Adjusting Corporate Default Rates for Rating Withdrawals

Transcription

1 Adjustng Corporate Default Rates for Ratng Wthdrawals Rchard Cantor Managng Drector, Credt Polcy Research Moody s Investors Servce, 99 Church Street, New York, NY 0007, USA; phone: 22) ; emal: rchard.cantor@moodys.com Davd. Hamlton Senor Vce Presdent, Credt Strategy Moody s Investors Servce, 99 Church Street, New York, NY 0007, USA; phone: 22) ; emal: davd.hamlton@moodys.com he authors would lke to thank Edward Altman, Lea Carty, Jerry Fons, Martn Frdson, Gus Harrs, Davd Lando, and l Schuermann for helpful dscussons and comments on earler drafts of ths paper. he vews expressed heren are solely those of the authors and Moody's Investors Servce.

2 In press, he Journal of Credt Rsk Adjustng Corporate Default Rates for Ratng Wthdrawals Rchard Cantor and Davd. Hamlton 3 May 2007 Abstract Many market practtoners base ther parameter estmates on results reported n ratng agency default studes. Although the comparablty of default rates reported by the agences has ncreased n recent years, many dfferences n default rate calculaton methodologes reman. One mportant and poorly understood methodologcal dfference s whether default rate estmates are or should be) statstcally adjusted for ssuer ratng wthdrawals, whch occur when borrowers shft from rated publc to unrated prvate debt fnance or when all ther debts are extngushed outrght. In ths paper we revew the mechancs and ratonale behnd the unadjusted and wthdrawal-adjusted default rate calculaton methodologes. We dscuss the relatve merts of adjustng or not adjustng for ratng wthdrawals and the mportance of the assumptons underlyng each method. We demonstrate that the assumpton of random data censorng posted by the wthdrawal-adjusted method s supported by the avalable data. We conclude that wthdrawal-adjusted default rates are the approprate estmates of expected default rates for oblgatons wth specfc expected tenors and provde common yardstcks for comparng default rsk for credt exposures across dfferent sectors, regardless of dfferences n realed ratng wthdrawal rates. Keywords: default probablty, credt ratngs, ratng agences, data censorng, rsk management 2

3 . Introducton he measurement of the probablty of default for a corporate exposure s often the frst step n credt rsk modelng, management, and prcng. Ratng agency default studes are wdelyused sources for estmates of these mportant parameter values. he default statstcs reported n ratng agency studes are based on rch source data sets, contanng a large number of corporate ratng hstores and credt events. It s frequently assumed that the default statstcs reported by the ratng agences are calculated usng more or less the same methodology and may, therefore, be used nterchangeably, compared, and nterpreted more or less consstently. Furthermore, t s often taken for granted that the default statstcs reported by the ratng agences are equally approprate measures of rsk for a gven purpose. In the past decade there has ndeed been a convergence n the methodologes used by the agences to calculate cumulatve default rates, and ther methodologes currently share many smlartes. Most ratng agences emphase ssuer-based default statstcs rather than dollar-volume based statstcs; average default rate estmates for an hstorcal tme perod are calculated usng a cohort-based approach; and, long-term mult-year default rates are derved usng a dscrete-tme haard rate method. Despte these smlartes, the default rates for correspondng ratng categores reported by the ratng agences often dffer sgnfcantly. Whle varatons n default rates by ratng category across agences are to be expected due to dfferences n ratng methodologes, dscongrutes n the dstrbutons of the underlyng rated populatons, varatons n the agences' defntons of default, the hstorcal tme perods under study and the perodcty of observaton, an addtonal reason to expect dfferences s that each ratng agency's default rate calculaton methodology dffers n ts statstcal treatment of ratng wthdrawals. Ratng agency default rate calculaton methodologes generally take one of two approaches to dealng wth ratng wthdrawals when calculatng default rates: gnore them and make no adjustment; or adjust for ratng wthdrawals by treatng them as randomly censored data. Under the no adjustment for wthdrawals method, ssuers whose ratngs are wthdrawn are treated as f they remaned n the data sample over the entre measurement horon. An attempt s made to montor ther default status over the entre measurement horon. If no default s observed, the frm s assumed not to have defaulted. Hence, the no adjustment method takes a relatvely smple vew of the evoluton of credt rsk n that there are only two possble outcomes, default or non-default. Ratng agences also report default rates derved by calculatng mult-perod ratng transton matrces. Although we do not dscuss ths method n ths paper, transton matrxderved default rates whch generally report ratng wthdrawals as a dstnct state are very close to those derved usng the unadjusted method dscussed later n ths study. 3

4 Under the wthdrawal-adjusted method, ssuers whose ratngs are wthdrawn are treated as randomly censored data, meanng that t s assumed that frms whose ratngs are wthdrawn would have faced the same rsk of default as other smlarly rated ssuers f they had stayed n the sample. he wthdrawal-adjusted method recognes that there are three possble end-of-perod outcomes: default, survval, and ratng wthdrawal. Ratng wthdrawals represent losses from the data sample before the fnal outcome of nterest default or survval) s observed. Most ratng agences calculate and report default rates usng both methods, but each tends to emphase dfferent sets of estmates. Moody's default statstcs, for example, are most often reported usng the adjusted-for-wthdrawals method Hamlton 2006), whereas Standard and Poor s has hstorcally emphased ts unadjusted statstcs Vaa, Aurora, and Schneck 2006)). Both calculaton methods have legtmate uses under the approprate assumptons, but each method makes a dfferent statement about default rsk. As they are derved from hstorcal corporate ratng hstores and default data, the default rate estmates generated by each method represent a vew of the "actual" default experence of a gven data sample. However, emprcal default rates are frequently used as proxes for expected default probabltes, and t s for ths purpose that the treatment of ratng wthdrawals becomes an mportant concern. Unadjusted default rates may be useful benchmarks for the expected lkelhood of default for oblgatons that have fxed maxmum potental tenors and expected ratng wthdrawal rates smlar to those exhbted by ssuers n the emprcal sample on whch default rates were estmated. In contrast, wthdrawal-adjusted default rates are the approprate estmates of expected default rates for oblgatons wth specfc expected tenors. Wthdrawal-adjusted default rates therefore provde common yardstcks for comparng default rsk for credt exposures across dfferent sectors, regardless of dfferences n realed ratng wthdrawal rates. In many respects, the ssue s smlar to that studed n Altman 989). Altman 989) mantaned that prevalng methods for calculatng mult-year bond default rates were based estmates of expected default rsk because they faled to account for maturtes, calls, and other early redemptons that occur pror to the end of a gven measurement horon. Altman's mortalty rate estmator recogned that calculatng default rates based on the survvng populaton was the relevant measure of expected default rsk. Comng to a smlar concluson, Asquth, et. al. 989) showed that bond default probablty estmates are materally affected by early bond redemptons, as nearly two-thrds of hgh yeld bonds n ther data sample had been called, defaulted, or exchanged wthn 0 years of ssuance. he adjustments advocated by Altman 989) and Asquth et. al. 989) therefore amounted to adjustng ther bond default rates for survval bas. More recently, Mählmann 2005) showed 4

5 that default probablty estmates that do not adjust for mssng ratngs are downwardly based. 2 However, ratng agency default rates are typcally ssuer or corporate famly) based, adjustng for wthdrawals depends crtcally on the assumpton of random data censorng. An ssuer s ratng may be wthdrawn for a varety of reasons. One common reason s that a company has extngushed all of ts rated publc debt due to scheduled maturtes, companyntated calls, nvestor-ntated puts, or mergers and acqustons. In many cases, the ssuer s no longer at rsk of default after a ratng wthdrawal because the wthdrawal event corresponds to the extngushment all of ts debt oblgatons. However, n many other cases an ssuer remans at rsk of default after ts ratng has been wthdrawn because t has replaced all of ts publc, rated debt wth unrated, typcally prvate, debt. he relevant queston s whether ssuer ratng wthdrawals are unnformatve events or are correlated wth changes n credt qualty. he remander of ths paper s organed nto fve sectons. In the next secton we revew the general cumulatve default rate calculaton methodology followed by the ratng agences. We also dentfy certan features of Moody's default rates that dstngush them from other approaches. In Secton 3 we explan the mechancs of the adjustment for ratng wthdrawals under the assumpton of unnformatve censorng and dscuss the ratonale underlyng the unadjusted and wthdrawal-adjusted methods. Followng a long lne of academc research, we argue that wthdrawal-adjusted default rates have the most general use for applcatons requrng estmates of expected future default rsk. In Secton 4 we analye the hypothess of the neutralty of ssuer ratng wthdrawals. We demonstrate that the avalable evdence suggests the assumpton of random censorng s reasonable. Secton 5 offers some concludng thoughts. 2. Cumulatve default rate methodology he cumulatve default rate calculaton methodology used by the major ratng agences s a dscrete-tme approxmaton of the nonparametrc contnuous-tme haard rate approach. 3 A pool of ssuers, called a cohort, s formed on the bass of the ratng held on a gven calendar date or set of dates), and the default/survval status of the members of the cohort s tracked over some stated tme horon. he tme horon for whch we desre to measure a default rate s dvded nto evenly spaced tme ntervals e.g. months, years) of length t. Hence, the data s dscrete n that the tme to default s not measured contnuously. In each tme 2 Moreover, Mählmann 2005) dscusses approprate adjustments to PD estmates for dfferent types of nonrandom censorng. 3 he method s essentally that of Cutler and Ederer 958). hs approach s sometmes referred to as the lfe-table or actuaral method. 5

6 nterval, some fracton of the cohort that has survved up to that tme may default. he margnal default rate s the probablty that an ssuer that has survved n the cohort up to the begnnng of a partcular nterval t wll default by the end of the tme nterval. 4 he - horon cumulatve default rate s defned as the probablty of default from the tme of cohort formaton up to and ncludng tme horon. Cohorts of ssuers can be formed on the bass of ther orgnal ratngs or on the ratngs held as of the cohort formaton date. he orgnal ratng method, studed by Altman 989), groups ssuers nto pools based on the frst ratng that was assgned to the ssuer or one of ts oblgatons); such pools consst only of frst-tme ssuers that were rated as of the cohort formaton dates). 5 In contrast, the cohort ratng method on whch ratng agences corporate default studes often rely are based on pools of ssuers holdng a gven ratng on the cohort date regardless of orgnal ratng or tme snce ssuance. Because long-term corporate ratngs address the lkelhood of default over multple tme horons, regardless of age or tme to maturty, agency corporate default studes usually report default rates based on ssuers ratngs held on the cohort date rather than on orgnal ratngs. 6 Mathematcally, the margnal default rate n tme nterval t, dt), for a cohort of ssuers formed on date y holdng ratng s defned as the number of defaults xt) from the cohort that occur n the tme nterval t dvded by the effectve se of the cohort, nt), at the start of tme t: 2.) x t) y d y t) = n t) Intally, nt) s equal to the number of ssuers n the pool holdng ratng on the cohort formaton date. As tme from the ntal cohort date passes the se of the denomnator falls because some ssuers n the cohort fal to survve to the next tme nterval. As we dscuss n detal n the next secton, dfferences n the default rates reported by the ratng agences arse to a large extent because each ratng agency models the default/survval process dfferently. y 4 he term margnal default rate s partcular to ratng agences and s usually referred to as the haard rate. 5 he orgnal ratng method captures the mpact of the now well-known agng or seasonng effect.e. the term structure of default rsk for a gven ssuance year and ratng category). Margnal default haard) rates based on orgnal ratngs exhbt more pronounced "humps" relatve to the cohort ratng method. 6 he major ratng agences assgn both oblgaton-level and ssuer-level credt ratngs. When a sutable ssuer-level ratng does not exst, one s often nferred from exstng oblgatonlevel ratngs. For Moody s approach see Hamlton 2005). Standard and Poor s methodology s descrbed n Vaa, Aurora, and Schneck 2006). 6

7 Cumulatve default rates for nvestment horons of length, denoted D), are bult up from the margnal default rates, and are found by subtractng the product of the fracton of survvng cohort members n each of the t tme ntervals from unty: 2.2) D y ) = t= [ d y t)] Or, expandng equaton 2.2 and droppng ndces for brevty): 2.3) D ) = d) + d2)[ d)] + d3)[ d)) d2))] d ) t= [ d t)]) Equaton 2.3 hghlghts the fact that a cumulatve default rate s a condtonal probablty. In the frst tme perod, a fracton of the credt exposures n the cohort ether defaults or survves. he credt exposures that survve perod one may then go on to default or survve n perod two; those that survve perod two may go on to default or survve n perod three, etc. Because the tme perods are non-overlappng and the probablty of default n each perod s assumed to be ndependent, the -perod cumulatve default rate s defned as one mnus the product of the margnal survval rates. Issuer-based default rates receve partcular emphass n the ratng process because the expected lkelhood of default of a bond ssuer holdng a gven ratng s expected be the same regardless of dfferences n the nomnal ses of the exposures. 7 For example, the expected lkelhood of default for a B-rated corporate ssuer should be the same whether the se of the exposure s $200 mllon or $2 bllon, everythng else equal. Issuer-based default rates gve equal weght to all ssuers n the default rate calculaton. Dollar volume based default rates, whch weght each exposure by the total face or market) value of ts outstandng bonds, are useful statstcs for portfolo benchmarkng, but they are less useful for formng expectatons about future default probabltes for ratngs. 8 he frequency wth whch cohorts are formed also mpacts the accuracy of the average default probablty estmates for a gven ratng category. he hgher the samplng frequency equvalently, the shorter the tme nterval between cohorts the more accurate 7 When a frm defaults on one bond t usually defaults on all ts bonds due to cross-default clauses n bond ndentures. Addtonally, n some bankruptcy codes e.g. U.S. Chapter and France's "sauvegarde" procedure) an automatc stay provson trggered upon a bankruptcy flng creates perfect cross default, causng all debt to default at the same tme unless the bankruptcy court grants a waver). hs approach s also consstent wth the structural vew of credt rsk e.g. Merton 974)) whch regards default as an ssuer-level phenomenon that s prmarly a functon of frm-level characterstcs, such as ts operatng performance and lablty structure. 8 Frdson 99) s an nterestng dscusson of the many dfferent ways to measure default rates that addresses ths and other topcs. 7

8 the estmates of expected default rates for a gven ratng category become. Closer cohort spacng captures ratng changes and default events that occur n small tme ntervals, an mportant consderaton when an ssuer's ratng s undergong rapd change. he effect of cohort spacng on default rate estmates becomes clear n the followng example. Consder the senor unsecured ratng hstory for LV Steel Company up to ts default on July 7, 986: able 2. LV Steel Company Ratng Hstory Ratng Date Ratng Credt Event /8/970 A Frst ratng assgned 4/26/982 A3 Alphanumerc ratng assgned 5/5/982 Baa2 Downgraded 0/8/982 Baa3 Downgraded /8/983 Ba Downgraded 3/20/985 Ba3 Downgraded 8/9/985 B3 Downgraded 7/7/986 Caa Defaulted Usng annual cohort spacng, LV Steel Company's default s recorded for the A- rated cohorts from , the Baa3-rated 983 cohort, the Ba-rated cohorts n 984 and 985, and the B3 986 cohort. If one nstead formed cohorts at monthly ntervals, the default event gets captured at the approprate tme horon for every ratng n ts ratng hstory, ncludng ts A3, Baa2, Ba3 and Caa ratngs that are gnored under annual cohort spacng. Moody's has tradtonally reported ts average cumulatve default rates calculated usng annual cohort spacng cohorts of ssuers formed on January of each year). In Moody's 2005 default study, Moody's moved to monthly cohort spacng n calculatng ts average cumulatve default rates. Moody's beleves that monthly cohort spacng strkes a reasonable balance between the competng goals of nformatonal effcency and tractablty. 9 Whle nvestors may be nterested n the cumulatve default experence of a partcular cohort, averages taken over many cohort perods whch capture the effects of several macroeconomc and credt cycle peaks and troughs) are requred to estmate expected cumulatve default probabltes. he average cumulatve default rate for a gven hstorcal tme perod s calculated by frst averagng the perod t margnal default rates across all 9 here s a tradeoff between nformatonal effcency and tractablty when calculatng default rates usng duraton methods. Default/survval tmes are precsely measured usng contnuous-tme methods, but the resultng output may be unweldy. Makng default event tmes dscrete by arbtrarly choosng the wdth of the margnal tme ntervals the dstance between cohort formaton dates results n some loss of effcency, but greatly facltates the presentaton and nterpretaton of cohort cumulatve default rates. For example, nvestors are often nterested n default rates for certan dscrete tme horons e.g. one, fve, ten years). As the tme nterval t s allowed to shrnk so as to be so small that at most one default occurs wthn an nterval, the derved default rates approach the contnuous tme estmate Kaplan and Meer 958)). More mportantly, the dscrete-tme cohort approach does not depend on the Markov assumpton see Lando and Skodeberg 2002)). 8

9 avalable cohort dates y n the hstorcal data set Y, then calculatng the cumulatve rates usng equaton 2.2 or 2.3. Most often, average cumulatve default rates are weghted averages, where each perod's margnal default rate s weghted by the relatve se of the cohort proporton of ssuers) n each tme nterval t. 0 Equaton 2.4 shows that the calculaton of the average cumulatve default rate for ratng class, D ), s derved from the weghted average margnal default rates, t) d, calculated from all the avalable cohort margnal default rates n the hstorcal data set Y: 2.4) where 2.5) D ) = d t) = t= y Y y Y [ d x t) y n t) y t)] If, for example, one were calculatng the average three-year cumulatve default rate for the tme perod wth annual cohort spacng), one would frst take the weghted average of the d) from each of the three cohort years. he second year's average margnal default rate would consst of the weghted average of the two cohort years 2003 and 2004) wth two years of exposure avalable, d2). he thrd year average margnal default rate would smply consst of the 2003 cohort's thrd year margnal default rate snce t s the only cohort wth three years of hstory avalable.e. t would receve 00% weght). he average cumulatve default rate would then smply be calculated accordng to equaton 2.4 usng the weghted average margnal default rates derved usng equaton 2.5. Note that ths procedure for calculatng average cumulatve default rates maxmes the exstng hstorcal nformaton by usng all the avalable ratng and margnal default rate data, not just ssuers wth ratng hstores that endure for a perod of at least length. Whle the thrd year's margnal default rate s calculated from just one cohort year the 2005 cohort), the three-year cumulatve default rate reflects nformaton on condtonal default/survval derved from all three cohort years. hs approach has the great advantage of allowng one to utle data for ssuers wth both long and short hstores to calculate default probabltes for any tme horon. 0 Weghted averages place greater weght on more recent cohorts as both the number and total dollar volume of bond ssuance has experenced secular growth over tme. hs s appealng from a statstcal samplng pont of vew, but also because defaults tend to be correlated wth perods of actve bond ssuance. Smple averagng may be approprate n some crcumstances; e.g. the mpact of macroeconomc fluctuatons on mult-year default rates. 9

10 What may seem lke the smplest method dervng average cumulatve default rates drectly from the cohort cumulatve default rates lmts the estmated average to the set of cohorts wth at least full perods of data. For long-horon default rate averages, ths requrement throws away much useful data as well as rases the nose of the estmate). More mportantly, however, dervng average cumulatve default rates drectly from cohort cumulatve default rates may result n serously based and nconsstent estmates of expected cumulatve default rsk. For example, average cumulatve default rates could possbly be decreasng f the hstorcal data sample conssts of default rates that have been very hgh n recent cohorts but very low n past cohorts. 3. Adjustng for ratng wthdrawals he calculaton methodologes for cohort and average cumulatve default rates descrbed n the prevous secton are generally followed by all the major ratng agences agan, wth mnor varatons). Agency default rate calculaton methodologes dverge, however, on ther assumptons about the default/survval process. Whereas unadjusted margnal default rates are ncrementally adjusted for defaults that occurred n the past, the wthdrawal-adjusted method also accounts for ratng wthdrawals that occur pror to the end of the measurement perod. Ratng wthdrawals complcate the calculaton of default rates because there wll be some ssuers ntally ncluded n a cohort that wll be lost from the data sample before the fnal outcome of nterest default or survval) s observed. In practce, a ratng agency's approach to modelng the survval process s reflected n ts calculaton of the effectve cohort se n each tme nterval;.e. the denomnator of equaton 2.. Under the unadjusted method, the effectve se of a cohort of ssuers rated formed on date y n tme nterval t s equal to the ntal se of the cohort less the total number of ssuers that have defaulted pror to the current tme nterval and therefore cannot default n the future). he denomnator of the cohort margnal default rate equaton 2.) for the unadjusted method s therefore calculated: 3.) n t) = n y y t 0) = 2 x ) y he unadjusted method s often referred to as the "statc pool" method. However, the term has been subject to some confuson. Sometmes, the term statc pool s meant to mply no adjustment for wthdrawals. Other tmes, the term statc pool has been used to refer to what we have defned n Secton 2) as the cohort approach to calculatng mult-year default rates. Usng our termnology, the statc pool method can be defned as a cohort-based method that does not adjust for ratng wthdrawals. 0

11 In contrast, the wthdrawal-adjusted method recognes that there are three possble end-of-perod outcomes: default, survval, and ratng wthdrawal. 2 he cohort se at tme t s calculated as n equaton 3., but wth an addtonal adjustment for the number of ssuers that have had ther ratngs wthdrawn n perods pror to the current tme nterval. Addtonally, a small adjustment s made for ratng wthdrawals that occur wthn the current tme nterval. Wthdrawn ratngs that occur wthn an nterval are treated as f they were censored at the mdpont of the nterval;.e. were at rsk for half the tme. 3 Equaton 3.2 shows the calculaton of the denomnator for the adjusted for wthdrawals method. Note that equaton 3.2 s smply 3. wth two addtonal terms subtracted to account for ratng wthdrawals. It becomes clear, then, that the denomnators of adjusted default rates are never larger than those usng the unadjusted method. Hence, default rates usng the adjusted method wll be hgher. 3.2) n t) = n y y 0) t = 2 x ) y t = 2 w ) y 2 wy t) Unadjusted default rates are hghly ntutve. hey report the share of ssuers that were observed to have experenced a default over a partcular tme horon. Unadjusted default rates are useful benchmarks for the lkelhood of default for oblgatons that have fxed maxmum tenors and expected ratng wthdrawal patterns smlar to those of the emprcal sample from whch the default rate estmate was derved. 4 In contrast, wthdrawal-adjusted default rates are more complex n both calculaton and nterpretaton. Wthdrawal-adjusted default rates are based n part on hypothetcal data whose accuracy depends on the assumpton that ssuers whose ratngs are wthdrawn would have defaulted at the same average rates as other smlarly-rated ssuers. One mght reasonably ask, therefore, why bother adjustng default rates for ratng wthdrawals? Unadjusted default 2 he three possble end-of-perod outcomes are usually consdered to be mutually exclusve. Issuers that are downgraded and default n the same tme nterval are treated as defaults, for example; ssuers that default and have ther ratng wthdrawn n the same tme nterval are categored as defaults, not wthdrawals. 3 he wthn-perod adjustment s vald only f one s confdent that defaults are observable after a ratng wthdrawal wthn the current tme nterval. he tme nterval must, therefore, be reasonably short such as one year or less). Of course, for small enough tme ntervals the effect of the wthn perod adjustment s mmateral and can be dropped from equaton A prme example s statc synthetc corporate CDOs, whch reference the debt oblgatons of a large number of corporatons over a common and fxed maturty. In the event that all of the publc debts and syndcated loans of a corporaton are pad off, the rsk n the CDO assocated wth that entty dsappears. In such a structure, the hstorcal average ratng wthdrawal pattern of the typcal corporate ssuer may be very relevant. For cash CDOs, on the other hand, the pattern of ssuer ratng wthdrawals s less relevant, snce t s unlkely to be closely related to the realed maturty patterns loans and bonds that comprse the structure s collateral pool.

12 rates, t turns out, have three shortcomngs not shared by wthdrawal-adjusted default rates that lmt ther usefulness as measures of expected default rsk for smlarly rated oblgatons. Frstly, unadjusted cumulatve default rates are downwardly based measures of default rsk because one cannot observe all defaults experenced by ssuers after ther ratngs are wthdrawn. 5 Although ratng agences make every attempt to montor default events for all formerly rated ssuers, successfully dong so s exceptonally dffcult. Fgure 3. gves an ndcaton of the magntude of the problem. Of the,20 Moody s-rated corporate bond ssuers snce 980 that have defaulted and had ther ratngs wthdrawn, the percentage of defaults observed after the ratng wthdrawal date 5%) s relatvely low compared to that before the wthdrawal date 95%). As we show n the next secton, many ratng wthdrawals occur when ssuers retre ther publc debt wth proceeds rased through prvate bank borrowngs. hese frms reman at rsk of default but ratng agences cannot easly track ther subsequent default experence. Hence, wthout adjustments for ratng wthdrawals, measured default rates are lkely to understate true long-term default probabltes. Fgure 3. Dstrbuton of Dstance between Wthdrawal and Default Dates 5 It has often been argued e.g. DeRosa-Farag, et. al. 999)) that wthdrawal-adjusted cumulatve default rates are "based" too hgh due to the correcton for data censorng. However, ths perspectve confuses concerns about sample se and statstcal sgnfcance wth ssues of bas. Consder the followng oft-used hypothetcal example. Suppose that there were 0 bond ssuers n a cohort, nne of whch had ther ratngs wthdrawn over a 0-year tme span for bengn reasons such as mergers or retrement of debt. If, n the 0th year, the one company that was stll rated were to default, the wthdrawal-adjusted margnal default rate would be 00%. hs sample statstc s not based. However, because only one ssuer was at rsk of default n ts tenth year, the statstcal relablty of the 00% pont estmate s vrtually nl. In order for the unadjusted default rate to reach 00%, all nne of the censored ssuers would need to default after ther ratngs were wthdrawn. he unadjusted method assumes that there were ten ssuers at rsk of default n the tenth year, lowerng the emprcal margnal default rate estmate to 0%. he small sample problem does not go away by changng the defnton of the default rate. 2

13 00% 90% 80% Cumulatve % of Issuers 70% 60% 50% 40% 30% 20% 0% N =,20 0% < >0 Years between Wthdrawal and Default Date t = 0) Secondly, the relevance of unadjusted default statstcs as gudes of future expected default rsk s lmted to sets of ssuers wth smlar ratng wthdrawal patterns. Whle all ssuers that carry the same ratng can reasonably be expected to have roughly the same mean wthdrawal-adjusted default rates, ther unadjusted default rates are lkely to vary sgnfcantly. Borrowers from dfferent ndustres wthn the non-fnancal corporate sector and across dfferent sectors altogether non-fnancal corporates, fnancal corporates, and soveregns) have very dfferent ratng wthdrawal patterns and should therefore be expected to have markedly dfferent unadjusted default rates by ratng category. Moreover, structured fnance securtes have ratng wthdrawal patterns that dffer consderably from one another and from those of the broad unverse of corporate ssuers. 6 As a result, t s hard to magne how one can realstcally use unadjusted corporate ssuer default rates to benchmark and compare the rsks of such dverse oblgatons. Wthdrawal-adjusted default rates, n contrast, facltate comparsons of default rates across asset classes wth markedly dfferent ratng wthdrawal patterns. Lastly, credt spreads are unlkely to be closely related wth unadjusted default rates. For a rsk neutral nvestor, the approprate dscount rate for debt oblgatons subject to default rsk s, n theory, equvalent to the rsk free rate rt) plus a spread to account for expected loss n default. 7 Hence, Rt) = rt) + dt)l, where dt) s the expected margnal default rate and L s the expected and assumed constant) rate of loss gven default. If we 6 See Hu 2004). 7 In addton to compensaton for expected credt losses, credt spreads may also be nfluenced by tax effects, nterest rate rsk prema, and a varety of other potental sources of rsk prema. he academc lterature n ths area s large. See Duffe and Sngleton 2003) for an overvew. 3

14 assume that nvestors recover nothng n the event of default.e. L=), then the requred spread st) for a rsk-neutral nvestor s smply the expected margnal default rate: st) = Rt)- rt) = dt). he approprate measure of dt) s the wthdrawal-adjusted margnal default rate, not the unadjusted margnal default rate. If an nvestor s expected nvestment horon were, say, 0 years, then s)he would only requre compensaton for default rsk only on exposures expected to survve for at least 0 years. In fact, as long as wthdrawal-adjusted margnal default rates are used n prcng, no further adjustments for realed ratng wthdrawals are requred. In Appendx B we demonstrate ths argument wth an example. As proxes for expected default probabltes, the advantages of wthdrawal-adjusted default rates are consequently threefold: they avod the downward bas that can arse from ncomplete knowledge of defaults for frms whose ratngs are wthdrawn; they provde a common yardstck for measurng default rsk for ssuers and oblgatons across dfferent sectors and asset classes regardless of dfferences n ratng wthdrawal rates and, thus, assocate a sngle tme profle of default rates for each ratng category for all types of credt exposures. Lastly, they provde useful and relevant data for prcng a wde varety of debt oblgatons. An example should make the dfferences between the two methods clear. able 3. shows detaled calculaton of the - through 0-year cumulatve default rates for the January, 996 cohort of B-rated corporate bond ssuers usng Moody s data. he table shows the number of defaults, xt) and ratng wthdrawals, wt), n each year after the cohort formaton date, as well as the effectve se of the denomnator n each tme nterval, nt), for each of the two methods. he table also shows the margnal default rates and the resultng cumulatve default rates for each method calculated usng equaton 2.2). able 3. 0-Year Cumulatve Default Rates: Adjusted vs. Unadjusted Methods January, 996 Cohort of B-Rated Corporate Issuers Wthdrawal-Adjusted Method Unadjusted Method t x t ) w t ) n t ) d t ) D t ) n t ) d t ) D t ) % 0.00% % 0.00% %.42% 59.35%.35% % 4.39% % 3.85% % 9.4% % 7.5% % 3.3% % 9.83% % 9.0% % 3.0% % 27.07% % 7.5% % 35.3% % 20.8% % 39.8% 4.95% 22.35% % 4.57% % 23.2% % 42.26% % 23.3% For each year t, xt) s the number of defaults, wt) s the number of ssuer wthdrawals, nt) s the effectve denomnator of the margnal default rate, dt), and Dt) s the cumulatve default rate. 4

15 able 3. shows that, at any gven measurement horon, the wthdrawal-adjusted method results n hgher default rate estmates than the unadjusted method, wth the dfference growng larger as the tme horon lengthens. he unadjusted 0-year cumulatve default rate shows that 23.3% of ssuers orgnally n the cohort defaulted by the tenth year. he unadjusted method s calculated as f the 322 ssuers whose ratngs were wthdrawn had remaned n the cohort and dd not default over the entre 0 year measurement perod. In contrast, the wthdrawal-adjusted 0-year cumulatve default rate method yelds an estmate of 42.26%. Default rates calculated usng the wthdrawal-adjusted method are based on the number of ssuers that reman at rsk.e. have not prevous defaulted nor had ther ratngs wthdrawn) of default n each tme nterval. For example, the margnal default rate n the tenth year s 25 bass ponts under the unadjusted method; under the wthdrawal-adjusted method, t s nearly fve tmes hgher,.9%. he wthdrawal-adjusted approach recognes that at the start of the tenth year only 84 ssuers actually remaned at rsk of default. Appendx A shows average cumulatve unadjusted and wthdrawal-adjusted default rates for a 20 year tme horon. In addton to the three advantages of the wthdrawal-adjusted method dscussed above, the method also generates default probablty estmates wth ntutve and appealng statstcal characterstcs. he data n able 3. llustrates that cumulatve default rates calculated usng the wthdrawal-adjusted method wll, at suffcently long tme horons, approach 00%. hs has a natural statstcal nterpretaton: condtonal on survval, all frms wll lkely eventually default. Cumulatve default rates for a gven cohort calculated usng the unadjusted method, on the other hand, may never approach 00% over any measurement horon. In order for the cumulatve default rate to approach 00%, all the ssuers whose ratngs were wthdrawn would need to be observed to ultmately default. As we have mentoned several tmes n the precedng sectons, the accuracy of the wthdrawal-adjusted default rate measure depends crtcally upon the assumpton of random data censorng. We analye the valdty of ths assumpton n the next secton. 4. Assessng the neutralty of ssuer ratng wthdrawals An ssuer ratng wthdrawal ndcates that a ratng agency has ceased to rate the ssuer and/or all of ts publcly rated bonds. 8 At the bond level, ratng wthdrawals are 8 Ratng wthdrawal polces vary across agences. At Moody s, an ssuer ratng wthdrawal almost always ndcates that all of an ssuer s debt ratngs have been wthdrawn. Standard and Poor s ssuer ratng wthdrawals, however, are not necessarly correlated wth debt ratng wthdrawals. Moody s polcy for ratng wthdrawals s descrbed n Moody s 2004). o 5

16 overwhelmngly correlated wth scheduled or antcpated redemptons. able 5. shows the reasons for bond ratng wthdrawals organed nto fve categores usng Moody s data. he table shows that of the 37,44 bond 9 ratng wthdrawals between 980 and 2005, 97% were assocated wth maturty, calls, puts, conversons, or mergers. he busness reasons category ncludes nstances where the ssuer chose to stop payng for a ratng or the se of the bond ssue was ncreased or decreased and re-rated), or Moody's removed the ratng because of lack of nformaton from the ssuer. he defaulted category ncludes cases where the bond ratng was wthdrawn on or shortly after the date of default. the authors knowledge, the other major ratng agences do not have publcly avalable methodologes descrbng ther crtera for the removal of ratngs. 9 Includes coupon, dscount, and convertble bonds. 6

17 able 5. Reasons for Ratng Wthdrawals, Reason %Bonds %Issuers Matured 68.84% 32.00% Called, put, converted, etc % 43.97% Reason unknown 3.5% 2.3% Busness reasons 0.% 2.02% Defaulted 0.05% 0.70% N 37,44 3,275 able 5. also shows that 76% of Moody s ssuer ratng wthdrawals corresponded to the fnal maturty, call, etc. of ts bonds. However, even f t were known that all the bonds of an ssuer were wthdrawn due to, say, maturty therefore makng default on those partcular bonds mpossble), the ratonale behnd the frm's decson ext the rated bond market mght reveal nformaton about ts default rsk. Bond ratng wthdrawals, whch are closely assocated wth maturtes and redemptons of specfc bonds, and ssuer ratng wthdrawals, whch are related to a frm's decson to ext or re-ssue n the rated publc bond market, reflect dfferent corporate fnance choces of a frm. An ssuer ratng wthdrawal mght sgnal heghtened future credt rsk. For example, a bond ssuer experencng fnancal dstress may be forced nto the prvate or short-term debt market. Contrarly, an ssuer ratng wthdrawal mght be negatvely correlated wth default rsk f ssuers experencng mprovng credt qualty choose to pay off ther rated debt oblgatons or replace debt wth equty. Moody's ratng polcy s that the ratng outstandng mmedately pror to a wthdrawal s ntended to reflect Moody's vew of the credt at the tme of the wthdrawal. 20 Hence, for Moody s data, ratng wthdrawals are supposed to be neutral events that are not systematcally correlated wth changes n default rsk. he neutralty of ssuer ratng wthdrawals s, ultmately, an emprcal queston, yet there s almost no publshed research on the subject. Carty 997) s the only study that has attempted to assess whether treatng ratng wthdrawals as randomly censored data s justfed. Carty's analyss usng Moody's data was, however, ndrect because he analyed the reasons for bond ratng wthdrawals and ther correlaton wth ssuer ratng wthdrawals. In ths secton we attempt to asses whether the assumpton that frms whose ratngs are wthdrawn would have faced smlar default rsk as frms that dd not wthdraw f had they remaned n the data sample s vald. We seek to answer two specfc questons. Frstly, does default rsk ncrease or decrease leadng up to and/or shortly followng the ratng wthdrawal date? Secondly, s the level of default rsk correlated wth ratng wthdrawal events? Establshng the neutralty of ssuer ratng wthdrawals s not straghtforward as there s no drect statstcal test for random versus nformatve censorng. We therefore attempt to nfer 20 See Moody's 2004). 7

18 the neutralty of wthdrawals by examnng several ndcatons of default rsk near ratng wthdrawal dates. Collectvely, the results we present n ths secton provde evdence that the assumpton of random censorng s reasonable. A large body of lterature 2 has shown that default rates are correlated wth past ratng actons: default rates are relatvely hgher condtonal on a past downgrade and relatvely lower condtonal on a past upgrade. If ratng wthdrawal rates exhbt the same dependence on past ratng actons, then we mght have cause to doubt the random censorng hypothess. For example, f ratng wthdrawal rates are hgher condtonal on a past downgrade, then ratng wthdrawals mght represent "hdden" defaults. able 5.2 shows mean one-year ssuer ratng wthdrawal rates condtonal on ratng upgrades, downgrades, and no changes n the pror year based on monthly cohorts of corporate ssuers between 983 and A ratng acton represents a change of one alphanumerc ratng notch or more; e.g. Ba2 to Ba3. Standard devatons are shown n parentheses. For nvestment-grade rated ssuers, mean ssuer ratng wthdrawal rates do not exhbt sgnfcant systematc dfferences when condtoned on ratng changes n the year pror to the ratng wthdrawal F2,794) = 2.20, p = 0.4). Among speculatve-grade rated ssuers there s no monotonc relatonshp between past ratng changes and wthdrawal rates: ssuers whose ratngs were unchanged n the past year exhbt the hghest mean rates of ratng wthdrawal, whle ssuers that experenced a ratng upgrade show the lowest mean ratng wthdrawal rates. he dfferences n the means for each sub-sample are statstcally sgnfcant F2,794) = 32.86, p < 0.00). One nterpretaton of these results s that rsky speculatve-grade ssuers that survve long enough.e. do not default) to experence a ratng upgrade are more lkely to pay off ther debts at maturty, convert them to prvate debt or equty, and have ther ratngs wthdrawn. Of course, ths s not knowable ex ante. Overall the lkelhood of a ratng wthdrawal does not appear to be strongly correlated wth ratng changes n the pror year. Smlar results are evdent when ssuer ratng wthdrawal frequences are condtoned on ratng outlook and revew Watchlst) status. Moody's ratng outlooks and revews provde ndcatons of the lkely drecton and tmng of future credt ratng changes. Cantor and Hamlton 2004) and Cantor and Hamlton 2005) showed that default rates for smlarly rated ssuers dffer when condtoned on ratng outlook and Watchlst status. Smlar to the analyss of ratng actons, a postve correlaton between outlooks/revew and ratng wthdrawal rates would cast a doubt on the valdty of the assumpton of unnformatve ratng wthdrawals. able 5.3 shows mean one-year ssuer ratng wthdrawal rates between 995 and 2005 condtonal on outlook and Watchlst status held at the start of 2 See, for example, Altman 99), Carty 997), and Cantor and Hamlton 2004). 8

19 each monthly cohort. 22 One-year ratng wthdrawal rates are remarkably smlar across the outlook categores, about 3.7% per annum for nvestment-grade ssuers and 8.2% for speculatve-grade ssuers. Moreover, statstcal tests of the equvalency of the means strongly ndcates no dfferences by outlook status. 23 able 5.2 Mean One-Year Ratng Wthdrawal Rates Condtonal on Ratng Changes n Pror Year Investment-Grade Speculatve-Grade All Rated Ratng Acton n Pror Year Upgraded Unchanged Downgraded 4.540% 2.04%) 8.069% 4.66%) 5.302% 2.34%) 4.549%.463%) 0.689% 3.84%) 6.35%.70%) 4.832%.927%) 9.082% 2.527%) 6.566%.93%) Sample perod: Standard devatons appear n parentheses able 5.3 Mean One-Year Ratng Wthdrawal Rates Condtonal on Outlook Status Investment-Grade Speculatve-Grade All Rated Outlook on Cohort Date Watch Up Postve Stable Negatve Watch Down 3.553% 3.66%) 8.030% 8.859%) 4.547% 3.376%) 3.592% 0.952%) 8.32% 2.857%) 4.47% 0.943%) 3.553%.59%) 7.629% 4.544%) 4.37%.59%) 3.739%.72%) 8.267% 3.567%) 4.553%.065%) 3.887% 2.602%) 9.090% 7.653%) 4.96% 2.689%) Sample perod: Standard devatons appear n parentheses Moody's KMV EDFs offer a drect way to analye changes n default rsk both before and after an ssuer ratng wthdrawal occurs. We analyed monthly Moody's KMV EDFs n the 2 months before and the 6 months after wthdrawal dates for 5,577 ssuers between 998 and he data was dvded nto two samples: 206 ssuers wth EDF data avalable that actually experenced a ratng wthdrawal, as well as a control group consstng of 5,37 ssuers that dd not experence a ratng wthdrawal. For the non-wthdrawn subset, we measured EDFs around the same ratng wthdrawal dates as for the wthdrawn subset. Because EDFs can vary between 0 and 0.20, and because we are nterested n changes n 22 Moody's ntroduced ts Watchlst n 99 and ratng outlooks n For the nvestment-grade subset, F4,600) = 0.59, p = For speculatve-grade ssuers, F4,600) = 0.98, p =

20 EDFs around wthdrawal dates, we normaled the EDFs so that they are equal to n the twelfth month pror to the ratng wthdrawal date. Fgure 5. shows the average EDF ndces around ratng wthdrawal dates for the two groups. he graph shows that the changes n the average EDFs of the two subsets exhbt very smlar patterns n the months leadng up to and after the ratng wthdrawal date. Both seres exhbt a slght upward trend leadng up to the ratng wthdrawal date, but the magntude of the change s relatvely small. Fgure 5. Average EDF Index around Ratng Wthdrawal Date EDF Index me to Ratng WIthdrawal Months) Not Wthdrawn Wthdrawn As a fnal assessment of the neutralty hypothess we compared the weghted average levels of credt ratngs for ssuers that experenced a ratng wthdrawal to those that dd not. Although ratng wthdrawal rates are nversely related to ratng level 24 as clearly demonstrated by agency default studes), the random censorng hypothess would be challenged f the average ratng levels for ssuers ntally rated the same moved far apart wth the passage of tme. For example, for two ssuers rated Caa on a gven cohort date, one of whch experenced a ratng wthdrawal n the future and one whch remaned outstandng, what was the relatve dfference n ther ratng levels wth the passage of tme? We formed annual cohorts for 4,833 corporate bond ssuers over the 983 to 2005 tme perod, and recorded ther estmated senor unsecured ratngs from the cohort year to cohort year plus 5 years. o calculate the average ratng level at each pont n tme, we frst 24 here are several reasons to expect hgher ratng wthdrawal rates for lower-rated ssuers. Investors prefer to lend money to hghly leveraged ssuers at shorter maturtes, so speculatve-grade ssuers must perodcally rase new captal to replace short-maturty debt. At the same tme, t may be optmal for hghly leveraged frms to choose to ssue debt wth relatvely shorter maturtes n order to mnme adverse selecton costs Mtchell 99)). Speculatve-grade ssuers also tend to be smaller relatve to nvestment-grade ssuers and have hstorcally been more lkely to refund rated publc bonds wth unrated prvate loans when t s economcal to do so for a related dscusson see tman and Wessels 988)). 20

21 mapped the Aaa-Caa3 ratngs to a lnear numercal scale -9), then weghted the ratngs usng Moody's CDO ratng factors. 25 Moody s CDO ratng factors place greater weght on lower ratng categores, so downgrades wll have a relatvely larger effect on weghted average ratngs. able 4.3 presents the results. he table shows the mean number of notches of dfference between the ratngs of the wthdrawn sub-sample and the non-wthdrawn subsample. By constructon, the notch dfferences are ero on the cohort formaton dates. Negatve values n the table ndcate the number of ratng notches lower the wthdrawn subsample s relatve to the non-wthdrawn sub-sample. he relevant queston s whether the sub-sample that experenced a ratng wthdrawal exhbted sgnfcant ratng mprovement or degradaton relatve to the sub-sample that dd not experence a ratng wthdrawal. he data shows that 47% of the tme the average ratngs of the sub-samples s the same at year 5; 42% of the tme the average ratngs of the wthdrawn sub-sample s lower than the not wthdrawn sample by one ratng notch at year 5. Hence, t appears that the average ratngs of a sub-set of ssuers whose ratngs are ultmately wthdrawn exhbt lttle dfference compared to the average ratngs of ssuers whose ratngs are not wthdrawn over the same tme perod. able 5.4 Wthdrawn vs. Non-Wthdrawn CDO Factor-Weghted Ratng Notch Dfferences Cohort Ratng + year +2 years +3 years +4 years +5 years Aaa Aa Aa Aa A A A Baa Baa Baa Ba Ba Ba B B B Caa Caa Caa Sample perod: Moody's CDO ratng factors are descrbed n Yoshawa and Wtt 2003). 2

22 5. Conclusons In ths paper we revewed the default rate calculaton methodology that s now generally followed by most major credt ratng agences. Ratng agency default rates are calculated usng a non-parametrc dscrete-tme approxmaton to the contnuous-tme estmator that ether does or does not adjust for ssuer ratng wthdrawals. We argued that unadjusted statstcs, whle useful statements of hstorcal fact, are generally less useful as proxes for expected default probabltes as they rely on certan problematc assumptons. Moreover, we argued that unadjusted default rates are downwardly based estmates of default rsk. Wthdrawal-adjusted default rates, on the other hand, are useful data for a varety of applcatons requrng expected default probabltes. We showed that the crucal assumpton of the wthdrawal-adjusted method, random data censorng, appears to be supported usng Moody s data on ratng wthdrawals. he results of ths paper have mplcatons for both nvestors and regulators. Investors need to be aware f data on whch they are relyng are adjusted for wthdrawals; default rate assumptons and parameter values are, as we have shown, sgnfcantly affected by adjustng for ratng wthdrawals. It s also crtcal for makng comparsons of default rsk across dfferent asset classes and for makng comparsons across ratng agency reports. he ssue also has mplcatons for ratngs-based regulaton and oversght of ratng agences. Default probabltes for ratng grades are vtal performance statstcs. Ratngs have been ncreasngly reled on by regulators to a large extent because of ther ablty to rank order default rsk. Hence, agency reported hstorcal default rates are not only vewed as backward-lookng data but as expected default probabltes as well. For example, regulatory captal standards usng the Standarded approach under Basle II were derved by assessng the emprcal default probabltes for varous ratngs from dfferent ratng agences. Addtonally, the default rate data requred for ECAI recognton s rather unclear wth regard to calculaton method. Whle a unform reportng standard may be desrable, at a mnmum agences applyng for ECAI recognton must be transparent about ther calculaton methods. he foregong dscusson also suggests that a ratng agency s polcy wth regard to ts wthdrawal of ratngs s an mportant part of ts overall ratngs management framework. Yet most ratng agences do not provde publc nformaton about ther polces for the removal of ratngs. Whether ratng wthdrawals represent hdden credt events s a concern that wth mportant mplcatons for nvestment decson makng. Our analyss showed that the assumpton of random data censorng holds for Moody s data, but the neutralty result may or may not hold for other agency ratngs. he statstcal propertes of ratng wthdrawals 22