,150(settleshortbond)+($5,150-$Spot6m)(settleforward)=$031Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallBablonics,Inc(Conclusion)Ifyournetrisk-freeinvestmentwaszero,andyoureceivenothingthatiswhatyoushouldexpectandyouexpectto:receivedpositivevaluewithnorisk,thentheruleofonepricehasbeenviolatedlosevaluewithnorisk,thenreversethedirectionofalltransactions,andagainyouprofitwithnorisk32Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall14.8The“Implied”RisklessRateRearrangingtheformula,theimpliedinterestrateonaforwardgiventhespotisThisisreminiscentoftheformulafortheinterestrateonadiscountbond33Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall14.9TheForwardPriceisnotaForecastoftheFutureSpotPriceFollowingthediagramsinChapter12wemightsupposethattheexpectedpriceofastockisIfthisisindeedcorrect,thentheforwardpriceisnotanindicatoroftheexpectedspotpriceatthematurityoftheforward34Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallTheForwardPriceisnotaForecastoftheFutureSpotPriceTheforwardpriceisobtainedwithoutriskfromthecurrentspotandrisklessbondThespotvalueatafuturedateisobtainedbyinvestinginthesecurityandaccepting(market)risk,andthisriskmustberewarded35Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall14.10Forward-SpotPrice-ParityRelationwithCashPayoutsSofarwehaveassumedthatthereisnodividendNowsupposethateverybodyexpectsanuncertaindividendin1yearofDItisnotpossibletoreplicateDbecauseofthisuncertaintyWewilltreatDasifitwereknownwithcertainty,andonlydealwith1-yearforwards36Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallForward-SpotParitywithCashPayoutsTheS0-FrelationshipbecomesNote:(forwardprice>thespotprice)if(D<rS)BecauseDisnotknownwithcertainty,thisisaquasi-arbitragesituation37Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall14.11“Implied”DividendsFromthelastslide,wemayobtaintheimplieddividend38Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall14.12TheForeignExchangeParityRelationRecallfromChapter2thefollowingdiagram:39Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallExchangeRateExample15000￥(Borrowed)15450￥15450￥(Repaid)

￡100(Invested)￡109(Matures)Time3%￥/￥(direct)3%￥/￡/￡/￥150￥/￡9%￡/￡Forward￥/￡JapanU.K.40Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallTheForeignExchangeParityRelationWeusedthediagramtoshowthatRecallthere