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BIS Working Papers

No 705

An Explanation of

Negative Swap Spreads: Demand for Duration from Underfunded

Pension Plans

by Sven Klingler and Suresh Sundaresan

Monetary and Economic Department

February 2018

JEL classification: D40, G10, G12, G13, G15, G22, G23 Keywords: duration, wap spreads, alance sheet constraints, unding status of pension plans, efined enefits, epo, LIBOR BIS Working Papers are written by members of the Monetary and Economic Department of the Bank for International Settlements, and from time to time by other economists, and are published by the Bank. The papers are on subjects of topical interest and are technical in character. The views expressed in them are those of their authors and not necessarily the views of the BIS.

This publication is available on the BIS website

(www.bis.org). © Bank for International Settlements 2018. All rights reserved. Brief excerpts may be reproduced or translated provided the source is stated. ISSN

1020-0959 (print)

IS

SN 1682-7678 (online)

AnExpla nationofNegativeSwapSpreads:

DemandforDuration fromUnderf undedPensionPlans

SVENKLINGLE RandSURESHSUNDARESAN

ABSTRACT

The30-ye arU.S.swapspreadshaveb eennegat ivesinceSept ember2008.Weo eranov elexplanationforthispersistentanomal y. Throughanillustrat ivemodel,weshowthatu n- derfundedpensionplansoptim allyuseswapsfordurati onhedging.Combi nedwithdealer

banksÕbalancesheetc onstraints,thisde mandcandrivesw apspreadstobecomenegative.Empirically,weconstructameasureoftheaggr egatefundi ngstatusofDeÞnedBeneÞt pen-

sionplan sandshowthatthi smeasurei sasigniÞcantex planatoryvar iableof30-yearswap

spreads.WeÞndasimilarli nkbetw eenpensi onf undsÕunderfundingands wapspreadsfo rtwoothe rregions.

Klingler(correspondingau thor)isfromtheDepartmentofFinance,BINorwegi anBusinessSchool and

SundaresanisfromColumbiaBus inessS chool.Wear egratefultoStefanNagel(the Editor),theAssociateEditor,twoanonymousre ferees,Dar rellDu!e,Robin Greenwood,W eiJiang,TomasKokholm,David

Lando,HarryMama ysky,Scot tMcDermott,StephenSchaefe r,PedroSerran o,MortenS¿rensen,Hyun

Shin,SavitarSun daresan,andDimitriVa yanosforhelpfulcomments.Klingle racknow ledgessupportfromtheCenter forFinancialFrictions (FRIC) ,grantno.DNRF102.Sundaresanack nowledgeswiththanksthe

productivesabbaticalspentatBISwhe rethepaperreceiveduse fulsuggestionsandc omme nts.Wealso

thankparticip antsintheseminarsattheSwissFinanc eInsti tuteinGe rzenseeandattheIndianSc hool ofBusinessfortheircomments. Theauth orshavenoconßicts ofinterest,asidentiÞedint heDisclos urePolicy.

InSep tember2008,shortlyafterthe defaultofLehman Brothers,thedi!erencebetweenthe swaprate( whichisthe Þxed-rateintheswap )ofa30-yeari nterestrateswap (IRS)and theyield ofaTreas urybondwiththe samematurit y,commonlyreferredto asswapspre ad, droppedsharplyandbeca menegative.Asweexplai ninmorede taillater,thisisa theoretical arbitrageopportunit yandanassetpricinganomaly. Incontrast toothercrises phenomena, the30-ye arnegativeswapspre adisverypers istentandstillataround -40basispointsas ofDecemb er2015.Inthispaper,we examinethep ersistentnegative30-y earswap spread ando eranew per spectiveon thepossiblereasonsbehindthis anomal y.Ourhypo thesisis thatdemandf ordurationhedgingb yunderfu ndedpensionplanscoupledw ithbalancesheet constraintsfacedbyswapdealersput spressureonlong -terms wapÞxedrate sandultimately turnedthe30-year swap spreadtobecome negative. Negativeswapspreadsare apricingano malyandpresentachall engetovie wst hathave beenheldpr iortotheÞnan cialcrisisthat sugges tedthatsw apspreadsareindicatorso f marketuncertainty,w hichincreaseintimes ofÞnancialdistres s.T hisisbecaus etheÞxed paymentinanIRSisexchang edagains taßoating payment,w hichis typicallybasedon Libor,andentailsc reditrisk. Hence,eventhoughIRSar ecollateralizedand viewedasfree of counterpartycreditrisk,theswaprate shouldbeabovet he(theoretical)ri sk-freeratebecau se ofthe creditris kthatisimplicitin Libor.Theref ore,swapspre adssho uldincreaseintimes ofelevat edbankcreditrisk(seeCollin-DufresneandSolnik,2001, foratreatmen tofthis andrelat edissues).Inadditionto that,treasuries(whichar etheb enchmarksagainstwhich swapspreadsar ecomputed)h aveasta tusasÒsafehavenÓ,i.e.,assetst hatinvestorsvalue fort heirsafetyandliqui dity.In timesofÞ nancialdistress,investorsvaluetheconvenience ofholdingsafe andliquidassets evenmore, whichdecreases thetreasuryyield andmak es themtradeata liquiditypre miumorc onve nienceyield(s ee,for instance ,Longsta ,2004, 1 KrishnamurthyandVissing-Jorgensen,2012, orFeldh¬ut terandLando,2008).Insummary, theseargumentsshow thatthe30-yearswaps preadshouldhaveinc rease daroundthe default ofLehman Brothers. Weo erade man d-drivenexplanationfornegativeswapspre ads.Inparticular,wede- velopamodelinwh ich underfundedpens ionpla nsÕdemandfordu rationhedgingleadsthem tooptimallyre ceiv etheÞxedrateinIRSwithlongmaturities.P ensio nfundshav elong-term liabilitiesintheform ofunf undedp ensionclaimsand inve stinaportfolioof assets,suchas stocks,aswellasinoth erl ong-termassets,lik egov ernment bonds.Theycanbalancet heir asset-liabilitydurationbyin vestingin long-termbondsorby receivingÞxedinanIRSwith longmaturit y.Ourtheorypredictsthat,ifp ension fundsareunderfunde d,theypreferto hedgetheirdurat ionriskwithIRS ratherthanbuyingTreasuri es,whichmayb enotfeasibl e giventheirfundingstatus.The preferencefor IRStohedge durationris karisesb ecausethe swaprequi resonlymodestinvestmentt ocovermargins, whereasbuyingagov ernmentbond tomatch durationrequiresoutright inve stment. 1

Thisdemand, whencoupledwithdealer

balancesheetconstrain tsresultsinneg ativeswapspreads. GreenwoodandVayanos(2010)show thatpen sionfundsÕdemandfordurat ionhedgin g inthe U.K.cana ectthete rmstructu reofBritish giltsbyloweringlong-termra tes.In this sense,ourpaperbea rsacloser elationshiptot heirwork.Howeve r,o urapproachdi ersfrom theirssincew efocusonunderfundedpensionfundsÕoptimalpr eferenceforthe useofIRS fordu rationhedging.Themodelthat wedevelopshowsthatthe demandfor IRSincreases asthe fundbecom esmoreunderf unded. Weprov idenon-parametricevi dencesuggestingthattheswapspreadstendtoben egative inperi odswhenDBplansareund erfunded.Wet husill ustrateanewchan nelthatma ybe atwor kindrivinglo ng-ter mswapspreadsdown.Usin gdatafromtheÞnancialaccoun ts 2 oftheUn itedSt ates(formerßow offundstable)fromt heFederalReserve,wec onstructa measureoftheaggregate fundi ngstatuso fDBplans(bothprivateandpubli c)intheUnited States.Wethenuse thismeasureto testtherelations hipbetw een theunderfundedratio (UFR)ofDBp lansan dlong- termswapspread sinaregre ssionsetting.Evenaftercont rolling foroth ercommondriv ersofswapspreads,recogn izedintheliterature,such ast hespread betweenLiborandrepora tes,Debt-to-GD Pratio,de aler-banksÕ Þnancialconstraint s,market volatility,andlevelaswellasthes lopeofthe yieldcurve,weÞnd thatUFRisas igniÞcant variableinexplaining3 0-year swapspreads.Inlinewithournarr ative,wealsoshowthat swapspreads ofshortermaturiti esare nota!ectedby changesinUFR. Wecond uctanumberofrobustne sst ests.Onepotentialc oncern aboutusingUFRasan explanatoryvariableforswapspreadsi sthatthesamefactorsthatha veb eenshownto a ect swapspreads canalsoa ectpensio nfunds.Forexample,ade creaseinthelev eloftheyi eld curvecana ectswapsp readsandals oincreasesthelevelofp ensionfu ndsÕunderfund ing.To addressthisconcern,we usestockretu rnsasaninstrumentalvari ablein atwo-s tageleast squaresetting.The ideahereisthatstockretur nsdirectl ya ectpensio nfundsÕfunding status(throughthea ssetside)butthereisnoobv iousecon omicreasonastow hytheyare relatedtoswapspreads. Ourre sultsarerobu sttothisadditionaltest. Next,weadd di erent controlvariables,such asU.S.corporatebondissuance,a ndalsotestth ee ectofpens ion fundÕsunderfunding onswapspreadsindi erenttimeperio ds.WeÞndthatt helinkbetween UFRandswap spreadsismostpronouncedinthe immediateaftermathof LehmanBrotherÕs default,whenderivativesd ealersfaced stringentbalancesheetconstraints .Finally,wetest thee ectofamodiÞed vers ionofUFRonswap spreadsandÞndthatourresults arerobust tothismo diÞcation.

Weconc ludeourpaperbytestingth ee

ectofpens ionfun dsÕunderfundingonswap 3 spreadsintwoaddition alcoun trieswit hsigniÞcantpensionplans:Japana ndtheNether- lands.Here,weÞndth atthefunding status ofJapanese pensionfund sisasigni Þcant explanatoryvariableforJapaneseswa pspreadswith10yearsand3 0yearstom aturity. Moreover,Dutchpensionfund sÕfundingstatusisal soasigniÞcantexplan atoryvariablefor

30-yearswapspreadsin Europe.Next, wereviewtherelatedlit eratu re.

Asme ntionedabove,GreenwoodandV ayanos(2010)showth atthedemandpressureby pensionfundslowerslo ng-termyieldsof Britishgilts.Inadd ition,GreenwoodandVayano s (2010)men tionthatpensionfundsals ofulÞll theirdemandforlong-datedasse tsbyusing derivativestoswapÞxedforßoatingp aymen ts.Theynotet hatpensionfun dshaveÒsw apped asmuc has£50billionof interestrate exposurein 2005and2006toincreasethe durationof theirassetsÓbut donotinvestigatethei mpactofsu chdem andonswaps preadsanyfurther. Theirfocuswason U.K.Giltmarkets .Hence,our paperc omplemen tstheiranaly sisby showingthatunderfunde dpensionfun dsÕdemandforlong-datedassetsc anhaveastrong impactonsw aprates ,globally. Moregeneral ly,swapratesandtreasuryyieldsha vebeenstudie dextensivelyin the previousliterature.A streamofliteraturecalibrate sdynamicte rm-structuremodelstoun- derstandthedynamicsofs waps preads(seeDu eandSingle ton,1997,Lang, Litzenberge r, andLiu,19 98,Collin-Duf resneandSolnik ,2001,Grinblatt,2001,Liu,Longsta ,an dMan- dell,2006,Johan nesandSundaresan ,2007,andFeldh¬ut terandLan do,2008,amongothers). Amongstthesepapers ,thepaperclose inspirittoourpaperisF eldh¬utt erandLando(2008) . Theydecomp oseswapspreadsintothree component s,creditriskinLi bor,theconvenien ce yieldofgove rnment bonds,andademand-basedcomponent.Inc ontrasttoourpaper,the ir studyfocuseson maturitiesbetweenonea ndteny earsandtheylinkthedemand-b ased componenttodurationhedgingi nthemo rtgagemarket. 4 Theusageofsw apsbynon -Þnan cialcompanies hasbeenstu diedby,amongothers,Faulk- ender(2005),Ch ernenkoandFaulkender (2012),JermannandYue(2013). Wefocuson pensionfundsÕunderfun dingissues,whichha vebeenstudiedby,amongothers,Sundare san andZapate ro(1997)andAng,Chen,andS undaresan(2013).W eaddtothi sliteratu reby linkingchangesinswaps preadstochangesinpen sionfu ndunderfundi ng. Weno tethatanyde mand-basedex planatio nwouldbeincompleteiftherewerenoÞ- nancialfrictionsfort hesupplyofIRS.Hence,wealsob uildonthe literatu reoflimitsof arbitrage(ShleiferandVishny ,1997,GrombandVayanos,2002 ,LiuandL ongsta ,2 004, ciallytheliteratur eondealer constraintsanddemandpressurei nthede rivativesmarke t (Garleanu,Pedersen,and Poteshman,2009).

Toth ebestofou rknowledge, wearet heÞrsttoo

eradem and -basedexplanationfor negativeswapspreads.Jerm ann(2016)st udiesthenegativeswapspr eads,o eringfric- tionsforholding long-ter mbondsasanexplanationb uttakingthedemandforswapsa s exogenouslygiven.Inhismodel,Jerm ann(2016)assumesth athol dingbonds iscostlyand showsthat,asthe holdingcostsin crease ,theswapra teconvergestotheLibo rrate,which istypic allybelowthelong-te rmTreasuryyield.Ourexplanationisdis tinctf romhiswork, astheUFRmeasureofunderfundeds tatusofDB pensionplansisasigniÞcant variablein explaining30-yearswapspreadsbutnotforswap spreadswi thotherm aturities.Further - more,controllin gfortermspreadsleavesourmainresu ltsuncha nged.Holdingo utrightlong positionsinbondsforunder-f undedp ensionplanstomat chdurati onhasanopportunity costi npracticean dthisiswhatwest ressinou rwork.Lou(2009)alsoo ersderiv atives dealersÕfundingcostsasane xplanationofnegative swapspreads.

Finally,thereisawider angeofindustry resear cho

eringavarietyof di erentreasons 5 forth epersistentnegat ive30-yearswapspread.Onefrequen tlyusedexplanationist he potentialcreditriskofU.S.Tr easuries. 2

Theprobl emwiththisargumentis thatwhile

Treasuriesarelinkedtothecredi triskoft heU.S.,swapratesare linke dtotheave rage creditriskoftheban kingsysteman dadefa ultoftheU. S.governmentwould mostlikely causedefaultsin thebankingsystemaswell. Weinve stigatet heimpactofU.S.creditri sk (usingdi erentmeasures) onswapspreadsandÞndthatitd oesnot signiÞcantly a ectswap spreads.Asecond,common ly-o eredexplan ation,isthedi erentfundin grequirements ofswaps andTreasuries. 3 Long-termTreas uryholdingsareoutrightcashpositionsw hile engaginginIRSrequireson lymode stcapital forinitialcollateral,ty picallyasmal lfraction oftheT reasuryb ondprincipal.Sophisticatedinvestors canuserepoagreements topurchase andÞnanceT reasuries,althoughÞnancing Treasurysecuritiesfor30 yearsw ouldrequireop en repopositions,whic hneedtoberolledove rforalongduration.The riskwithsuchas trategy isthat thecashlende rsmayref usetorenewthe repoagreement.Thesec onsiderati onsare animpor tantlimittothenegatives wapspreadsarbit ragea ndcouldex plainwhythereis ali mitedsupplyoflong-da tedswaps.Asweexplai ninmor edetailbelow,theyarenot relevantforpensionfunds,who, typically,donot userepotransactions. Theroadma pofthepaperisasfollo ws.Sec tionIofth epaperprovidess omemot ivatin g evidence.InSectionII,wep resent theswapspreadsand theund erlying driversforthe demandforrec eivingÞxedrates inlong-termswapsfromp ensionfunds. InSectionI II, wea simpletheorythatlink spensionfundsÕ underfunding anddealersÕ balancesheetconstrai nts toswap spreads.Sect ionIVcontainsourempirica lresultsfortheU.S.Sec tionVp rovides additionalevidenceforJapanandt heNeterlands.SectionVIcon cludes. 6

I. Motivating Evidence

We motivate our model, by documenting a few stylized facts. We first show in Figure 1 that the 30-year swap spread became negative following the bankruptcy of Lehman Brothers, and has been in the negative territory since then.[Figure1here] We can see from Figure 1 that the term structure of swap spreads track each other closely until the end of 2007 when long-term swap spreads start decreasing relative to short-term spreads. 4 Since then, the dynamics of the 30-year swap spreads have decoupled from the dy- namics of the other tenures. In the month after the default of Lehman Brothers, highlighted by the first vertical line, the 30-year swap spread drops sharply and turns negative. During that period, there is also a decline in the 10-year swap spread, while swap spreads of shorter maturities increase. Between 2008 and 2014 the 30-year swap spread slowly converges close to 0 and starts decreasing again in 2015. In August 2015, highlighted by the second vertical line, the Libor-Repo spread turns negative, which causes a decrease in swap spreads of all maturities. 5 We perform a principal components analysis (PCA) of swap spreads before and after September 2008 to see if there is a significant change in the PCs driving the swap spreads after the crisis, relative to the drivers prior to the crisis. We use month-end data for this analysis and the results of our PCA are shown in Table I next. We present the loadings of each PC before and after September 2008 as well as the proportion of the spreads explained by each PC.

6[TableIhere]

7 Notethatpr iortothecris is,theÞrstPCex plaine dmoretha n75%ofthevariationsin swapspreads forallmaturities.The explanator ypoweroft hesecondPCvariedfrom23.1% for3-year swapspread sto1.7%for 10-yearsw apspreads.Afterthecri sis,theÞrstP C becameevenmoreimpo rtantinexpl ainingtheswap spreadsofmaturitiesuptoÞve years, andlessso formaturitiesfrom sevento thirtyy ears.Butt hedrop initsexplanatorypow er forth e30-yearswapspread sisdramatic: itfellfr om77.0%tojust 3.1%.Infact ,thesec ond PCb ecamethedomin antcomponentin explainingtheswapspreads for30-yearmaturity, insharp contrastwith swapspreadsassociated withshorter maturitiesof10yearsofle ss. Similarly,buttoasmallerextent ,theexpl anator ypo weroftheÞrstPCdecreas edfrom

78.10%forthe 20-yearsw apspreadto 24.8%,whiletheexplana torypoweroft hesecondPC

increasedfrom17.3%to70 .2%.Ourresul tsinTableIdemonstratet hatth edeterminant sof

30-yearswapspreadsunderw entabigcha ngeafterSeptem ber2008.Thischangeappears

tobe uniqueforswap spreads withmaturitiesabo ve10-years. Takentogether, Figure1andTableIsuggestthat thelonger-terms wa pspreads, especially the30-ye arswapspreadsbe havedqualitativelydi erentfromtheresto ftheswaps preads afterSeptemb er2008.Thisprovidesthemotivation forboth ourtheoryand empiricalwork. Wepr ovidenextapossibleli nkbetweenthe abo veevidenceandthefunding statusofdeÞn ed beneÞt(DB)pension plans.DBPen sionfundshavelong- datedliabilitiesa ndthey uselong- terminterest rateswapstohedgetheirdu rationriski nswapoverlaystr ategie s.Adams andSmith( 2009)showhowinte restrateswapsareus edbypens ionfun dstomanagetheir durationrisk.Furthermore ,CGFS(2011)docu mentsthatinsurancecompaniesandpensi on fundsneedtobala nceasset-li ability durationsandcandosou singswaps.Weprovidemore evidenceontheswapusageofp ension plansinth enextsecti onanddocu ment additional anecdotalevidenceontheirsw apusageinTableIA.1inthei nterne tappendix. 8 Intheo ry,asophisticatedinve sto rwithfullaccesstorepoÞnancing,canbu yTreasury bondsandusether epomarket toobtaina nalmostun fundedpositi on.Thisrepotransac tion requiresaninitialfundingofappro ximately6%. 7

Atthes ametime,e ngaginginan IRScould

alsorequirea ninitialmarginandreg ularcol lateralposting.Withth eimplementationof mandatorycentralclearingthi sisbecomingmoreofanis suerecently.Neverthele ss,as notedearlier,Þnanc ingalong-termbondfor thirtyyears remainsa lesspracticalproposition thanme relyenteringintoan interestrateswap.Overall, pensionf undsÞndlong-te rmIRS asasim ple rvehicletotakelevera gethanutilizingthere pomark etfordurati onhedging purposes. 8 Asno tedinarecentBlo omberg ar ticle(seeLeising,2 013),U.S.pensionfundsuseIRS markets.Furtheranecdotale videnceofpensionf undsÕdemandforIRSandre sultingdemand pressureisbestsummarize dby thefollowingquotefromarec entBloombergarticle: ÒPension fundsneedtohedge long-terml iabilit iesbyreceivin gÞxedonlong-maturit yswaprates. WhenLehma ndissolved,pension fundsfoundthemselveswithunmatc hedhedgingneeds andthenneeded tocov erthesep ositionsinthe marketwithothercounterparties.This demandforre ceivingÞxedin thelongenddroveswapspre adstighter.Ó 9 Weco ncludethissectionbyprov idingsomepe rspectiveaboutthesize ofDBp ension fundsintheUnited States .Thetota lsizeofallpriva teaswellasstateandlo calgovern ment pensionplanassetsint heU.S.isabout $8.23trilliondoll arsaso fthethir dquartero f

2015.To makethecasethat thedemandbypension fundstorec eiveÞxed inthelong-

termswap contractscanpoten tiallyinßuencethe30-yearswaps pread,wenext comparethe totalamountofUS D-denominatedIRSwi th30o rmoreyearstomaturitywiththetotal unfundedliabilitiesofprivateas wellasstate andloc algovernme nte mployeeDBpension plans,whicharethe focusofthispap er.Accordi ngtothede positorytrust& cleari ng 9 corporation(DTCC),thetotalamoun tofUSD-denominatedIRS with30orm oreyearsto maturitywas1,330billion USDinSepte mber2015.Incomp arison,theclaimsofU.S .DB pensionplansontheirsp onsors,whichwe re2,04 4billionUSDinQ3 2015,arehuge.

II.Demandf orandSupplyofDuratio n

Inthis sectionwedis cusspensionfunds,the irdura tionmatchingneedsandh owun- derfundinga ectstheirdemandfor long-datedIRS. Webrießyrevie wtheimplicationsof regulationssuchasthepensionprotect ionactof2006 andth ediminish edincentivesto over- fundpensionp lans,duetosometax policydevelopment s.Weconcludewi thanover viewof thedemand forreceivingÞxedin long-dat edIRSaswellasthesupplyoflon g-datedIRS.

A.PensionF undsÕDurationMatching Needs

Themosti mportant customersinthelongendofthesw apcurvearepensionfunds andinsurancecompanies, whoha vea naturaldemandfor receivingÞxedforlongertenors. Pensionfundshavelong- termliabilitie stowardsthei rclientsandthePensionProtect ion Actof20 06requ iresthemtom inimizeunderfundingbysti pulatingfund ingsta ndardsand remedialmeasurestoreduce under-fundedstatus.Thisp romot estheincentivetoma tch thedurat ionoftheirassetportfoli oswith thedurationofth eseliabilities :Anyduration mismatchcanproducef utureshortfalls.I ncreasingthedurationofthe irassetp ortfolios couldbeachi evedbyrecei vingÞxedinanIRSorbyb uyingb ondswithlongmaturities. GreenwoodandVayanos(2010)p rovideev idencefromthe2004pen sionreformintheUnit ed Kingdomwherepensionfu ndsstartedbu yinglong-datedgil tsandmorerecentlyD omanski, Shin,andSus hko(2015) showthatGermaninsuranc ec ompaniesincreasedtheir holdings 10 ofGer manlong-termbondss igniÞcantlyoverthepastyears .Inlinewithpre viousresearch (see,forinstanc e,Angetal .,2013orRing,2014,amongman yother s)wedo cumentthat manyU.S.pensi onfundsar eunderfunded.UsingIRSi nsteadoflong-d atedTreas uriesfor durationhedging allowspens ionfundstousetheirlimite dfundingtoinvestinmore risky assetssuch asstocks. Todocu mentthatpensionfundsind eeduselong-d atedIRStohedgetheirdu rationrisk, west artbycollecting surve ydatafromtheChiefInvestmentO cermagazi ne,whoconducts regularsurveysonU.S.pe nsionfundsandtheirin vestm entstrate gies.quotesdbs_dbs28.pdfusesText_34

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