Class Note 12Hedging Interest Rate Risk

1•Objectives:»AnalyzethevalueofinterestrateswapsandhowtheyeffectthedurationofaFI’snetworth.»AnalyzethevalueofforwardrateagreementsandhowtheyeffectthedurationofaFI’snetworth.»ValueforwardandfuturescontractsonbondsanddeterminehowtheyeffectthedurationofaFI’snetworth.»Considerhowinterestrateoptionssuchasbondoptions,caps,floors,collars,andswaptionscaninsureagainstinterestraterisk.HedgingInterestRateRisk2•Wehaveanalyzedhowtovaluefixed-cashflowandfloating-cashflowbondsandloans.•Wealsohavediscussedhowtodeterminetheduration(interestraterisk)ofthesefixedandfloatingrateinstrumentsaswellasthedurationofafinancialintermediary’s(FI’s)networth.•ThebestwaytolimittheinterestrateriskofaFI’snetworthmaynotbetomatchthedurationsofitsassetsandliabilities.•ItmaybebesttolettheFI’scustomersdeterminethedurationsofitsassetsandliabilities,andthentocontroltheresultinginterestrateriskusinginterestratederivatives.3•Swapcontractsareagreementsbetweentwopartiestoexchangeaseriesofassetsorcashflowsatspecifiedfuturedates.•Inparticular,aninterestrateswapisacontracttoexchangeinterestpaymentsonagivenamountof“notional”principalatspecifiedfuturedates.•Themostcommontypeof(plainvanilla)interestrateswapiswhereonepartypaysfloatingrateinterestpayments(usuallyequaltosix-monthLIBOR)inexchangefortheotherpartypayingfixedrateinterestpayments.•TheseswapsaresoldbydealersinlargebankstoFIsandothercorporationsthatseektohedgeinterestraterisk.InterestRateSwaps4•Example:Abank’sdepositorsusuallyprefershortmaturitiesthatcanbereadilyliquidated.Itsborrowingcustomersmaypreferlongermaturityloansatfixed-interestratesbecausetheloansfinancelongermaturityprojectsandborrowerswishtoknowtheirexactfixed-interestborrowingcosts.•Ifabanksatisfiesbothitsborrowinganddepositorcustomers,itslongerdurationloansfinancedbyshorterdurationdepositsexposesthebanktointerestraterisk.•Considerabankthatmakesa$1million,five-yearloanatafixed8%interestrate,wheretheborrowerisrequiredtomakesemi-annualpaymentsof½(.08)($1m)=$40,000andrepaythe$1mprincipalatmaturity.Thebankfinancesthisloanbyissuing$1mofsix-monthmaturityCDs.5•Thesetransactionsexposethebanktointerestraterisk.Ifsix-monthmarketinterestratesriseabove8%,thebank’sinterestpaymentsonitsCDswillexceedits8%loanpayments.•Thebankcanhedgethisinterestrateexposurebybecomingafixed-ratepayerinafive-yearinterestrateswapcontract.Theswapagreementwillrequirethebanktopaysemi-annualinterestata7%annualrateonanotionalprincipalof$1m.Inreturn,thebankreceivessemi-annualsix-monthLIBORpayments.Withthisswap,thebank’sonandoff-balancesheetassetsandliabilitiesarenow:UnhedgedBankBalanceSheetAssetsLiabilitiesFixed-Rate5yearLoanSix-MonthCDs(LongDuration)(ShortDuration)6BankBalanceSheetAssetsLiabilitiesFixed-Rate5yearLoanSix-MonthCDs(LongDuration)(ShortDuration)Off-BalanceSheet(Swap)AssetsLiabilitiesLIBORSwapPaymentsFixed-RateSwapPayments(ShortDuration)(LongDuration)•Becausesix-monthLIBORwillmovewiththeinterestratethatthebankpaysonitsCDs,theLIBORswappaymentswillcoverthebank’srequiredCDinterestpayments.Thenetresultisthatthedurationofon-andoff-balancesheetassetsareequaltothedurationofon-andoff-balancesheetliabilities.7•HowcanwevalueaninterestrateswapandcalculateitseffectonthedurationofaFI’snetworth?Thisiseasyoncewerecognizethataninterestrateswapisidenticaltooppositepositionsinafixed-couponbondandafloatingcouponbond.•Afloating(fixed)ratepayerinann-yearinterestrateswaphasalong(short)positioninann-yearfixed-couponbondandashort(long)positioninann-yearfloating-couponbond.•Example:Aninsurancecompanyhaslongerdurationliabilities(insurancepolicies)thanassets.Tohedgeitsrisk,itbecomesafloatingratepayer(fixedratereceiver)ina$5m.10-yearswaptiedto6-monthLIBORandhavingafixed-rateof6%.•Thus,thevalueofthisswapisthedifferencebetweena$5m.,10-yearcouponbondwithanannualcouponrateof6%lessa$5m.,10-yearfloatingratebondtiedtosix-monthLIBOR.8•Specifically,consideraswaphavingexactlynyearsuntilmaturityandmakingsemi-annualpayments,withthenextpaymentbeingexactly6monthsfromnow.LetFV=swap’snotionalprincipal.c=annualcouponrateofswap(½cFVpaidevery6months).i½()bethesemi-annuallycompoundedyieldonaZCBthatmaturesinyears,sothatP()=1/[1+½i½()]2.•Thevalueofthefixed-ratecomponentoftheswap,PVfx,issimplythepresentvalueofann-yearfixed-couponbond:112222121221112222=11ntfxtntnttcPVPFVPnFVcFVFViin9•Thevalueofthefloatingratecomponentoftheswap,PVfl,isPVfl=FVbecauseafloating-ratebondequalsitsparvalueatthecouponresetdate.•Hence,thevalueoftheswaptothefloatingratepayer(fixedratereceiver)is•Whenthetwopartiesfirstagreetotheswap,itsvalueequalszerobecausethemarket-determinedcouponrate,c,issetsothatthefixed-ratecomponentoftheswapsellsforitsparvalue,FV,thatis,cequalsthefixed-ratebond’sinitialYTM.221=2swapfxflnttPVPVPVcPFVPnFVFV10•However,aftertheswapisagreedto,changesinmarketinterestratesimplythatPVswapwillhaveanegative(positive)valueifmarketratesincrease(decrease).•Example:A5-year$100m.swapwasagreedto3yearsagowithac=8.00%couponrate.Currently,theswaphasexactly2yearstomaturityandthesemi-annuallycompounde