銀行是否使用利率互換 Do Banks Hedge Using Interest Rate Swaps

NBERWORKINGPAPERSERIES

DOBANKSHEDGEUSINGINTERESTRATESWAPS?

LihongMcPhail

PhilippSchnabl

BruceTuckman

WorkingPaper31166

/papers/w31166

NATIONALBUREAUOFECONOMICRESEARCH

1050MassachusettsAvenue

Cambridge,MA02138

April2023

Theresearchpresentedinthispaperwasproducedineachauthor’sofficialcapacityasaresearcheconomistorconsultantwiththeCommission.TheOfficeoftheChiefEconomist(OCE)hasapprovedthepaperforreleasetothepublic.OCEandCFTCeconomistsproduceoriginalresearchonabroadrangeoftopicsrelevanttotheCFTC’smandatetoregulatecommodityfuturemarkets,commodityoptionsmarkets,andtheexpandedmandatetoregulatetheswapmarketspursuanttotheDodd-FrankWallStreetReformandConsumerProtectionAct.Theanalysesandconclusionsexpressedinthispaperarethoseoftheauthor(s)anddonotreflecttheviewsofotherCommissionstaff,theOfficeoftheChiefEconomist,theCommission,ortheNationalBureauofEconomicResearch.Thepaperisconsideredagovernmentworkproductandmaynotbeindividuallycopyrighted.

NBERworkingpapersarecirculatedfordiscussionandcommentpurposes.Theyhavenotbeenpeer-reviewedorbeensubjecttothereviewbytheNBERBoardofDirectorsthataccompaniesofficialNBERpublications.

?2023byLihongMcPhail,PhilippSchnabl,andBruceTuckman.Allrightsreserved.Shortsectionsoftext,nottoexceedtwoparagraphs,maybequotedwithoutexplicitpermissionprovidedthatfullcredit,including?notice,isgiventothesource.

DoBanksHedgeUsingInterestRateSwaps?

LihongMcPhail,PhilippSchnabl,andBruceTuckman

NBERWorkingPaperNo.31166

April2023

JELNo.G21,G32

ABSTRACT

Weaskwhetherbanksuseinterestrateswapstohedgetheinterestrateriskoftheirassets,primarilyloansandsecurities.Tothisend,weuseregulatorydataonindividualswappositionsforthelargest250U.S.banks.Wefindthattheaveragebankhasalargenotionalamountofswaps--$434billion,ormorethan10timesassets.Butafteraccountingforthesignificantextenttowhichswappositionsoffseteachother,theaveragebankhasessentiallynonetinterestrateriskfromswaps:a100-basis-pointincreaseinratesincreasesthevalueofitsswapsby0.1%ofequity.Thereisvariationacrossbanks,withsomebankswappositionsdecreasingandsomeincreasingwithrates,butaggregatingswappositionsatthelevelofthebankingsystemrevealsthatmostswapexposuresareoffsetting.Therefore,asadescriptionofprevailingpractice,weconcludethatswappositionsarenoteconomicallysignificantinhedgingtheinterestrateriskofbankassets.

LihongMcPhail

CommodityFuturesTradingCommission

115521stStreet,NW

Washington,DC20581

lmcphail@

BruceTuckman

44West4thSt

NewYork

NY10012,USA

btuckman@

PhilippSchnabl

SternSchoolofBusiness

NewYorkUniversity

44WestFourthStreet

NewYork,NY10012

andNBER

schnabl@

1

I.Introduction

Banksareinthebusinessofborrowingshortandlendinglong,whichexposesthemtointerestraterisk.Inparticular,onthelendingside,thevaluesof?xed-rateloansandinvestmentsin?xed-ratesecuritiesdeclineswhenmarketinterestratesrise.

MarketinterestratesincreasedfromJanuary2022toMarch2023ascentralbankstight-enedmonetarypolicytocombatin?ation.IntheUnitedStates,theFederalReserveBankincreasedthemarketshort-termrate,i.e.,theFedFundsrate,fromcloseto0%inearlyJanuary2022toaround4.5%inFebruary2023.Furthermore,overthesameperiod,thelong-termormorespeci?cally10-yearrate–whichcanbeconceptualizedasdependingontheexpectedsequenceofshort-termratesplusatermpremium–increasedfromaround1.5%to4%.Notsurprisingly,thesesigni?cantincreasesinmarketinterestratessigni?-cantlyloweredthevalueofbankloansandsecurities.Drechsleretal.(2023a),conductingasimpleback-of-the-envelopecalculation,estimatethattheU.S.bankingsectorlostaround$700billiononsecurityinvestmentsandatotalof$1.75trilliononbothsecuritiesandloans.

Theselargelossesraisethequestionofwhetherbanksuseinterestrateswaps(“swaps”)tohedgetheirholdingsofsecuritiesandloans.Becauseswapvaluesarethemselvessubjecttointerestraterisk,swapscanandarecommonlyusedtomanageinterestrateriskexposures,notonlyinthebankingsectorbutacrossthe?nancialsystem.AccordingtotheCommodityFuturesTradingCommission,thenotionalamountoutstandingofswapsattheendof2021was$215trillion.

2

Thereis,ofcourse,acosttohedgingsecuritiesandloanswithswaps:whatevertermpremiumisearnedfromholdingsecuritiesandloansislikelygivenupbyhedgingwithswaps.Butthisobservationdoesnotdiminishtheimportanceofourprimaryquestion,namely,whetherornotbanksuseswapstohedgethevalueoftheirassetsagainstchangesinrates.

Itisdif?cultforresearchersandthepublictoanswerthisquestionbecausegranulardataastobankswappositionsarenotpubliclyavailable.Intheory,thereportedmarketvaluesofswapspositionsovertime,asinterestrateschange,canbeusedtoback-outtheinterestrateexposureofthosepositions.Inpractice,however,theseeffortsarecomplicatedbyaccountingcomplexitiesandbythefactthatswappositionstypicallychangebetweenthereportingdatesoftheirmarketvalues.

Bycontrast,thispapercanpreciselymeasuretheinterestrateexposureofbankswappo-sitionsbecausewehaveregulatory(non-public)contract-leveldataonthosepositions.Our

2Baker,Mixon,andOrlov(2022).

2

analysisfocusesonthepositionsofthelargest250U.S.commercialbanks,whichamounttomorethan8millioncontractsandconstitutenearlytheentiretyofswappositionsoftheU.S.bankingsector.Inthisway,ourdataallowustomeasureandevaluatetheinterestrateexposureofswapsbothatthelevelofindividualbanksandforthebankingsectorinaggregate.

Wepresentbankswappositionsusingtwocommonmetrics.The?rst,notionalamount,measuresthetotaldollaramount(orforeigncurrencyamountconvertedtodollars)thatisreferencedbyallrelevantswappositions.Forexample,thenotionalamountofa?xed-for-?oatinginterestrateswapisthedollaramountusedtocalculatetheinterestratepaymentsrequiredbythecontract.Notionalamountsarestraightforwardtocomputeandwidelyreported,althoughasdiscussedlater,theycannotbeinterpretedasmeasuringtheinterestrateexposureofswappositions.

Thenotionalamountoftheswappositionsofthelargest250U.S.banksis$95trillion,whichislargeandequaltoaboutseventimesthetotalassetsoftheU.S.bankingsystem.Themagnitudeisevenlargerforbankswapdealers,thatis,forbanksthatmakemarketsinswaps.Thenotionalamountoftheirswappositionsis$94trillionor11timestheirassets.Alternatively,theaveragenotionalamountofbankswapdealersis$8.5trillionandtheiraverageratioofnotionalamounttoassetsis52.

ThesecondmetricweusetopresentbankswappositionsisDV01(thedollarvalueofan’01),whichisthechangeinvalueofaswappositionduetoaone-basis-pointdeclineinasuitably-de?nedinterestrate.Computingthisdirectmeasureofriskisimpossiblewithoutdetailedinformationabouttherelevantswappositionsthatisnotpubliclyavailable.DV01isusedtomeasureinterestraterisknotonlybybanks,butwidelyacrossthe?nancialindustry,andnotonlyforswaps,butforallassetswithvaluesthataresensitivetointerestrates,includingabank’ssecuritiesandloans.

Despitethelargenotionalamountsjustdescribed,we?ndthattheswappositionoftheaverageU.S.bankhasessentiallyzeroexposuretointerestrates.Thestarkdifferencebe-tweenthetwometricsarisesmostlybecausethenotionalamountofaportfolioofswapsaddsthenotionalamountsofindividualpositions,eventhoughtypicallysomepositionsin-creaseinvalueasratesdeclinewhileotherpositionsdecreaseinvalueasratesdecline.Putanotherway,theinterestraterisksofswappositionswithinabanktypicallyoffseteachother.

3

Inanycase,theaverageDV01acrossthelargestU.S.banksisonly$3millionandthemedianDV01isonly$10,000.Toputthesevaluesintoperspective,comparebanks’swapDV01–theirinterestrateriskexposureinswaps–tobankequity–theircapacityto

3Anotherreasonforthediscrepancyisthatthereisaverylargenotionalamountofshort-termswaps,whichhaveparticularlylowexposuretointerestrates.SeeBakeratal.(2021).

3

absorbrisk.ThemeanratioofDV01tobankequityisonlyx0.001%andthemedianratio

islessthan0.001%.Putanotherway,a100basis-pointincreaseininterestrateschangesaveragebankequitybylessthan0.1%.

TheDV01ofbankswappositionsisalsoeconomicallysmallwhencomparedwiththeinterestrateriskofbankassets.Drechsleretal.(2021)reportthattheaverageU.S.bankhasanassetdurationofaround3.9years(i.e.,a100-basis-pointincreaseininterestratesreducesassetvalueby3.9%).Givenbanksleverageofabout10to1,thisdeclineinbankassetsreducesbankequityby39%.Hence,bankswappositionsdonothavesigni?cantinterestrateriskrelativetothatofbankassets.Equivalently,theaveragebankdoesnotrelyonswapstohedgetheinterestriskofitssecuritiesandloans.

Thisconclusionholdsbothforthelargebanksthatareandthatarenotswapdealers.TheaverageswapdealerhasanaverageDV01of$52million,orabout0.01%ofbankequity,whichmeansthata100basis-point-increaseinratesreducesbankequityby1.0%.Fortheaveragenon-swap-dealer,DV01islessthan$10,000and,inmagnitude,about0.002%ofbankequity.Again,theseestimatesareeconomicallysmallwhencomparedtotheinterestrateriskofbankassets.

WegainadditionalinsightfromthevariationofDV01acrossthe250largestbanks.DV01

variesfromx$1millionatthe5thpercentileto$3millionatthe95thpercentile,andthe

ratioofDV01tobankequityvariesfrom-0.031%to0.025%.ThedistributionoftheratioofDV01toequityisclosetosymmetric,implyingthatlossesfrominterestratechangesatonebankareoffsetbygainsatanotherbank.Furthermore,forsomebanksthenegativeDV01ofswappositionsoffsetssomeoftheDV01ofassets,whileforotherbanksthepositiveDV01ofswappositionsaddstotheDV01ofassets.But,asdiscussedabove,theseoffsettingoradditivecontributionstoDV01arelimitedrelativetotheDV01ofassets.Hence,theswappositionsofbanksdonotseemtobemotivatedbytheinterestrateriskofbankassets.

Wealsoanalyzetheinterestrateriskofswappositionsforthebankingsystemasawhole,proxiedbythatofthelargest250banks.AggregateDV01is$585million,or0.038%ofaggregatebankequity.Alternatively,a100-basis-pointincreaseinrateswouldlowerthevalueofaggregatebankequityby3.8%.Thesuggestion,again,isthatswappositionsinthebankingindustryarenotprimarilymotivatedbytheinterestriskofbankassets.

4

Insummary,whilethenotionalamountofbankswappositionsisverylarge,theinterestrateriskofthosepositionsfortheaveragebankisclosetozero,bothforswapdealersandnon-swap-dealers.Furthermore,whiletheaggregateinterestrateriskofswappositionsof

4NotethatdatafromtheCommodityFuturesTradingCommissionforQ12023showthatswap-dealerbankshavepositiveDV01,non-swap-dealerbankshavenegativeDV01,and,whencombined,thesepositionseffectivelycancelandresultinanessentiallyzeroexposureacrossthesector.

/sites/

default/files/2023-01/ENNs_IRS_2022Q3_ada.pdf

.

4

thebankingsectorissmall,forsomebanksswapssomewhatoffsettheriskofassetsandforothersswapssomewhataddtotheriskofassets.Weconcludethatbankswappositionsarenoteconomicallysigni?cantinhedgingtheinterestrateriskofbankassets.

Weemphasizethatthese?ndingsdonotimplythatindividualbanksorthebankingsys-temisunhedgedtointerestraterisk.Drechsleretal.(2021)showsthatbankshedgelong-termassetholdingswiththeirdepositfranchise.Whilethedepositfranchiseisdif?-culttoanalyze,asitsvaluationdependsonassumptionsaboutdepositorbehavior,Drechsleretal.(2023b)provideback-of-the-envelopeestimates.They?ndthatfromJanuary2022toMarch2023,asinterestratesincreased,thevalueofthebankingsector’sdepositfranchiseincreasedbyaround$1.7trillion,whichisthesameorderofmagnitudeasthelossesonbankassetsoverthatperiod.Theyemphasizethatthisvaluationisuncertainanddependsonbehavioralassumptionsregardingdepositorbehavior.

Ourpapercontributestotheliteratureontheinterestrateriskofbankswappositions.Brewer,Minton,andMoser(2000)showthatbanksusinginterestratederivativesexpe-riencegreatergrowthintheirbooksofcommercialandindustrialloans.Purnanandam(2007)?ndsthatbanksusingderivativesdonotneedtoadjusteitherlendingvolumesorthegapbetweenthematuritiesofassetsandliabilitiesinresponsetotightermonetarypol-icy.GortonandRosen(1995)deviseamethodologytoinferexposurefromacombinationofnotionalamounts,reportedswapmarketvalues,andassumptionsabouttheevolutionofswappositionsovertime.Stulz(2004)analyzesthecostandbene?tsofderivativessuchasinterestrateswaps.Begenauet.al(2015)estimatetheinterestrateexposureofbankswappositionsfromchangesinthemarketvaluesofswappositionsovertime.Hoffmannet.al(2019)analyzethedistributionofinterestrateriskofEuropeanbanksusingregulatorydata.Drechsleretal.(2021)showthatthedepositfranchisefunctionslikeswappositionsinhedgingtheinterestrateriskofbankassets.Bakeretal.(2021)studyhowswapsareused

totranferinterestrateriskfromvarioussectorstoothers,includingbanks.OurpaperisuniqueintheexistingliteratureinstudyingthissubjectusingregulatorydataonindividualswappositionsthroughouttheU.S.bankingsystem.

II.Aggregateinterestratederivativepositions

InterestratederivativepositionsintheU.S.bankingsectorhavegrownenormouslysincethebirthofthemarketinthe1980s.PanelAofTable

1

givesvarioussummarystatisticscomputedfromcallreportsonbanks’usageofinterestratederivativesfrom1985to2019,in?ve-yearintervals.While1995andlaterdataincludeinterestratederivativesother

5

thanswaps,e.g.,exchange-tradedderivatives,thevastmajorityofpositionsareswaps,asdiscussedfurtherbelow.Inanycase,thenotionalamountofinterestratederivativesin1985was$186billion,whichwasroughlythesizeofbankequityatthetime.By2010,notionalvaluehadincreasedmorethan1,000-foldto$193.4trillion,whichwas148timesbankequity.Notionalamountsdeclinedafter2010becausetheregulatorymandatetoclearswapsfacilitated“compression,”thatis,thereductionofnotionalamountswithoutalteringriskpro?les.

5

Interestratederivativenotionalamountsarehighlyconcentratedinthelargestbanks.PanelAofTable

1

showsthatthepercentageofallcommercialbankswithinterestratederivativepositionsincreasedfrom2%to25%from1985to2019.Hence,whiletheper-centageofbankshavingexposuretothesederivativesgraduallyincreased,thatpercentageremainslimited.Or,putanotherway,themedianbankhasnoexposuretothesederivatives.Furthermore,PanelBshowsthattheparticipationratesofthelargest250banks,byassetsize,aremuchmoresigni?cant,growingfrom53%to91%,andthattheirnotionalamountsdominatethemarket.Eventhoughthelargest250banksconstitutelessthan5%ofbanks,

theirnotionalamountsaccountformorethan99.9%ofallnotionalamountovertheentire

history.Notsurprisinglythen,notionalamountrelativetoassetsortoequityisgreaterforthelargestbanksthanforbankingsectorasawhole,peakingatabout19timesassetsin2010andremainingatarelativelyhighmultipleof8timesassetsin2019.

PanelCofTable

1

focusesonbanksregisteredwiththeCFTCasswapdealers,adesigna-tioncreatedbytheDodd-FrankActthatessentiallyidenti?esmarketmakers.Therewere12registeredswapdealersfrom2010to2018,and11in2019.Thedatashowthattheserelativelyfewdealersaccountforabout99%ofinterestratederivativenotionalamounts,$191trillionofthetotal$193trillionin2010and$122trillionofthetotal$125trillionin2019.Notionalamountrelativetoassetsforthisgroupislargerthanforthelargest250banksat29timesassetsin2010and13timesassetsin2019.

Table

2

providesadditionalinsightintotheconcentrationofnotionalamountsacrossbanksbylistingeachofthe20bankswiththelargestnotionalamountsasofDecember2019.Thefourlargestinthislistarealsothefourlargestbyassets;the?fth-largestwithrespecttonotionalamountisasigni?cantswapdealer;andthesixth-largestisasubsidiaryofoneofthelargestEuropeanbanksbyassets.Thesesixbanksareallswapdealers,and

5Beforetheclearingmandate,swapcontractswerebilateral,thatis,betweenpairsofindividualmarketparticipants.Sincethemandate,thevastmajorityofswapnotionalamountisbetweenindividualmarketparticipantsandaclearinghouseorcentralcounterparty(CCP).ThischangeinmarketstructureenabledcompressioncyclesinwhichtherisksofallswapsbetweeneachmarketparticipantandaCCPareaggregated,netted,andthenreplacedbyasmallernumberofswapsthatpreserveeachoftheseaggregatedandnettedrisks.

6

standoutwithnotionalamountsfrom$21.1trillionto$2.4trillion.Thesenotionalamountsarealsolargemultiplesofassets,rangingfromnearly35tomorethan4.5.Theremaining

14banksonthistop-20listhavesigni?cantlylowernotionalamounts.Fourofthemareswapdealers,butcollectivelytheyareprimarilyregional,mid-sizedbanks.Theirtotalno-tionalamountrangesfrom$413billionto$26billion,or,asmultiplesofassets,from1.56toabout0.34.

Allinall,Tables

1

and

2

showthatthenotionalamountofinterestratederivativesishighlyconcentratedinasmallnumberofbanks.Notonlyisalmostalloftheoutstandingnotionalamountaccountedforbythelargest250banks,butnotionalamountisalsoconcen-tratedintheverylargestofthesebanks,particularlyinswapdealers.Motivatedbythese?ndings,ourempiricalworkfocusesonthelargest250banksandwepayspecialattentiontoswapdealers.

III.Background,Data,andMeasurement

A.PrimeronInterestRateSwaps

Themostprevalentformofswapsisa?xed-for-?oatingswap,inwhichonepartyagreestoreceivea?xedrateandtopaya?oatingrateonsomenotionalamountfora?xedterm,whiletheotherpartyagreestopaythat?xedrateandtoreceivethat?oatingrateonthesamenotionalamountforthesameterm.Toillustratewithasimpleexample,supposethatBankAandBankBenterintoanagreementinwhichBankAwillreceiveannualinterestpaymentsfromBankBatarateof2%peryearfor10yearsonanotionalamountof$100millionand,inexchange,BankAwillpayBankBquarterlyinterestpaymentsonfuturerealizationsof3-monthLIBORfor10yearsonthesame$100million.

6

Inotherwords,BankAandBankBagreetoexchangeinterestpaymentssuchthatBankAreceivespaymentsbasedona?xedrateandmakespaymentsbasedona?oatingrate,whileBankBreceivespaymentsbasedona?oatingrateandmakespaymentsbasedona?xedrate.

The?xedrateof2%ontheswapintheexampleiscalledtheswaprateandisdeterminedbymarketconditionsatthetimeofthetrade.Moregenerally,theswaprateissetsuchthatthetwocounterpartiesarewillingtoenterintotheswapwithouteitherpayingtheotheranupfrontamount,or,equivalently,suchthatthevalueoftheswapatinitiationiszero.

6The?oating-rateindexofswapshastransitionedawayfromLIBORtoSOFR(SecuredOvernightFinanc-ingRate).Fordetailsonthistransitionsee,forexample,TuckmanandSerrat(2022),pp.289-295.Inanycase,becausethesampleperiodofthispaperfalls?rmlyintheLIBORregime,thetextdescribesswapsintermsofLIBOR.

7

The$100millioniscalledanotionalamountratherthanaprincipalamountorfaceamountbecauseitisusedonlytocalculatecontractualinterestratepayments.Thenotionalamountisnotpaidorreceivedbyeithercounterpartythroughtheswap.

Whilethevalueofaswapiszeroatinitiation,itsvaluechangesovertimeasinterestratechange.Intheexample,supposethatjustaftertheinitiationoftheswapthemarket10-yearswapratesuddenlydeclinedfrom2%to1%.FromtheperspectiveofBankA,thevalueoftheswap–commonlyreferredtoasits“netpresentvalue”orNPV–wouldthenincreasefrom$0toabout$9.5million:itlockedinreceiving2%over10yearsinamarketinwhichthefairrateisnowonly1%.Bythesamelogic,theNPVoftheswaptoBankBisapproximatelynegative$9.5million.If,ontheotherhand,themarket10-yearmarketswapratesuddenlyrosefrom2%to3%,thentheNPVoftheswapwouldbeaboutnegative$8.5milliontoBankAandpositive$8.5milliontoBankB.NotethatthepositiveNPVofonecounterpartytoaswapistypicallywellprotectedfromadefaultoftheothercounterpartythecollateralormarginpostedbythatcounterparty.

7

A?xed-for-?oatingswapessentiallyresemblesaleveredpurchaseofadefault-freebond?nancedbyshort-termborrowing.Inthecontextoftheexample,BankApaysnothingattheinitiationoftheswap;receives2%on$100millionover10years;andpaysthe?oatinginterestrateonthesameamountoverthesametimeperiod.Butthesecash?owsarethesameasthosefrompurchasinga10-yearbond?nancedfullybyshort-termborrowingovertimeatprevailingshort-termrates.Hence,the?xedreceiverina?xed-for-?oatingswap(BankAintheexample)maybesaidtobe“l(fā)ong”theswap,justasthepurchaserofabondislongthebond,whilethe?xedpayer(BankBintheexample)maybesaidtobe“short”theswap,justasashortsellerofabondisshortthebond.

8

Withthisbackground,thediscussioncanturntometricsof“exposure”forswaps.Forasingleswap,notionalamountisdirectlyrelatedtothesizeoftheinterestpaymentsex-changed,butisaverycoarsemeasureofinterestraterisk:theNPVofa1-year?xed-for-?oatingswapwithanotionalamountof$100millionismuchlessexposedtointerestrateriskthana30-year?xed-for-?oatingswapwiththesame$100millionnotionalamount.Andthenotionalamountofasingle?xed-for-?oatingswapisaverypoormeasureofcoun-terpartydefaultrisk:thecontractnevercallsfortheexchangeofnotionalamountsand,asjustmentioned,collateralarrangementtypicallyprotectpositiveNPVsfromcounterparty

7Formoredetailonthepricingofswapsandcollateralprotection,seeTuckmanandSerrat(2022),Chapters

2and13.

8Whilethisterminologyisconvenienthere,notethatpractitionersalmostalwaysspeakintermsof"re-

ceiving?xed"and"paying?xed"ratherthan”long"and”short,"respectively.Notetoothat,historically,theconventionwasactuallythereverseofthatsuggestedinthetext,namely,torefertoreceiving?xedas"short"andpaying?xedas”long,"asinGortonandRosen(1995).

8

defaults.

Foraportfolioofswaps,“l(fā)ongnotionalamount”isde?nedasthesumofthenotionalamountsofallindividualswapsthatincreaseinvaluewhenratesfall;“shortnotionalamount”isde?nedasthesumofthenotionalamountsofallindividualswapsthatdecreaseinvaluewhenratesfall;and“notionalamount”isde?nedasthesumoflongandshortno-tionalamounts.Longandshortnotionalamountssufferasmeasuresofinterestrateriskandcounterpartyriskalongthesamelinesasdoesthenotionalamountofanindividualswap.Totalnotionalamountisanevenworsemetricasitaddslongandshortexposures,whiletherisksofthelongandshortsidestypicallyoffseteachother.Netnotionalamount,de?nedasthedifferencebetweenthelongandshortnotionalamounts,correctsthisprob-lem,andisametricthatiscomparabletothenotionalamountofanindividualswap.

Anothercommonmetricofexposureforswapsisthemarketvalueofanindividualorofaportfolioofswaps,whichisde?nedasthesumoftheNPVsoftheindividualswapsinthatportfolio.Marketvalueisnotameasureoftheinterestrateriskofaswap,asitsimplyre?ectsthechangeinNPVfromtheinitiationoftheswaptothepresent.Putanotherway,theinterestrateriskofaswapcanbehighevenifitsmarketvalueofzero.Forthisreason,wedonotconsiderthemarketvalueasinformativeaboutaswap’sinterestraterisk.

9

OurpreferredmeasureoftheinterestrateriskofaswaporofaportfolioofswapsisDV01,whichisde?nedasthechangeintheNPVoftheswaporportfolioofswapsinresponsetoaone-basis-pointdeclineininterestrates.DV01isoneofthemostcommonly-usedmetricsofinterestrateriskfortradingandinternalriskmanagementacrossthe?nancialindustry,bybanksalongwithother?nancialinstitutions,andforswapsalongwithbondsandstructuredproducts.

10

Ourdiscussionsofarfocusedon?xed-for-?oatingswaps,whichisthemostprevalentformofaninterestrateswap,butthereareotherformsofswaps,mostnotablyovernightindexswaps(OIS),swaptions,forwardrateagreements(FRA),andcapsand?oors.OISareverysimilartointerestrateswaps,but?xed-ratepaymentsareexchangedfor?oatingpaymentsthatarebasedoncompoundedinterestofanovernightrate,likethefederalfundsrate,ratherthanonatermrate,likeLIBOR.FRAsrequireasinglepaymentthatd