ChapterOutline25.1ForwardContracts25.2FuturesContracts25.3Hedging25.4InterestRateFuturesContracts25.5DurationHedging25.6SwapContracts25.7ActualUseofDerivatives25.8Summary&ConclusionsChapterOutline25.1ForwardCo25.1ForwardContractsAforwardcontractspecifiesthatacertaincommoditywillbeexchangedforanotherataspecifiedtimeinthefutureatpricesspecifiedtoday.Itsnotanoption:bothpartiesareexpectedtoholduptheirendofthedeal.Ifyouhaveeverorderedatextbookthatwasnotinstock,youhaveenteredintoaforwardcontract.25.1ForwardContractsAforwar25.2FuturesContracts:PreliminariesAfuturescontractislikeaforwardcontract:Itspecifiesthatacertaincommoditywillbeexchangedforanotherataspecifiedtimeinthefutureatpricesspecifiedtoday.Afuturescontractisdifferentfromaforward:Futuresarestandardizedcontractstradingonorganizedexchangeswithdailyresettlement(“markingtomarket”)throughaclearinghouse.25.2FuturesContracts:PrelimFuturesContracts:PreliminariesStandardizingFeatures:ContractSizeDeliveryMonthDailyresettlementMinimizesthechanceofdefaultInitialMarginAbout4%ofcontractvalue,cashorT-billsheldinastreetnameatyourbrokerage.FuturesContracts:PreliminariDailyResettlement:AnExampleSupposeyouwanttospeculateonariseinthe$/￥exchangerate(specificallyyouthinkthatthedollarwillappreciate).Currently$1=￥140.The3-monthforwardpriceis$1=￥150.DailyResettlement:AnExampleDailyResettlement:AnExampleCurrently$1=￥140anditappearsthatthedollarisstrengthening.Ifyouenterintoa3-monthfuturescontracttosell￥attherateof$1=￥150youwillmakemoneyiftheyendepreciates.Thecontractsizeis￥12,500,000Yourinitialmarginis4%ofthecontractvalue:DailyResettlement:AnExampleDailyResettlement:AnExampleIftomorrow,thefuturesrateclosesat$1=￥149,thenyourposition’svaluedrops.Youroriginalagreementwastosell￥12,500,000andreceive$83,333.33:Youhavelost$559.28overnight.But￥12,500,000isnowworth$83,892.62:DailyResettlement:AnExampleDailyResettlement:AnExampleThe$559.28comesoutofyour$3,333.33marginaccount,leaving$2,774.05Thisisshortofthe$3,355.70requiredforanewposition.Yourbrokerwillletyouslideuntilyourunthroughyourmaintenancemargin.Thenyoumustpostadditionalfundsoryourpositionwillbeclosedout.Thisisusuallydonewithareversingtrade.DailyResettlement:AnExampleSelectedFuturesContractsSelectedFuturesContractsFuturesMarketsTheChicagoMercantileExchange(CME)isbyfarthelargest.Othersinclude:ThePhiladelphiaBoardofTrade(PBOT)TheMidAmericaCommoditiesExchangeTheTokyoInternationalFinancialFuturesExchangeTheLondonInternationalFinancialFuturesExchangeFuturesMarketsTheChicagoMerTheChicagoMercantileExchangeExpirycycle:March,June,September,December.Deliverydate3rdWednesdayofdeliverymonth.Lasttradingdayisthesecondbusinessdayprecedingthedeliveryday.CMEhours7:20a.m.to2:00p.m.CST.TheChicagoMercantileExchangCMEAfterHoursExtended-hourstradingonGLOBEXrunsfrom2:30p.m.to4:00p.mdinnerbreakandthenbackatitfrom6:00p.m.to6:00a.m.CST.SingaporeInternationalMonetaryExchange(SIMEX)offerinterchangeablecontracts.There’sothermarkets,butnoneareclosetoCMEandSIMEXtradingvolume.CMEAfterHoursExtended-hoursWallStreetJournalFuturesPriceQuotesExpirymonthOpeningpriceHighestpricethatdayLowestpricethatdayClosingpriceDailyChangeHighestandlowestpricesoverthelifetimeofthecontract.NumberofopencontractsWallStreetJournalFuturesPrBasicCurrencyFuturesRelationshipsOpenInterestreferstothenumberofcontractsoutstandingforaparticulardeliverymonth.Openinterestisagoodproxyfordemandforacontract.Somerefertoopeninterestasthedepthofthemarket.Thebreadthofthemarketwouldbehowmanydifferentcontracts(expirymonth,currency)areoutstanding.BasicCurrencyFuturesRelatio25.3HedgingTwocounterpartieswithoffsettingriskscaneliminaterisk.Forexample,ifawheatfarmerandaflourmillenterintoaforwardcontract,theycaneliminatetheriskeachotherfacesregardingthefuturepriceofwheat.Hedgerscanalsotransferpricerisktospeculatorsandspeculatorsabsorbpriceriskfromhedgers.Speculating:Longvs.Short25.3HedgingTwocounterpartiesHedgingandSpeculatingExampleYouspeculatethatcopperwillgoupinprice,soyougolong10coppercontractsfordeliveryin3months.Acontractis25,000poundsincentsperpoundandisat$0.70perpoundor$17,500percontract.Iffuturespricesriseby5cents,youwillgain: Gain=25,000×.05×10=$12,500Ifpricesdecreaseby5cents,yourlossis: Loss=25,000×-.05×10=-$12,500HedgingandSpeculatingExamplHedging:Howmanycontacts?Youareafarmerandyouwillharvest50,000bushelsofcornin3months.Youwanttohedgeagainstapricedecrease.Cornisquotedincentsperbushelat5,000bushelspercontract.Itiscurrentlyat$2.30centsforacontract3monthsoutandthespotpriceis$2.05.Tohedgeyouwillsell10cornfuturescontracts:Nowyoucanquitworryingaboutthepriceofcornandgetbacktoworryingabouttheweather.Hedging:Howmanycontacts?You25.4InterestRateFuturesContractsPricingofTreasuryBondsPricingofForwardContractsFuturesContractsHedginginInterestRateFutures25.4InterestRateFuturesConPricingofTreasuryBondsConsideraTreasurybondthatpaysasemiannualcouponof$CforthenextTyears:TheyieldtomaturityisrValueoftheT-bondunderaflattermstructure=PVoffacevalue+PVofcouponpayments…0 123 2TPricingofTreasuryBondsConsiPricingofTreasuryBondsIfthetermstructureofinterestratesisnotflat,thenweneedtodiscountthepaymentsatdifferentratesdependinguponmaturity=PVoffacevalue+PVofcouponpayments…0 123 2TPricingofTreasuryBondsIfthPricingofForwardContractsAnN-periodforwardcontractonthatT-Bond…0 N

N+1 N+2N+3 N+2TCanbevaluedasthepresentvalueoftheforwardprice.PricingofForwardContractsAnFuturesContractsThepricingequationgivenabovewillbeagoodapproximation.Theonlyrealdifferenceisthedailyresettlement.FuturesContractsThepricingeHedginginInterestRateFuturesAmortgagelenderwhohasagreedtoloanmoneyinthefutureatpricessettodaycanhedgebysellingthosemortgagesforward.Itmaybedifficulttofindacounterpartyintheforwardwhowantstheprecisemixofrisk,maturity,andsize.It’slikelytobeeasierandcheapertouseinterestratefuturescontractshowever.HedginginInterestRateFutur25.5DurationHedgingAsanalternativetohedgingwithfuturesorforwards,onecanhedgebymatchingtheinterestrateriskofassetswiththeinterestrateriskofliabilities.Durationisthekeytomeasuringinterestraterisk.25.5DurationHedgingAsanaltDurationmeasuresthecombinedeffectofmaturity,couponrate,andYTMonbond’spricesensitivityMeasureofthebond’seffectivematurityMeasureoftheaveragelifeofthesecurityWeightedaveragematurityofthebond’scashflows25.5DurationHedgingDurationmeasuresthecombinedDurationFormulaDurationFormulaCalculatingDurationCalculatethedurationofathree-yearbondthatpaysasemi-annualcouponof$40,hasa$1,000parvaluewhentheYTMis8%semiannually?CalculatingDurationCalculateCalculatingDurationDurationisexpressedinunitsoftime;usuallyyears.CalculatingDurationDurationiDurationThekeytobondportfoliomanagementProperties:Longermaturity,longerdurationDurationincreasesatadecreasingrateHighercoupon,shorterdurationHigheryield,shorterdurationZerocouponbond:duration=maturityDurationThekeytobondportfo25.6SwapsContracts:DefinitionsInaswap,twocounterpartiesagreetoacontractualarrangementwhereintheyagreetoexchangecashflowsatperiodicintervals.Therearetwotypesofinterestrateswaps:Singlecurrencyinterestrateswap“Plainvanilla”fixed-for-floatingswapsareoftenjustcalledinterestrateswaps.Cross-CurrencyinterestrateswapThisisoftencalledacurrencyswap;fixedforfixedratedebtserviceintwo(ormore)currencies.25.6SwapsContracts:DefinitiTheSwapBankAswapbankisagenerictermtodescribeafinancialinstitutionthatfacilitatesswapsbetweencounterparties.Theswapbankcanserveaseitherabrokeroradealer.Asabroker,theswapbankmatchescounterpartiesbutdoesnotassumeanyoftherisksoftheswap.Asadealer,theswapbankstandsreadytoaccepteithersideofacurrencyswap,andthenlaterlayofftheirrisk,ormatchitwithacounterparty.TheSwapBankAswapbankisaAnExampleofanInterestRateSwapConsiderthisexampleofa“plainvanilla”interestrateswap.BankAisaAAA-ratedinternationalbanklocatedintheU.K.andwishestoraise$10,000,000tofinancefloating-rateEurodollarloans.BankAisconsideringissuing5-yearfixed-rateEurodollarbondsat10percent.Itwouldmakemoresensetoforthebanktoissuefloating-ratenotesatLIBORtofinancefloating-rateEurodollarloans.AnExampleofanInterestRateAnExampleofanInterestRateSwapFirmBisaBBB-ratedU.S.company.Itneeds$10,000,000tofinanceaninvestmentwithafive-yeareconomiclife.FirmBisconsideringissuing5-yearfixed-rateEurodollarbondsat11.75percent.Alternatively,firmBcanraisethemoneybyissuing5-yearfloating-ratenotesatLIBOR+?percent.FirmBwouldprefertoborrowatafixedrate.AnExampleofanInterestRateAnExampleofanInterestRateSwapTheborrowingopportunitiesofthetwofirmsare:AnExampleofanInterestRateAnExampleofanInterestRateSwapBankATheswapbankmakesthisoffertoBankA:YoupayLIBOR–1/8%peryearon$10millionfor5yearsandwewillpayyou103/8%on$10millionfor5yearsSwapBankLIBOR–1/8%103/8%AnExampleofanInterestRateAnExampleofanInterestRateSwapHere’swhat’sinitforBankA:Theycanborrowexternallyat10%fixedandhaveanetborrowingpositionof-103/8+10+(LIBOR–1/8)=LIBOR–?%whichis?%betterthantheycanborrowfloatingwithoutaswap.10%?%of$10,000,000=$50,000.That’squiteacostsavingsperyearfor5years.SwapBankLIBOR–1/8%103/8%BankAAnExampleofanInterestRateAnExampleofanInterestRateSwapCompanyBTheswapbankmakesthisoffertocompanyB:Youpayus10?%peryearon$10millionfor5yearsandwewillpayyouLIBOR–?%peryearon$10millionfor5years.SwapBank10?%LIBOR–?%AnExampleofanInterestRateAnExampleofanInterestRateSwapTheycanborrowexternallyatLIBOR+?%andhaveanetborrowingpositionof10?+(LIBOR+?)-(LIBOR-?)=11.25%whichis?%betterthantheycanborrowfloating.

LIBOR+?%Here’swhat’sinitforB:?%of$10,000,000=$50,000that’squiteacostsavingsperyearfor5years.SwapBankCompanyB10?%LIBOR–?%AnExampleofanInterestRateAnExampleofanInterestRateSwapTheswapbankmakesmoneytoo.?%of$10million=$25,000peryearfor5years.LIBOR–1/8–[LIBOR–?]=1/810?-103/8=1/8?

SwapBankCompanyB10?%LIBOR–?%LIBOR–1/8%103/8%BankAAnExampleofanInterestRateAnExampleofanInterestRateSwapSwapBankCompanyB10?%LIBOR–?%LIBOR–1/8%103/8%BankABsaves?%Asaves?%Theswapbankmakes?%AnExampleofanInterestRateAnExampleofaCurrencySwapSupposeaU.S.MNCwantstofinancea￡10,000,000expansionofaBritishplant.TheycouldborrowdollarsintheU.S.wheretheyarewellknownandexchangefordollarsforpounds.Thiswillgivethemexchangeraterisk:financingasterlingprojectwithdollars.Theycouldborrowpoundsintheinternationalbondmarket,butpayapremiumsincetheyarenotaswellknownabroad.AnExampleofaCurrencySwapSAnExampleofaCurrencySwapIftheycanfindaBritishMNCwithamirror-imagefinancingneedtheymaybothbenefitfromaswap.IfthespotexchangerateisS0($/￡)=$1.60/￡,theU.S.firmneedstofindaBritishfirmwantingtofinancedollarborrowingintheamountof$16,000,000.AnExampleofaCurrencySwapIAnExampleofaCurrencySwapConsidertwofirmsAandB:firmAisaU.S.–basedmultinationalandfirmBisaU.K.–basedmultinational.Bothfirmswishtofinanceaprojectineachother’scountryofthesamesize.Theirborrowingopportunitiesaregiveninthetablebelow.AnExampleofaCurrencySwapC$9.4%AnExampleofaCurrencySwapFirmB$8%￡12%SwapBankFirmA￡11%$8%￡12%$9.4%AnExampleofaCurrencyAnExampleofaCurrencySwap$8%￡12%FirmBSwapBankFirmA￡11%$8%$9.4%￡12%A’snetpositionistoborrowat￡11%Asaves￡.6%AnExampleofaCurrencySwap$AnExampleofaCurrencySwap$8%￡12%FirmBSwapBankFirmA￡11%$8%$9.4%￡12%B’snetpositionistoborrowat$9.4%Bsaves$.6%AnExampleofaCurrencySwap$AnExampleofaCurrencySwap$8%￡12%FirmBTheswapbankmakesmoneytoo:AtS0($/￡)=$1.60/￡,thatisagainof$124,000peryearfor5years.Theswapbankfacesexchangeraterisk,butmaybetheycanlayitoff(inanotherswap).1.4%of$16millionfinancedwith1%of￡10millionperyearfor5years.SwapBankFirmA￡11%$8%$9.4%￡12%AnExampleofaCurrencySwap$VariationsofBasicSwapsCurrencySwapsfixedforfixedfixedforfloatingfloatingforfloatingamortizingInterestRateSwaps

zero-forfloatingfloatingforfloatingExoticaForaswaptobepossible,twohumansmustliketheidea.Beyondthat,creativityistheonlylimit.VariationsofBasicSwapsCurreRisksofInterestRateandCurrencySwapsInterestRateRiskInterestratesmightmoveagainsttheswapbankafterithasonlygottenhalfofaswaponthebooks,orifithasanunhedgedposition.BasisRiskIfthefloatingratesofthetwocounterpartiesarenotpeggedtothesameindex.ExchangeRateRiskIntheexampleofacurrencyswapgivenearlier,theswapbankwouldbeworseoffifthepoundappreciated.RisksofInterestRateandCurRisksofInterestRateandCurrencySwapsCreditRiskThisisthemajorriskfacedbyaswapdealer—theriskthatacounterpartywilldefaultonitsendoftheswap.MismatchRiskIt’shardtofindacounterpartythatwantstoborrowtherightamountofmoneyfortherightamountoftime.SovereignRiskTheriskthatacountrywillimposeexchangeraterestrictionsthatwillinterferewithperformanceontheswap.RisksofInterestRateandCurPricingaSwapAswapisaderivativesecuritysoitcanbepricedintermsoftheunderlyingassets:Howto:Plainvanillafixedforfloatingswapgetsvaluedjustlikeabond.Currencyswapgetsvaluedjustlikeanestofcurrencyfutures.PricingaSwapAswapisaderi25.7ActualUseofDerivativesBecausederivativesdon’tappearonthebalancesheet,theyarepresentachallengetofinancialeconomistswhowhichtoobservetheiruse.Surveyresultsappeartosupportthenotionofwidespreaduseofderivativesamonglargepubliclytradedfirms.Foreigncurrencyandinterestratederivativesarethemostfrequentlyused.25.7ActualUseofDerivatives25.8Summary&ConclusionsThischaptershowsanumberofhedgingstrategies.Ashorthedgeinvolvesanagreementtoselltheunderlyingassetinthefuture.Alonghedgeinvolvesanagreementtobuytheunderlyingassetinthefuture.Swapscanalsobeusedtohedge;aswapcanbeviewedasaportfoliooffutureswithdifferentmaturities.25.8Summary&ConclusionsThisChapterOutline25.1ForwardContracts25.2FuturesContracts25.3Hedging25.4InterestRateFuturesContracts25.5DurationHedging25.6SwapContracts25.7ActualUseofDerivatives25.8Summary&ConclusionsChapterOutline25.1ForwardCo25.1ForwardContractsAforwardcontractspecifiesthatacertaincommoditywillbeexchangedforanotherataspecifiedtimeinthefutureatpricesspecifiedtoday.Itsnotanoption:bothpartiesareexpectedtoholduptheirendofthedeal.Ifyouhaveeverorderedatextbookthatwasnotinstock,youhaveenteredintoaforwardcontract.25.1ForwardContractsAforwar25.2FuturesContracts:PreliminariesAfuturescontractislikeaforwardcontract:Itspecifiesthatacertaincommoditywillbeexchangedforanotherataspecifiedtimeinthefutureatpricesspecifiedtoday.Afuturescontractisdifferentfromaforward:Futuresarestandardizedcontractstradingonorganizedexchangeswithdailyresettlement(“markingtomarket”)throughaclearinghouse.25.2FuturesContracts:PrelimFuturesContracts:PreliminariesStandardizingFeatures:ContractSizeDeliveryMonthDailyresettlementMinimizesthechanceofdefaultInitialMarginAbout4%ofcontractvalue,cashorT-billsheldinastreetnameatyourbrokerage.FuturesContracts:PreliminariDailyResettlement:AnExampleSupposeyouwanttospeculateonariseinthe$/￥exchangerate(specificallyyouthinkthatthedollarwillappreciate).Currently$1=￥140.The3-monthforwardpriceis$1=￥150.DailyResettlement:AnExampleDailyResettlement:AnExampleCurrently$1=￥140anditappearsthatthedollarisstrengthening.Ifyouenterintoa3-monthfuturescontracttosell￥attherateof$1=￥150youwillmakemoneyiftheyendepreciates.Thecontractsizeis￥12,500,000Yourinitialmarginis4%ofthecontractvalue:DailyResettlement:AnExampleDailyResettlement:AnExampleIftomorrow,thefuturesrateclosesat$1=￥149,thenyourposition’svaluedrops.Youroriginalagreementwastosell￥12,500,000andreceive$83,333.33:Youhavelost$559.28overnight.But￥12,500,000isnowworth$83,892.62:DailyResettlement:AnExampleDailyResettlement:AnExampleThe$559.28comesoutofyour$3,333.33marginaccount,leaving$2,774.05Thisisshortofthe$3,355.70requiredforanewposition.Yourbrokerwillletyouslideuntilyourunthroughyourmaintenancemargin.Thenyoumustpostadditionalfundsoryourpositionwillbeclosedout.Thisisusuallydonewithareversingtrade.DailyResettlement:AnExampleSelectedFuturesContractsSelectedFuturesContractsFuturesMarketsTheChicagoMercantileExchange(CME)isbyfarthelargest.Othersinclude:ThePhiladelphiaBoardofTrade(PBOT)TheMidAmericaCommoditiesExchangeTheTokyoInternationalFinancialFuturesExchangeTheLondonInternationalFinancialFuturesExchangeFuturesMarketsTheChicagoMerTheChicagoMercantileExchangeExpirycycle:March,June,September,December.Deliverydate3rdWednesdayofdeliverymonth.Lasttradingdayisthesecondbusinessdayprecedingthedeliveryday.CMEhours7:20a.m.to2:00p.m.CST.TheChicagoMercantileExchangCMEAfterHoursExtended-hourstradingonGLOBEXrunsfrom2:30p.m.to4:00p.mdinnerbreakandthenbackatitfrom6:00p.m.to6:00a.m.CST.SingaporeInternationalMonetaryExchange(SIMEX)offerinterchangeablecontracts.There’sothermarkets,butnoneareclosetoCMEandSIMEXtradingvolume.CMEAfterHoursExtended-hoursWallStreetJournalFuturesPriceQuotesExpirymonthOpeningpriceHighestpricethatdayLowestpricethatdayClosingpriceDailyChangeHighestandlowestpricesoverthelifetimeofthecontract.NumberofopencontractsWallStreetJournalFuturesPrBasicCurrencyFuturesRelationshipsOpenInterestreferstothenumberofcontractsoutstandingforaparticulardeliverymonth.Openinterestisagoodproxyfordemandforacontract.Somerefertoopeninterestasthedepthofthemarket.Thebreadthofthemarketwouldbehowmanydifferentcontracts(expirymonth,currency)areoutstanding.BasicCurrencyFuturesRelatio25.3HedgingTwocounterpartieswithoffsettingriskscaneliminaterisk.Forexample,ifawheatfarmerandaflourmillenterintoaforwardcontract,theycaneliminatetheriskeachotherfacesregardingthefuturepriceofwheat.Hedgerscanalsotransferpricerisktospeculatorsandspeculatorsabsorbpriceriskfromhedgers.Speculating:Longvs.Short25.3HedgingTwocounterpartiesHedgingandSpeculatingExampleYouspeculatethatcopperwillgoupinprice,soyougolong10coppercontractsfordeliveryin3months.Acontractis25,000poundsincentsperpoundandisat$0.70perpoundor$17,500percontract.Iffuturespricesriseby5cents,youwillgain: Gain=25,000×.05×10=$12,500Ifpricesdecreaseby5cents,yourlossis: Loss=25,000×-.05×10=-$12,500HedgingandSpeculatingExamplHedging:Howmanycontacts?Youareafarmerandyouwillharvest50,000bushelsofcornin3months.Youwanttohedgeagainstapricedecrease.Cornisquotedincentsperbushelat5,000bushelspercontract.Itiscurrentlyat$2.30centsforacontract3monthsoutandthespotpriceis$2.05.Tohedgeyouwillsell10cornfuturescontracts:Nowyoucanquitworryingaboutthepriceofcornandgetbacktoworryingabouttheweather.Hedging:Howmanycontacts?You25.4InterestRateFuturesContractsPricingofTreasuryBondsPricingofForwardContractsFuturesContractsHedginginInterestRateFutures25.4InterestRateFuturesConPricingofTreasuryBondsConsideraTreasurybondthatpaysasemiannualcouponof$CforthenextTyears:TheyieldtomaturityisrValueoftheT-bondunderaflattermstructure=PVoffacevalue+PVofcouponpayments…0 123 2TPricingofTreasuryBondsConsiPricingofTreasuryBondsIfthetermstructureofinterestratesisnotflat,thenweneedtodiscountthepaymentsatdifferentratesdependinguponmaturity=PVoffacevalue+PVofcouponpayments…0 123 2TPricingofTreasuryBondsIfthPricingofForwardContractsAnN-periodforwardcontractonthatT-Bond…0 N

N+1 N+2N+3 N+2TCanbevaluedasthepresentvalueoftheforwardprice.PricingofForwardContractsAnFuturesContractsThepricingequationgivenabovewillbeagoodapproximation.Theonlyrealdifferenceisthedailyresettlement.FuturesContractsThepricingeHedginginInterestRateFuturesAmortgagelenderwhohasagreedtoloanmoneyinthefutureatpricessettodaycanhedgebysellingthosemortgagesforward.Itmaybedifficulttofindacounterpartyintheforwardwhowantstheprecisemixofrisk,maturity,andsize.It’slikelytobeeasierandcheapertouseinterestratefuturescontractshowever.HedginginInterestRateFutur25.5DurationHedgingAsanalternativetohedgingwithfuturesorforwards,onecanhedgebymatchingtheinterestrateriskofassetswiththeinterestrateriskofliabilities.Durationisthekeytomeasuringinterestraterisk.25.5DurationHedgingAsanaltDurationmeasuresthecombinedeffectofmaturity,couponrate,andYTMonbond’spricesensitivityMeasureofthebond’seffectivematurityMeasureoftheaveragelifeofthesecurityWeightedaveragematurityofthebond’scashflows25.5DurationHedgingDurationmeasuresthecombinedDurationFormulaDurationFormulaCalculatingDurationCalculatethedurationofathree-yearbondthatpaysasemi-annualcouponof$40,hasa$1,000parvaluewhentheYTMis8%semiannually?CalculatingDurationCalculateCalculatingDurationDurationisexpressedinunitsoftime;usuallyyears.CalculatingDurationDurationiDurationThekeytobondportfoliomanagementProperties:Longermaturity,longerdurationDurationincreasesatadecreasingrateHighercoupon,shorterdurationHigheryield,shorterdurationZerocouponbond:duration=maturityDurationThekeytobondportfo25.6SwapsContracts:DefinitionsInaswap,twocounterpartiesagreetoacontractualarrangementwhereintheyagreetoexchangecashflowsatperiodicintervals.Therearetwotypesofinterestrateswaps:Singlecurrencyinterestrateswap“Plainvanilla”fixed-for-floatingswapsareoftenjustcalledinterestrateswaps.Cross-CurrencyinterestrateswapThisisoftencalledacurrencyswap;fixedforfixedratedebtserviceintwo(ormore)currencies.25.6SwapsContracts:DefinitiTheSwapBankAswapbankisagenerictermtodescribeafinancialinstitutionthatfacilitatesswapsbetweencounterparties.Theswapbankcanserveaseitherabrokeroradealer.Asabroker,theswapbankmatchescounterpartiesbutdoesnotassumeanyoftherisksoftheswap.Asadealer,theswapbankstandsreadytoaccepteithersideofacurrencyswap,andthenlaterlayofftheirrisk,ormatchitwithacounterparty.TheSwapBankAswapbankisaAnExampleofanInterestRateSwapConsiderthisexampleofa“plainvanilla”interestrateswap.BankAisaAAA-ratedinternationalbanklocatedintheU.K.andwishestoraise$10,000,000tofinancefloating-rateEurodollarloans.BankAisconsideringissuing5-yearfixed-rateEurodollarbondsat10percent.Itwouldmakemoresensetoforthebanktoissuefloating-ratenotesatLIBORtofinancefloating-rateEurodollarloans.AnExampleofanInterestRateAnExampleofanInterestRateSwapFirmBisaBBB-ratedU.S.company.Itneeds$10,000,000tofinanceaninvestmentwithafive-yeareconomiclife.FirmBisconsideringissuing5-yearfixed-rateEurodollarbondsat11.75percent.Alternatively,firmBcanraisethemoneybyissuing5-yearfloating-ratenotesatLIBOR+?percent.FirmBwouldprefertoborrowatafixedrate.AnExampleofanInterestRateAnExampleofanInterestRateSwapTheborrowingopportunitiesofthetwofirmsare:AnExampleofanInterestRateAnExampleofanInterestRateSwapBankATheswapbankmakesthisoffertoBankA:YoupayLIBOR–1/8%peryearon$10millionfor5yearsandwewillpayyou103/8%on$10millionfor5yearsSwapBankLIBOR–1/8%103/8%AnExampleofanInterestRateAnExampleofanInterestRateSwapHere’swhat’sinitforBankA:Theycanborrowexternallyat10%fixedandhaveanetborrowingpositionof-103/8+10+(LIBOR–1/8)=LIBOR–?%whichis?%betterthantheycanborrowfloatingwithoutaswap.10%?%of$10,000,000=$50,000.That’squiteacostsavingsperyearfor5years.SwapBankLIBOR–1/8%103/8%BankAAnExampleofanInterestRateAnExampleofanInterestRateSwapC