Summary of Liquidity Premium Estimation Methods Research Document

Research Document
John Hibbert, Axel Kirchner, Gavin
Kretzschmar, Ruosha Li, Alexander McNeil, Jamie Stark
Version 1.2
October 2009
Summary of Liquidity Premium Estimation
Methods
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Contents
1
Overview .................................................................................................... 3
2
Methods Summary ......................................................................................... 5
3
2.1
Model free negative CDS basis approach .................................................... 5
2.2
Structural Merton-style model ................................................................ 7
2.3
Direct computation – covered bonds ......................................................... 9
Results ...................................................................................................... 11
3.1
Model free negative CDS basis approach ................................................... 13
3.2
Structural Merton-style model ............................................................... 14
3.3
Direct computation – covered bonds ........................................................ 15
References ....................................................................................................... 16
Acknowledgements:AlexandrePages,LindaSchilling
Acknowledgements:
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1
Overview
Thisreportisconcernedwiththeestimationofliquiditypremia(LP)embeddedinthepricesoffinancial
instruments.Theexistence,magnitudeandmeasurabilityofLPremainthesubjectofalivelydebateamong
practitioners,accountants,actuariesandregulators.Theoutcomeofthedebatewillhaveanimpactonthe
futurepriceofcertainfinancialproductsand,arguably,thecostoffinanceforfirmsusingthecapitalmarkets.
ItshouldbenotedthatthisreportisnotconcernedwithhowtoapplyanLPestimatetothevaluationof
insurers’liabilities.OurfocusisonhowtoestimatebenchmarkLPsandtounderstandthepracticalchallenges
andsensitivitiesoftheestimationapproachesandnotthecomparisonoftheestimates.Itisworthstressing
thateachestimateismerelyforapointonawidespectrumofLP,witheachofourmethodsestimatinga
differentpointofthisspectrum.Thesearelikelytovaryacrosstypeoffinancialinstrumentandaccordingto
characteristicssuchas,term,creditrisk,etc–notleastbecauseofthedifferentlevelsofliquidity(transactions
costs)amongtheinstrumentsthemselves.Itshouldbenotedthatourresultsarenotanticipatedtobedirectly
comparableandthatanLPappliedtoaspecificclassofliabilitiescouldbelargerthanthebenchmarkLPs
presentedhere.
OuraimhereistocontrastresultsfromdifferentpracticalapproachestoLPestimationappliedtotherecent
past(i.e.aperiodspanningthemarketcrisis)aswellashighlightingsensitivitiesandimplementation
challenges.Inourpreviousreport(“LiquidityPremium:Literaturereviewoftheoreticalandempirical
evidence”,September20091)weprovidedasurveyofresearchers’findingsonthesequestions.Keyfindings
fromthatreportwere:
•
Thereisaclearconsensus(acrossanextensiveresearchliteratureaccumulatedovermorethan30
years)thatLPdoexistacrossmanymarkets,theycanbesubstantialandvarythroughtime.For
certainmarkets,i.e.corporatecredit,thereisstrongevidencethatLPincreaseinstressedmarket
conditions.
•
Althoughdifferentestimationapproacheshavebeenadopted,researchers’empiricalresultsare
broadlyconsistent.
Inthemainbodyofthisreportwepresentthreecommonestimationmethodswiththepurposeofinforming
achoiceoftheongoingestimationofa‘benchmark’LP–thatistheliquiditypremiumassociatedwitha
specificpoolofilliquidfinancialinstrumentsrelativetosomeliquidreferenceportfolio.
Thethreemethodsconsideredare:
CDSbasis
Creditdefaultswapsprovideamechanismforinsuringagainstthedefault
ofabondissuer.Thespreadonaninsuredportfolio(whichhasrelatively
lowliquidityandisfreeofcreditrisk)relativetoaliquidrisk-freebondisa
widely-usedmethodforestimatingLP.
Structuralmodel
Thismethodcomparestheyieldonanilliquidcorporatebondportfolio
withthecost/yieldonaliquidpositionwithotherwiseequivalentrisk
characteristicsconstructedfromrisk-freebondsandnotionaloptions,
usingtheMertonmodel.
Coveredbondspreads
If(illiquid)coveredbondsareviewedasbeingessentiallyfreeofcredit
risk,thespreadovertherisk-freereferencerate(intheanalysisshown
herethisisassumedtobetheswaprate)canbeconsideredasan
estimateforLP.
Thesemethodsarediscussedinmoredetailinsection2ofthisreport.Wepresentresults,relativetothe
swaprate,insection3.
Results
Results
WhilsttheexistenceofLPiswidelyaccepted,theestimationofthepriceofliquidityforaspecificfinancial
instrumentorportfolioataspecificpointintimeisclearlyanon-trivialchallenge.Althoughwemightseekto
quantifyLPacrosstypesoffinancialinstrumentandtheircharacteristics,suchasterm,riskandcurrency,this
turnsouttobeadifficulttask.ThesechallengesarenotrestrictedtoLP–unravellingtheexpectationsand
variousriskpremiaembeddedinanyfinancialinstrumentisanotoriouslydifficulttask.So,whatobservations
canwemakeontheresults?
1
Availableathttp://www.barrhibb.com/documents/downloads/Liquidity_Premium_Literature_Review.PDF
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•
Individualestimatesvaryconsiderably,throughtime,acrosseconomiesandcomparedtoeach
other.
•
Inaggregate,clearpatternsemergefromtheanalysisirrespectiveofthemethodused.EstimatedLP
riseovereachoftheyearendsfrom2006to2008withadramaticincreaseoverthelastquarterof
2008.
•
Fromtheendof2005untilmid2007weestimatelittleornoliquiditypremium–althoughitshould
benotedthatduringthisperiodbondspreadsandmarketpremiumswereunusuallylowandfar
fromtypicalhistorically.
•
LPestimatesgenerallyappearhigherfortheUSDthanfortheEURandGBPsectors.
•
TheEURestimatesderivedusingthestructuralmodelarefarlowerduringthestressperiodsthan
bothUSD/GBPestimatesusingthesamemodelandotherEURestimates.
Sensitivities&Practicalchallenges
Sensitivities&Practicalchallenges
TheCDSmethodshavemuchtorecommendthemgiventheirrelativesimplicity(inprincipleatleast)and
theirfoundationintradesthatshouldbeachievable.Ouranalysisdoesshowthatcareneedstobetakenin
theconstructionofcalculations–aligningestimatedCDScostswithactualbondsheldcanmakeamaterial
differencetoestimates.Themostappropriatecalculationwilldependonthereferenceportfolioofbonds
beingusedinagivenapplication.Onthedownside,thereislimitedcoverageoftheCDSmarketsfor
estimationandthehistoricestimatesareundoubtedlybiased(upwards)bythepresenceofcounterpartyrisk.
Onamorepositivenote,thereareanumberofinitiativestodevelopcentralcounterpartyclearing
mechanismsforCDScontracts.ThisisanimportantdevelopmentforthoseusingtheCDSbasisasameasure
ofLPsinceithasthepotentialtoeffectivelyremovecounterpartyriskfromthebasisequation2.
Thestructuralapproachprovidesapowerfulframeworkforunderstandingtheforcesthatdrivecredit
spreads.Ofthedifferentapproachesitdoeshavethegreatestparameterandmodelrisk(thepotentialfor
mistakesinparameterselectionandmodelspecification)andrequiresthelargestnumberofparameter
estimates.Nevertheless,themodeldoesdeliveraconsistentsetofresultsalongsidetheothermethodsand
thereforestrengthensourconfidenceinoverallestimates.Ontheplusside,themodelcan–inprincipleat
least–beextendedacrossmaturitiesandmarketssubjectivetotheavailabilityofcredibleparameter
estimates.
Thecoveredbondsmethodusedhere–essentiallyobservingspreads–issimpletoimplementandis
relativelyfreefromjudgment.Aquestionweneedtoaskhereiswhetherthespreadsareinfluencedby
factorsotherthanliquidity.
Wayforward
Wayforward
Thisreportillustratesresultsfromsomeeasy-to-computemethodsforLPestimationforwhichdatainputsare
readilyavailable.Ineverycase,thereisscopetorefinethemethodsfurtherthroughadditionalresearchand
extensionofdatasets.Also,therearemoresophisticatedapproachesthatcouldbeaddedtothelistof
candidateapproachestoLPestimation.Theseincludedata-intensiveregressionmethods(seeforexample
Dick-Nielsenetal.(2009))and‘scorecard’methodswhichaimtoexploitinformationfromavarietyof
indicatorsincludingproxies.
Wheredoesthisleaveusintermsofbuildingcredible,robustestimatesofliquiditypremia?Unravelling
expectations,riskpremiaandliquiditypremiafromthepricesoffinancialinstrumentsisnotoriously
challenging.However,themeasuresanalysedinthisreport,andresearchliteratureanalysedpreviously,
suggestthat,inaggregate,weareabletoidentifyLPduringperiodsofstressaswellasmorebenignperiods.
Whilstnosinglemeasureoffersasimple,satisfactoryapproachtoquantification,theremainingchallengeis
howtocombinetherichinformationsetdiscussedinourreportsintoarobustestimationmethod.
Audience
Audience
Thispapershouldbeofinteresttoallthoseconcernedwiththevaluationofassetsandliabilitieswhere
marketpricescanbedemonstrated,inpart,tobedeterminedbyliquidityfactors.Giventheongoing
developmentofmarket-consistent,‘fair’valuations,themagnitudeandmeasurabilityofLPwillbeofinterest
toaccountants,actuaries,financialintermediariesandregulators.
2
FormoredetailsseetheBISquarterlyreviewSeptember2009–“Centralcounterpartiesforover-the-counter
derivatives”,availablefromhttp://www.bis.org/publ/qtrpdf/r_qt0909f.htm.
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Methods Summary
ThepurposeofthissectionistosummarisethedifferentmethodsusedtoestimateLPaswellashighlighting
keyassumptionsandsomepracticalconsiderations.
LPestimationmethodsaimtoquantifythedifferencebetweentheyields(orprices)offinancialinstruments
whichareconsideredidenticalinallrespectsotherthanliquidityi.e.theanticipatedcostoftrading.Here,we
willfocusonfixedincomemarkets,inparticularcorporateandcoveredbonds,andconsiderthefollowing
approachestoestimation:
1. A comparison of yields on risk-free liquid bonds with an equivalent position in corporate bonds
protectedagainstdefaultriskusingCreditDefaultSwaps(CDS)-the‘negativeCDSbasis’.
2. AStructural(‘Merton‘)modelusedtoinferafairspreadonaliquidassetusingoptionpricingtheory
whichcanbecomparedwithmarketyieldsonequivalentilliquidbonds.
3. DirectcomputationofaspecificLPbyconsideringthespreadbetweencoveredbondsandswaps.
2.1 Model free negative CDS basis approach
2.1.1 Summary
ACreditDefaultSwap(CDS)isacontractinvolvingtwoparties-theprotectionbuyerandtheprotection
sellerwhichallowsholdersofcorporatebondstoinsureagainsttheriskofbonddefault.Theprotection
buyerwantstohedgetheriskthatabondofagivenissuer(thereferenceentity)willdefault.Heentersintoa
contracttopaytheprotectionselleraperiodicpremiumcalledtheCreditDefaultSwappremium.This
premiumrepresentsafixedpercentageofthenotionalamountspecifiedinthecontractandisusuallypaid
quarterly.IfnodefaulteventoccursbeforethematurityoftheCDS(notthereferencebond),theprotection
sellermakesnopaymenttotheprotectionbuyerandthecontractexpires.Ontheotherhand,ifadefault
occursduringthelifeofthecontract,theprotectionsellerpayscompensationtotheprotectionbuyerandthe
protectionbuyerceasestopayperiodicpremia.Alternatively,forsomecontractstheCDSbuyerwilldeliver
anagreedquantityof(defaulted)bondsinexchangeforacashpaymentequaltothefacevalueofthebonds.
HowcaninformationonCDScontractsbeusedtoestimateliquiditypremia?Usingarbitrageargumentsitcan
beshownthatthespreadofacorporatefloatingratenote(FRN)overadefaultfreeFRNshouldbeequalto
theCDSpremium.Thisargumentiscommonlyappliedtoordinaryfixedincomecouponbondsaswell,
althoughitisanapproximation.Inpractice,empiricalresultsshowameaningfulnegativedifferencebetween
theCDSpremiumandthebondspread.Thisdifferenceiscalledthenegativebasisandprovidesevidencefor
theexistenceofothercomponentspricedinthecorporatespreadsuchastheliquidityriskoftheunderlying
bond.This(negativebasis)canbeviewedasthedifferencebetweentheyieldonan(illiquid)corporatebond
(orportfolio)insuredwithCDS(i.e.risk-free)andtheyieldonaliquidrisk-freebond.
Foragivenreferenceentity,CDSandcredit-riskybondsmightbeexpectedtotradesimilarly,sinceboth
shouldreflectmarketviewsondefaultrisk.CDSaresyntheticinstrumentsthataredesignedtoimplement
purecreditviews.Inprinciple,ahigherCDSspreadreflectsdeteriorationintheperceivedcreditworthiness
ofanissuerandthemarketpriceofbearingthecreditrisk.
FollowingLongstaffetal.(2005),weusethecreditdefaultswappremiumdirectlyasameasureofthedefault
componentofcorporatebondspreads(andhencethenon-defaultcomponentorliquiditypremium)3.In
otherwords,weassumethesimplerelationof:
CDSbasis=CDSpremium–corporatebondspread
LiquidityPremium=-CDSbasis=Corporatebondspread–CDSpremium
OnewaytothinkabouttheLongstaffetal.(2005)approachisaseffectivelycreatingasyntheticcredit-riskfreecorporatebondbybuyingaCDSonthereferenceentity.Theresidualspreadisinterpretedasameasure
ofthepriceofcorporatebondliquidity.
Syntheticdefaultablebond=default-freebond+CDSprotectionsellerposition
Thismethodrequiresus(ideally)to:
• Identifyasuitablesampleofcorporatebondsandcollateprices/yields.
3
Notethatthiscomponentcontainsanallowanceforexpected(i.e.average)defaultsandanassociatedcreditrisk
premiumtocompensateforunexpecteddefaults.
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•
CollateCDSpricesforequivalentmaturitiesorinterpolatethemfromadjacentmaturities.
•
Collatedataonrisk-freebonds.
Inpractice,aligningthesamplesandmaturitiesisnotatrivialtaskanditmaybenecessarytoapply
approximations.Wehaveadoptedtwoapproachestoproducetheanalysisshowninsection3,bothrelying
onanexistingCDSindex.
•
UsetheCDSindex(e.g.iTraxx)toidentifyasampleofbondsandcollatebonddatatomatchthe
CDSintheindex.
•
UseaCDSindexandaseparatebondindex,whichmaynotbealignedintermsofconstituent
composition.
Somecareneedstobetakentounderstandtheimpactofanymismatchbetweenconstituents.Asaresultthe
choiceofmethodwilldependonapplicationandthesepracticalconsiderations.
Ourfocushasbeenoneasy-to-computemethods.Otherapproachestoestimationarepossible,including
startingwithabondindexandthenidentifyingissuesforwhichCDSquotesareavailableattherelevant
maturities.Furtherworkisrequiredtounderstandhoweasyitistoobtaindataandotherpractical
implications.
2.1.2 Key Assumptions and Data
ThekeyassumptionofthisapproachisthattheCDSspreadmeasuresthepurecreditriskcomponentofthe
corporate-bondspread.InpracticetheCDSspreadmayalsopricethecounterpartyriskthattheprotection
sellerwilldefault.Whilstthismaynotbematerialinbenignmarketconditions,itmaybeimportantintimesof
extremestress.ThesharpriseinCDSspreadsfollowingtheLehmancollapseandAIG’sproblemsin
September2008suggestthat,instressconditions,otherfactorscaninfluenceCDSprices.
OneoftheeffectsofthedislocationinCDSmarketsin2008hasbeenamovebyregulators,dealersand
investorstodevelopcentralcounterpartyclearingmechanismsforCDScontractsandgreaterstandardisation
ofcontracts.Theseinitiativesarebeginningtodevelopmomentum-particularlyinEuropewithEurex
clearingasampleofCDScontractsfromtheendofJuly2009.Thisisanimportantdevelopmentforthose
usingtheCDSbasisasameasureofLPsinceithasthepotentialtoeffectivelyremovecounterpartyriskfrom
thebasisequation2.
NotethattheCDSmarketsaretypicallymoreactiveforinvestmentgradeissuersthanspeculativegrades.
TheiTraxxindexofCDSconsistsexclusivelyofinvestmentgradeissuers.
WhencalculatingtheLPrelativetoswapsweuse5yearswapspreads,matchingthetermofboththeCDS
andbondindicesused.
Althoughwearenotdirectlyconsideringtheapplicationofourliquiditypremiumestimateshere,thereisan
implicitassumptionthattheconstituentsofCDSindexaresomehowrepresentativeoftheportfoliofinancial
instrumentsforwhichweaimtomeasuretheLP.
2.1.3 Practical Implementation considerations
DirectCDSspread-basedapproachesareattractivebecauseoftheirsimplicitybutarealsosensitivetothe
choiceofbondsampleandstronglydependentondataavailabilitywhichmaynotmatchtheportfoliobeing
considered.
Nomodeldependenceandrelativelyeasytocompute–onlyrequiresustotakeyielddifferences
betweentwomarketobservableinstruments.
ProvidesevidenceoftheexistenceofLPfromatradethattakesadvantageofit.
Emergingcentralclearingcounterpartiesshouldensurethenegativebasisbecomesa‘cleaner’
estimatefortheLP,evenintimesofmarketstress.
PastestimatescouldbebiasedduetoCDSliquidityrisk,counterpartycreditrisk,etc.
ThepracticalitiesofmatchingCDSandbondsbyissuerandmaturityandperformingcalculationsin
atimelymannerarenottrivial.Relyingoneasy-to-computemethodsusingavailableindicesmay
createamismatchwhichcouldhaveamaterialimpactontheresults.
Attemptstoadjustfordifferentapplicationsusingeasy-to-calculatemethodswillbelimitedbythe
availabilityofCDSindices.
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CDSindicesarenotavailableforabroadrangeofeconomies(e.g.noCDSindexforGBP),making
themeasuresmoredifficulttocalculate.Furtherworkisrequiredtounderstandhowtousethis
methodinothermarketsandwhetherconversionofnegativebasistodifferentcurrenciesprovides
ameaningfulmeasureofLP.
2.2 Structural Merton-style model
2.2.1 Summary
Analternativeapproachisbasedonastructuralmodelofthedefaultofafirm(proposedbyMertonin1974).
StructuralapproachesusingtheMertonmodelarerelatedtothedirectmethod,asdiscussedbelow,inthata
corporatebondyieldiscomparedtothecostofmanufacturinganeconomicallyequivalentsyntheticposition
fromarisk-free(liquidbond)andanoptionontheissuingfirm’stotalassets.Thefairspreadonthesynthetic
bondisobtainedbyviewingcompanies’equityasacalloptiononitstotalassetswherethestrikeistheface
valueofdebt.Similarly,debtcanbeviewedasapackagewhichcombinesarisk-freebondwithawrittenput
optiononthefirm’sassets.Assuch,themodelexclusivelydescribescreditriskandexcludesliquiditycosts.
Theliquiditypremiumistheninferredastheresidualbetweenthefairspreadandthemarketspread4.Figure
1illustratesthedecompositionofthecorporatebond(market)spread.
Liquidity Premium
Market Spreads
Residual spread
,
interpreted as
liquidity premium
Credit
Risk Premium
Merton Model
implied fair spread
Expected Losses
Figure1
Figure1:Decompositionofcorporatebondspread
Decompositionofcorporatebondspread(nottoscale)
(nottoscale)
Asanaside,althoughwearenotinterested(forthepurposesofthisreport)inunderstandinghowthefair
spreadiscomprised,themodeldoesprovidesomeimportantadditionalinsights.Thefairspreadcanbe
consideredtobecomprisedoftwoelements.First,anallowanceforexpected,averagedefaultlosses.
Second,acreditriskpremium.Inprinciple,thisexistsbecausetheholderofacredit-riskybondbearsmarket
riskandshouldberewardedforcarryingthatriskinexactlythesamewaythatequityinvestorsdemandarisk
premium.Indeed,itcanbeshownthatthereplicatingpositionfortheshortputnotionallyheldbybond
holdersisagearedpositioninfirmassets,sothisrequiredriskpremiumisquitenatural.Althoughtherisk
premiumissometimesdescribedasanallowanceforunexpecteddefaultsitshouldnotbeseensimplyasa
prudentallowance.Rather,itisapriceforriskbearingandwillfluctuateinlinewithotherriskpremia.Finally,
notethatFigure1isnotdrawntoscale.Thesplitbetweenthevariouselementsofthespreadwilldependon
bothindividualbondcharacteristicsandmarketconditions.
TheoptionswewanttovaluedonottradebutsuchnotionalderivativesbutcanbevaluedusingMerton's
model.Themodelusestheassumptionthatthefirm'sassetsfollowtheclassicalmodeloffinance:geometric
Brownianmotion.
Themodelrequiresanumberofinputs:
•
Assumptionsforthematurityofthedebtofthecompany(T)anditsfacevalue(B)
•
Thevolatilityofthefirm'sassets(sigma)
•
Arisk-freeinterestrate(r)
•
Theinitialvalueoftotalfirmassets(V).
4
ResidualspreadisobservableiftheMertonmodelfaircreditspreadestimationdoesnotmatchthemarketspread.In
additiontoliquidityrisk,residualspreadcouldalsobedrivenbyamismatchbetweenconstituententitiesofthecorporate
bondspreadandtheMertonmodelportfolio.Furthermore,residualspreadcouldalsoreflectdifferencesinmodel
choicesandparameterisation.
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Inprinciple,itispossibletoapplythemodelattheleveloftheindividualissuer.KMV'smethodologyfor
creditriskisbasedonthistypeofthinkingalthoughtheyhavetheirownproprietaryapproachtoexploiting
equitymarketinformation.Inpractice,thecalculationspresentedbelowarebasedonanalysisofatypicalfirm
ofagivenratingandbondofaspecifiedmaturity.Thetypicalspreadisthencomparedtoamarketaverage
spreadfortheratingandmaturity.Theapproachfollowedherecanbesummarisedintermsofthefollowing
steps:
1.
Settheimpliedlevelofdebtatbondmaturitytobeconsistentwithhistoriccumulativedefaultrates
assumingfirmassetsexhibitvolatilityinlinewithde-leveragedfirm-specificequityvolatility.
2.
Setoptionvolatilitybasedonobservedmarketoptioncostsandde-leverageassumption.
3.
Collaterisk-freeinterestratedata.
4.
PricethesyntheticcorporatebondusingtheMertonmodelasariskfreebondplusashortput
optionplusashortbinaryoptiononbankruptcycost.
5.
Liquiditypremium=marketspread–Fairspread(yieldoncorporatebond)
NotethatthefrictionalcostsofbankruptcyarenottakenintoconsiderationintheoriginalMertonmodel.It
assumesthatintheeventofadefault,theassetsofthecompanyaresoldwithoutanydiscountandthe
proceeds,intheamountoftheactualvalueoftheassets,aredistributedamongdebtholders.Inreality,this
costlesstransferisveryunlikelyduetolegalandaccountingimplicationswhenliquidationoccurs.Webelieve
thattheexistenceofbankruptcycostshasamaterialimpactonthevaluationofdebtandtheextended
implementationoftheMertonmodelusedinouranalysisdoestakeintoaccountthesecosts.Bankruptcy
costshavehigherprioritythanbondsandthereforereducetheproceedsthatbondholderswillreceivein
liquidation.Hence,thevalueofdebtdecreaseswhensuchcostsexist.Bankruptcycostsarecapturedby
valuinganadditionalputoption(notionallywrittenbybondholders)thatpaysafixedamount(thebankruptcy
cost)iffirmassetsfallbelowthedefaultthresholdatbondmaturity.
NotethattheBankofEnglandhasadoptedasimilarstructuralmodelapproachintheirLPestimationwork
(seeWebber2007).Theirestimatestendtobeslightlyhigherthanourown,whichwebelieveisinpart
becausetheydonotincludingabankruptcycostelementintheircalculations.
2.2.2 Key Assumptions and Data
Ourimplementationofthestructuralmodelincludesanumberofsimplifyingassumptions:
•
Ratherthanlookatfirmbalancesheets,thedefaultbarrierissimplyadjustedtoaligntheprobability
ofdefaultwithobservedlong-termdefaultfrequencies.
•
TheassetvalueprocessfollowsageometricBrownianmotionwithconstant,non-stochasticasset
volatilityandinterestrates.
•
Debtcanbeadequatelyrepresentedbyasinglezero-couponbond.
•
Defaultonlyoccursatmaturity.
Inadditionitrequiresustoinputanumberofparameters:
•
Weprovidequarterlyupdatesofourdividendyieldexpectations.
•
Expecteddefaultrates(forUSDandGBPwetwoalternativedatasetsareused-from1920and
from1970,forEURweuseadatasetstartingin1985).
•
Estimatesforaveragefirmleverageandtheaveragecostofbankruptcy.
Thecalculationsalsorequirethefollowinginputdata:
•
Interestrates.
•
Marketspreads:MerrillLynchmarketspreadsovergovernmentbondyieldsforEUR,GBPand
USD,adjustedbysubtractingtheswapspread.
•
Firmassetvolatilityisestimatedbycombiningequityindeximpliedvolatilityandestimatesforfirmspecificequityvolatility.Aquarterlysurveyofbanks’OTCpricesprovidesestimatesforoptionimpliedindexvolatilitiesandamarketdatavendorprovidesestimatesforspecificstockvolatilities.
Therelevantindexfortheoption-impliedindexvolatilityischosenaccordingtotheeconomy-
EuroStoxxforEUR,FTSE100forGBPandS&P500forUSD.
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Intermsofapplicationwemakenoimplicitassumptionofunderlyingportfoliosinceweareabletoprovide
inputparametersfordifferentratingandmaturityprofiles.However,inpresentingourresultsweusethe
constituentweightingofaMerrill-Lynchinvestmentgradebondindextoweightouraverage.Fordifferent
applications,alternativeweightswillbemoreappropriateandmayresultinhigherestimates.
2.2.3 Practical Implementation considerations
Thisapproachisappealingduetoitsintuitiveexplanationandtheoreticalfoundations.However,LPresults
relyheavilyonthequalityofthemodelparameterchoicesandwillalsobesensitivetomodelspecification
choices.
IntuitiveexplanationofLPeffectsforcorporatebonds.
Requireddatasourcesavailableformostmajoreconomies,norelianceonhighfrequencytrade
data.
Calculationsarefeasiblefordifferentrating/maturitycombinations.
Theresultsaresensitivetomodelparameterestimatesandmodelchoicewhichareoften
underpinnedbystrongassumptions.
Modelcalibrationrequiresexpertjudgement.
Inpractice,implementationofthemodelcanbecomplicatedwhichmayobscuresensitivities.
TheequitymarketvolatilityassumptionsusedrelyonOTCpricequotationsratherthanactualtraded
data.Thisrelianceonmarketinformationwhichdoesnotmeetthedemanding‘deep,liquidand
transparent’definitionofEuropeanregulatorsmaybeanissueforsomeusers.
2.3 Direct computation – covered bonds
2.3.1 Summary
Directmethodsinvolvechoosingapairoffinancialinstrumentswhich–otherthanliquidity–areassumedto
offerequivalentcashflowsandthencomparingprices,expectedreturnsoryieldstoinferanLPforthe
relativelyliquidassetorportfolio.Inprinciple,therearemanypotentialpairings.Inthisstudywefocuson
comparingcoveredbondstoswaps.
Adefiningfeatureofcoveredbondsisthedualnatureofprotectiontheyofferaninvestor.Likeanormal
bond,theissuer(typicallyabank)isliabletorepaythebond,intheeventofdefault.Unlikeanormalbond
theinvestoralsohasapriorityclaimonanactivelymanagedpoolofhigh-gradeassets.Toensurequality,the
typesofassetsallowedaresubjecttolegalisation(orcontractsinsomecountries).
Giventhestructureoftheseinstrumentsmanyinvestorsassumethatcoveredbondsarevirtuallyriskfree.
Thisisnotanunfairassumptiontomake,giventhattheyhaveaverylonghistorywithnodefault,havean
activelymanagedcollateralpoolandtheinvestorhasdualrecourseontheissuer.Wefoundsomeevidence
tosupportthisview–theauthorsoftheBISSeptember2007quarterlyreview5claimthat“coveredbonds
offeranalternativetodevelopedcountrygovernmentsecuritiesforbondinvestorsinterestedinonlythe
mosthighlyratedsecurities.”Theireventstudyanalysisshowsthatcoveredbondspreadshavebeenrobust
toshockstobothissuercreditworthinessandthevalueoftheunderlyingcollateral–althoughitshouldbe
notedthatthisworkwascompletedbeforetheonsetoftherecentcrisis.Anydifferenceinyieldsbetween
theseinstrumentsmightthereforebeattributedtoliquidity.
Apracticalapproachreliesonhavingayieldcurveforacoveredbondindexandoneforswaps.The
calculationissimply:
NotethisgivesusatermstructureforLP.
2.3.2 Key Assumptions and Data
Sincewewereinterestedinexaminingthetermstructurewewantedtouseanindexwithareadilyavailable
yieldcurve.Wewereunabletoobtaina‘pure’coveredbondyieldcurvefromreadily-availablemarketdata
sources,soaEURCompositeAAAcurveisusedasaproxy.Thisiscomprisedoffiveeuro-denominatedfair
marketcurveswitharatingofAAAfromS&P,Moody's,Fitchand/orDBRS.Theconstituentsattheendof
September2009includedatotalof480,bonds59%ofwhicharecoveredand21%ofwhichhaveacentral
5
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governmentorFDIC6guarantee.5%havesomesortofassetbackingaresecuredorhaveacompanyorlocal
governmentguarantee.Oftheremainingbondsthevastmajorityhaveimplicitgovernmentguarantees.
TheobviouskeyassumptionhereisthatAAA-ratedcoveredbondsarerisk-free.Fromapracticalstandpoint
webelievethatassumingAAA-ratedcoveredbondsareriskfreeisavalidassumptiontomake.Giventhe
significantlevelsofimplicitguaranteesinthecurveweareusingasaproxy,webelieveitcurrentlycontains
verylittle,ifany,creditrisk.Note,however,thatwedidnotlookathistoricconstituents,orhaveany
guaranteesthatthiswillbecaseinthefuture.Toverifythiswecomparedthespreadoverswapsbetween
particularmaturitiesonthecompositecurveandanindexofcoveredbonds(e.g.iBoxxCovered5-7years)
withasimilaraveragematurity.
Intermsofapplicationthismethodmakesastrongimplicitassumptionthattheportfolioofinstrumentswe
aretryingtoestimatetheLPforhasverysimilarfeaturestocoveredbonds.Itisnotimmediatelyclearhow
theseestimatescanappliedtoaportfoliocontaininglessliquidinstruments,butwebelievethisapproachis
useful–potentiallyasaprudentmeasureofLPinthecorporatebondmarket.
2.3.3 Practical Implementation considerations
Thisisastraightforwardmeasuretocalculateandexplain.
Nomodeldependenceandrelativelyeasytocompute.Onlyrequiresyieldcurvedifferences
betweentwomarketobservableinstruments.
Doesnotrelyonexpertjudgement.
Allowsanalysisofthetermstructure.
Thesimplemethodusedherereliesonareadilyavailableindexthatcontainssomeothernoncovered/governmentguaranteedbonds.Whiletheseareveryhighqualitytheywillnotberiskfree.
Potentiallybiasedbyotherriskfactorsaffectingspreads.Forexample,despitetheactive
managementandratingprocesstherecouldbeadditionalcreditriskresultingfromcollateral
liquidationconcernsforcoveredbonds.
Whilethereisanincreasinginterestincoveredbonds,thereisstillonlyalimitedrangeof
instrumentssothismethodisnotreadilyavailableforabroadrangeofeconomies.
6
TheFederalDepositInsuranceCorporation(FDIC)isaUSgovernmentcorporationthatprovidesdepositinsuranceto
guaranteethesafetyofdepositsinmemberbanks.
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3
Results
Inthissectionwepresenttheresultsoftheanalyticalapproachesdescribedinsection2.Whenreviewing
theseresultsweaskthereadertokeepfollowingthingsinmind:
periodanalysedisfarfromtypicalwhenviewedinalong-termcontext.Duringthe2005-2006
1) Theperiodanalysedisfarfromtypical
periodanalysedisfarfromtypical
periodbondspreadsandmarketriskpremiawereunusuallylow.Bycontrast,the2008-2009period
isevenmoreexceptionalspanningtheextraordinaryfallsinassetpricesanddisruptionofmarkets.
2) WedonotconsiderhowthesemethodscanbeusedtoestimatetheLPforaparticularportfolio.
Eachofthemethodsmakean(implicitorexplicit)assumptionabouttheportfoliooffinancial
instrumentsweareestimatingtheLPfor.Theabsolutelevelofourestimateisdirectlyrelatedto
theseassumptionswhichwesummarisein.Consequentlyestimatesarenotdirectlycomparable
estimatesarenotdirectlycomparable
estimatesarenotdirectlycomparable
andforanyapplication(suchasdeterminingthevalueofinsuranceliabilities)actualestimatescould
actualestimatescould
belowerorhigherthanthosepresentedhere
belowerorhigherthanthosepresentedhere.
anthosepresentedhere
3) Despitethebroadlyconsistentoverallpatternofresults,individualresultsdoraisequestionsabout
questionsabout
therobustnessofindividualmethodsandmodelchoices.
therobustnessofindividualmethods
4) Allresultsshowninthissectionarerelativeto
relativetos
relativetoswaprates.Measuresrelativetogovernmentbonds
waprates
requireaddingtheappropriateswapspread.Notethatoverthisperiodswaprateshavebeenfar
fromstable-seeFigure2.
5) Althoughn
negativeLPisnotintuitiveandmostpractitionersbelieve
egativeLPisnotintuitiveandmostpractitionersbelieveit
itshouldbenolessthan
itshouldbenolessthan0
shouldbenolessthan0some
0
ofourestimatesagainstswapsarenegative.Althoughwehavenotexploredthereasonforthisfully
wethinkthiscouldbepartlyduetotheextremelylowbondspreadsduring2005and2006and
instrumentspecificfactorssuchasdifferencesincouponratesorthequotationbasisandother
practicalmeasurementissues.
Table1
Table1:Referenceportfolioassumptionsusedinthedifferentmethods
:Referenceportfolioassumptionsusedinthedifferentmethods
inthedifferentmethods
Method
Method
ReferencePortfolio
Assumption
Assumption
CDSBasisapproachwithCDS
Indexandsyntheticbonds
portfolio
Investmentgrade
bonds,
CDSBasisapproachwithCDS
Indexandbondindex
Investmentgrade
bonds,
Issues
Issues
CDSindexnottypicallyrepresentativeof
investableportfolio.
5yearmaturity
CDSandbondindicesarenotwellmatched–
Bondindexdoesnotnecessarilymatchthe
assumption.
5yearmaturity
StructuralMethods
Investmentgrade
bonds,
Averagematuritychangeswithindex
constituentsusedtocreateaverage.Provides
resultsfordifferentmaturityandcreditratingso
cantargetwhatweneedto.
7-10yearaverage
maturity
CoveredBonds
AAAcoveredbonds,
Non-coveredbondsusedinourproxycurve.
Variousmaturities
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150
EUR5yearSwapSpread
USD5yearSwapSpread
GBP5yearSwapSpread
bps
100
50
0
Dec-2005
Dec-2006
Dec-2007
Dec-2008
Figure2
Figure2:5yearswapspreads
:5yearswapspreadsrelativetogovernmentbonds
relativetogovernmentbonds
Letusexamineindividualresultsinmoredetail7.
7
Forreference,theBankofEnglandmodelispublishedintheirfinancialstabilityreviewsavailablefrom
http://www.bankofengland.co.uk/publications/fsr
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3.1 Model free negative CDS basis approach
ThisapproachdirectlyestimatestheLPincorporatebondmarkets.Weconsiderthreedifferentpairings:
1.
iTraxxCDSindex(EUR)andasyntheticcorporatebondindexconsistentwithiTraxx8.
2.
iTraxxCDSindex(EUR)andtheiBoxx3-5yearinvestmentgradecorporatebondindex.
3.
CDXCDSindex(USD)andaMerrillLynch3-5yearinvestmentgradecorporatebondindex.
Figure3showshowtheseestimatesvaryovertimeusingswapsastherisk-freerate.Weseeageneral
increaseinLPstartinginmid-to-late2006andjumpingagaininmid-to-late2007.Thetwoestimatesforthe
Eurohighlightthesensitivityofthismethodtochoiceofreferenceportfolio.WhiletheiBoxx-Traxxpairingis
morereadilyavailableandeasiertocompute,thesyntheticindexisconsistentwiththeactualconstituentsof
iTraxxandproducesanestimatesomewhatlower.Asaresult,careisrequiredwhenchoosingwhich
approximationsaremadewhenapplyingthismethod.
Onewaytoincreasetheusabilityandrobustnessofthismethodfordifferentapplicationswouldbetocreate
ratingandmaturityspecificbucketsfromunderlyingCDSandbonddata.Workwouldberequiredto
exploretheliquidity,determiningtherulesforinclusionandmakingsimplifyingassumptionsforeachbucket.
450
Syntheticindex- Swapspread- iTraxx
400
350
300
iboxx-SwapSpread- iTraxx
MerrillLynch- Swapspread- CDX
250
bps
200
150
100
50
0
Dec-2005
-50
Dec-2006
Dec-2007
Dec-2008
-100
Figure3
LPestimatesderivedusingthemodelfreenegativeCDSbasisapproachusingswapsasrisk--freerate.
Figure3:LPestimatesderivedusingthemodelfreenegativeCDSbasisapproachusingswapsasrisk
freerate.
8
Notethisdataseriesstopsattheendof2008asthenamematchingprocessweusedtocreateaniTraxxportfoliogave
toofewratingandmaturitymatchesformorerecentobservations.
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3.2 Structural Merton-style model
WeuseourownmodelandassumptionstoestimateLPatdifferentpointsintime.Weareonlyableto
providequarterlyupdatessincewerelyhereonlong-termmaturityequityindexoptiondatacollatedfroma
panelofinvestmentbanks9.Weproduceresultsforeachcreditclassanddurationbucketandaggregatethis
intoanaverage,usingthecreditclassandmaturitycharacteristicsoftheMerrillLynchinvestmentgradebond
index.
Figure4showsourstructuralmodelestimatesforthethreeeconomiesandfortwosetsofdefault
assumptionsfortheUSandUK(wherewehavealongtime-seriesavailable)usingthespreadoverswap
rates.ForUSDandGBPsimilarbehaviourtotheaboveestimatescanbeobserved.ForEUR,althoughan
increaseisapparent,itisnotassteepandisyettofall.Althoughwearenotentirelyclearwhythisisthecase,
itcouldbeduetotherelevanceofUSdefaultexperienceforcalibratingthemodelforEURissuers,or
samplingerror.
250
GBP(1920)
USD(1920)
EUR(1985)
GBP(1970)
USD(1970)
200
150
bps
100
50
0
-50
Jun-2009
Mar-2009
Dec-2008
Sep-2008
Jun-2008
Mar-2008
Dec-2007
Sep-2007
Jun-2007
Mar-2007
Dec-2006
Sep-2006
Jun-2006
Mar-2006
Dec-2005
-100
Figure4
Figure4:Weightedaveragesofliquiditypremium
Weightedaveragesofliquiditypremium
liquiditypremiumforEUR(1985calibration)
forEUR(1985calibration),GBPandUSD
(1985calibration),GBPandUSD
,GBPandUSD(1970and1920calibration)forinvestment
(1970and1920calibration)forinvestment
gradebondsrelativeto
gradebondsrelativeto
relativetothespreadoverswaps
thespreadoverswaps.
swaps.
9
Otherdatasourcesareavailablewhichwillprovidethisdatamorefrequently,buttheywillmakeanumberof
interpolationandextrapolationchoicesthatneedtobeconsidered.Wearecurrentlyinvestigatingotherdatasourcesto
provideamorefrequentservice.
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3.3 Direct computation – covered bonds
Figure5plotsthespreadofacoveredbondindex(hereaEURAAACompositebondindexisusedasa
proxy)throughtimefordifferentmaturities.Weobserveasimilarpatterntothatseenabove–witha
significantriseinspreadsfromtheonsetofthefinancialcrisis.Recallthatourmethodologylooksatthe
differenceinfittedyieldcurvessothismethodgivessomeindicationforhowthetermstructureofLPvaries
throughtime.Wealsonoteachangeinthetermstructureattheendof2008forallbut1yearmaturity.
BeforethisweseethatthereisalargerLPinlongermaturities,butin2009itcanbeseenthattheLPfor15
yearmaturitiesislower,attimes,thanboththatfor5and10maturities.Furtheranalysisisrequiredto
understandwhy,butthisdoesraisequestionsabouthowLPestimatescanbetransformedtoinstruments
withdifferentmaturities.
Purecoveredbondindicesareavailablebutnotasyieldcurves,soanobviousextensionhereistoconstructa
coveredbondcurvewhichcontainsonlycoveredbonds.
140
1Year
5Years
120
10Years
15Years
100
80
bps
60
40
20
0
-20
-40
Dec05
Jun06
Dec06
Jun07
Dec07
Jun08
Dec08
Jun09
Figure5
Figure5:EUR
:EURcovered
EURcovered
coveredbondindex
bondindex
ndexproxy
proxy-EURswapsatdifferentmaturities
EURswapsatdifferentmaturities
wapsatdifferentmaturities
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References
Dick-Nielsen,J.,Feldhütter,P.,andLando,D.(2009).Corporatebondliquiditybeforeandaftertheonsetof
thesubprimecrisis.Workingpaper.
Longstaff,F.,Mithal,S.,andNeis,E.(2005).Corporateyieldspreads:Defaultriskorliquidity?Newevidence
fromthecreditdefaultswapmarket.TheJournalofFinance,60(5):2213–2253.
Merton,R.(1974).Onthepricingofcorporatedebt:Theriskstructureofinterestrates. J.Finance,29:449–
470.
Webber,L.(2007).Decomposingcorporatebondspreads.BankofEnglandQuarterlyBulletin.
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