he Use of Cedi ueau Ifomaio i he simaio of ppopiae Capial ad Povisioig Requiemes Michael Falkeheim ad dew Powell Ceal ak of geia Pepaed fo he Wold ak Poec o Cedi ueaus. Pelimiay Commes Welcome he auhos would like o hak Veóica alzaoi Guillemo scudé ad Geoge Mcdless fo ivaluable commes. ll emaiig eos emai he auhos. he opiios epessed i his pape ae eiely hose of he auhos ad do o ecessaily eflec hose of he Ceal ak of geia.
. Ioducio I commo wih he maoiy of he cedi bueaus ceaed by Ceal aks ad aalyzed i his publicaio he oigial moivaio fo he ceaio of he cedi bueau i he Ceal ak of geia i 99 was also pudeial i aue. I paicula he pimay coce was o collec ifomaio o he lage debos of he fiacial sysem ad o udesad how hose debos povoked isks fo he fiacial sysem ad fo idividual baks. Fo his easo he cedi bueau bega life as a daabase icludig oly ifomaio o lage debos. Ove ime howeve he powe of his ool fo ohe obecives was ealized. Fis he impoace of shaig ifomaio bewee fiacial isiuios was ealized ad a a ealy sage he daabase was give o viually all he fiacial isiuios a low cos. Secod he powe of his ifomaio o addess willigess o pay issues pomped boh a eesio of he daabase ad is wide disibuio. oday he daabase coves viually all loas i he fiacial sysem ove si millio eies is updaed mohly ad is feely available o ayoe fo cosulaio hough he Iee. s he daabase gew i became clea ha hee wee ye fuhe poeially ieesig uses of his daa. I aohe sudy i his publicaio Mille e al (999) use he daa o sudy he elaios bewee ledes ad boowes (especially small ad medium sized eepises). Howeve a fuhe eciig use of his daabase is o aalyze appopiae capial ad povisioig saegies fo baks ad i paicula o assess whehe cue capial ad povisioig egulaios mach up o acual isks. his is he he focus of his pape. I paicula we develop simple echiques o esimae he epeced loss ad he vaiace of poeial losses of a pofolio of geie loas. We advocae ha povisios should cove epeced losses ad ha capial equiemes should cove poeial losses ove ad above epeced losses subec o some saisical level of oleace. We he assess how acual capial ad povisioig equiemes mach up o esimaed equiemes give by ou heoeical model ad calibaed usig a paicula sample of ece daa. he pape is ogaized as follows. I secio we give a vey bief accou of he hisoy of he cedi bueau. I secio 3 we descibe a poeial diffeeiaio bewee povisioig ad capial equiemes wih efeece o he pobabiliy disibuio of loss of a pofolio of loas. I secios 4 ad 5 we descibe biefly he ece debae egadig he defiiio of povisioig ad capial equiemes ad sugges ha capial equiemes may eed o eflec pofolio cosideaios. I secio 6 we pese he mehodology ad esimaes fo implied povisioig equiemes give a simple model o See he websie of he Ceal ak; www.bca.gov.a
deive epeced losses ad compae hese esimaes o acual povisioig equiemes. I secio 7 we pese a simple pofolio model o evaluae cedi isk ove ad above epeced losses ad i secio 8 pese esuls compaig implied o acual capial equiemes. Secio 9 cocludes.. he Hisoy of he Ceal de Deudoes del Sisema Fiacieo Daabase Ou souce of daa fo sudyig cedi isk is he Ceal de Deudoes del Sisema Fiacieo (CDSF) daa se which cuely caies ifomaio o viually evey loa i he geie fiacial sysem. he CDSF oigiaed i Jauay 99 whe he Ceal ak of geia bega o collec ad disclose ifomaio abou he lages debos (wih debs ove $00000) of he fiacial sysem. Fiacial isiuios povided he ifomaio ad afe validaio i was he e-disibued o all coibuos. he ifomaio o debos oigially icluded oly he "classificaio" assiged o each debo by each fiacial fim. Lae he Ceal ak equied baks o epo moe deailed ifomaio icludig he picipal aciviy of he debo is liks if ay o he ledig isiuio he busiess goup o which i beloged debs by cuecy deomiaio collaeal povisios ad e woh. I Sepembe 994 he CR decided o make he ifomaio available o he public by chagig a modes fee hough a agecy amed he Risk Cee (Diaz 998 Roisezvi 999). I 995 he CR decided o eed he age of debos hough he ceaio of he Cedi Ifomaio Cee (CIC). his ew egise icluded ifomaio o debos fom he o-fiacial seco wih debs geae ha $50 hus coveig pacically he eie age of boowes. he CIC bega o opeae i Jauay 996 ogehe wih he Risk Cee. Fo each debo he CIC povided he followig ifomaio o he public: picipal aciviy oal deb collaeal ad he fiacial isiuio s classificaio of he debo. I Ocobe 996 he CR decided o disclose he ifomaio coaied i he CIC fo a aual fee. y Mach 997 he amou of ifomaio pocessed pe moh by he Risk Cee was appoimaely 45000 ecods coespodig o 5000 debos while he CIC pocessed aoud 4500000 ecods pe moh. I July 997 boh isk cees wee uified i he "Ceal de Deudoes del Sisema Fiacieo" CDSF. his Ceal ak agecy ow allows access o he public via he Iee. his hisoy is summaized i able. I geia a basic sysem of 5 caegoies ("classificaios") is used o classify loas whee is "omal" ad 5 coespods o "loss" - see fuhe commes below.
able Hisoy of he Ceal de Deudoes del Sisema Fiacieo Daabase Jauay 99 daabase is esablished wih ifomaio o debos wih cedis of moe ha $00000 Sepembe 994 Jauay 996 Ocobe 996 July 997 he ifomaio is made available o he public hough he Risk Ceal agecy he Cedi Ifomaio Cee (CIC) begis o opeae epoig ifomaio o debs lage ha $50. he Ceal ak begis o disclose he CIC ifomaio fo a mohly fee. he Risk Ceal ad CIC ae uified i he Ceal de Deudoes del Sisema Fiacieo (CDSF) daabase mployig he CDSF o he sudy of cedi isk eails a umbe of pacical poblems. Fo eample he daabase does o coai ifomaio o idividual debs ad isead goups all of he debs of each idividual a a fiacial isiuio ogehe. May cedi isk models developed ecely such as JP Moga s CediMeics M (see Gupo e al 997) equie ifomaio o he iees ae ad sucue of paymes of debs. 3 he CDSF does o povide ifomaio abou he sucue of debs ad oly ecely begu o povide ifomaio o loa duaio ad he iees ae of debs. Moeove uil ecely i was difficul o ack idividual debos ove ime. Recely he Ceal ak has begu a poec o soe hisoical daa i a moe accessible fom ad also o impove he ifomaio o he iees ae ad duaio of debs. hese impovemes will be ivaluable fo his ype of eseach goig fowad. Fo his pape we decided fo hese pacical cosideaios o use daa fom Jauay 998 givig us some 5 mohs of ifomaio. 3. Povisios Capial Requiemes ad Cedi Risk Povisioig ad capial equiemes boh aemp o cool cedi isk by ceaig a buffe agais cedi losses (asle Commiee o akig Supevisio 999a 999b). O 3 Oe model ha does o equie much ifomaio is CediRisk (Cedi Suisse Fiacial Poducs 997). I a paallel sudy we have applied ha model o he same ifomaio. 3
a pacical level i is someimes difficul o diffeeiae bewee povisios ad capial. Fo eample i he asle 988 ccod i was ageed ha a geeal povisioig equieme migh be ecoded as capial agais equiemes. Howeve i heoy we believe ha povisios ad capial seve wo quie disic puposes. I ou view povisios should poec baks agais odiay levels of cedi loss while capial equiemes should poec baks agais ufoesee losses. I saisical ems while povisios should eflec he epeced value of cedi losses capial equiemes should poec agais uepeced losses subec o some level of saisical oleace. his meas ha i heoy boh povisioig ad capial equiemes may be specified fom he same disibuio (he disibuio of poeial cedi losses) bu hey eflec diffee saisics of ha disibuio. Gaph illusaes he implied level of povisios ad capial equiemes by meas of a eample. he gaph plos a disibuio of poeial cedi losses (fo a sigle loa o a loa pofolio). Maked o he gaph is he epeced loss $500 i he eample ad his is he he appopiae level of povisios. Capial equiemes o he ohe had should eflec uepeced losses which ae usually defied as he diffeece bewee a give peceile level ad he epeced loss. I ou eample we calculae appopiae capial equiemes as equal o he diffeece bewee he 99.9 h peceile of cedi losses ad he epeced value. he 99.9 h peceile defies a lie which places us 0.% of he disibuio o he igh ad i ou eample is a $8000. hus appopiae capial equiemes i ou eample ae $8000-$500 $5500. Noe ha cedi losses should eceed he 99.9 h peceile i oly ou of 000 possible ecoomic sceaios (us ove oce evey 83 yeas cosideig mohly dawigs fom his disibuio. 4
Gaph : he cedi loss disibuio Pobabiliy 0 500 5000 7500 0000 500 5000 7500 0000 500 5000 7500 Povisios Capial peced Loss Requiemes Uepeced Loss Cedi Loss ($) 4. Povisioig Requiemes: Discussio I geia as elsewhee he Ceal ak equies a miimum level of povisios fo each idividual loa which depeds o he ecoomic classificaio of he debo. Fo commecial loas fiacial isiuios ae equied o ae he debo o a scale of o 5 depedig o he ecoomic codiio of he obligo hough a aalysis of hei epeced cash flow. Fo cosume ad housig loas fiacial isiuios mus base he classificaio of debos o hei cue payme saus. Commecial loas less ha $00000 accodig o cue egulaios may be eaed as cosume loas i ems of hese equiemes. Oe of he ceal puposes of his sudy is o evaluae he cue sysem of povisioig equiemes. I paicula we use he cedi bueau daa o assess whehe he level of povisios fo each classificaio is adequae give obseved loss pobabiliies. I evaluaig he cue levels of povisios we fis develop a fiacial model of loa value which akes io accou epeced cedi losses. We he esimae his model wih he available cedi bueau daa i ode o esimae he level of povisios eeded o cove hose epeced losses. 5
5. Capial Requiemes: Discussio he ece lieaue sesses he eed fo capial equiemes o maiai a healhy fiacial sysem by limiig he isk of bak failues. While i he pas he level of equiemes efleced 'ules of humb' o aguably wee he oucome of comple poliical egoiaios moe ecely hee have bee geae aemps o quaify appopiae levels of egulaoy capial. he mehodology omally applied is o coside wha sock of capial would cove poeial losses i all bu a small peceage of sceaios ha could pevail i he eleva hoizo. he eleva hoizo is omally see o be he ime eeded o ake isk-miigaig acios such as he sale of isky loas o he epleishme of capial. he asle 988 Capial ccod fomally esablishes he cue fom of capial equiemes fo "ieaioally acive" baks i G-0 couies. Howeve ove 00 couies icludig geia have eplicily adoped he ccod eihe i hei ow bakig egulaios o i some cases i Law. I may couies howeve he ules ae applied o oly o ieaioally acive baks bu also o domesic baks. Moeove i some couies while he geeal asle mehodology has bee adoped he acual equiemes adoped have bee sice ha he miimum 8% of asses a isk ecommeded by he asle docume. Couies have he adoped hei ow limis wihi he geeal mehodology depedig o he peceived level of cedi isk. I geia he Ceal ak ses capial equiemes fo he bakig sysem ad has esablished (sice he ed of 994) a miimum aio of.5% fo capial o isk-weighed asses fo couepay isk. he asle ccod defied isk-weighs fo diffee asses i a aemp o capue he diffee levels of isk i hei eus. I geia hese weighs ae used bu ae complemeed wih a isk idicao ha is based o he iees ae chaged o each loa. his addiioal isk idicao is a faco ha muliplies he base capial equieme. Ude his sysem loas wih highe iees aes have highe capial equiemes because hey ae pesumed o have a highe level of isk. geie capial equiemes also iclude a faco ha depeds o he CMLS aig assiged by he Supeiedecy o each fiacial isiuio. O op of couepay isk capial equiemes he Ceal ak has also imposed capial equiemes fo make isk ad fo iees ae isk. he cue geie capial equiemes may he be specified accodig o he followig fomula: Oveall Capial Requieme.5*IR*W*K Make Risk Iees Rae Risk Whee IR is he iees ae faco W is he aveage asle isk weigh fo asses ad K is he CMLS faco assiged by he Supeiedecy. Oe shocomig of asle-syle capial equiemes is ha hey do o ake io accou how idividual eposues ae combied i he loa pofolio. Oe lage loa o a sigle compay fo $00m has he same capial equieme as 000 loas of $00000 each o 000 diffee compaies if hese loas ae i he same isk caegoy. Howeve maiaiig a divesified pofolio will i geeal educe he oal cedi isk of a 6
isiuio. Moeove equiemes do o diffe accodig o he level of coelaio of asse eus i a pofolio. pofolio of loas eclusively o compaies i he eile seco would have he same capial equieme as a pofolio of loas spead acoss vaious idusies agai assumig hey wee all i he same isk caegoy. Naually if he sadad ules do o eflec well he acual isks of fiacial isiuios cedi pofolios he his may esul i eihe oo lile o oo much capial ad diso capial allocaio decisios. ece poposal o emedy his is he use of ieal models o assess capial adequacy. Ude his sysem fiacial isiuios would apply o use hei ow measues of cedi isk o deemie he capial equieme. Regulaoy auhoiies would eed o decide which models deseve auhoizaio based o hei echical mei ad hisoical pefomace. Howeve ece aalyses of such models sill place his possibiliy a a ealy sage of developme. Ideed he ece poposal o modify he asle 988 ccod while icludig may ideas o impove cedi isk assessme of idividual debos shies away fom mehods o aalyze pofolio isk icludig ieal models. I is heefoe impoa i usig a cedi isk model o evaluae povisio ad capial equiemes o ecogize he cue limiaios of his appoach. he asle Commiee ad ohe isiuios sudyig cedi isk models all cocluded ha hey wee o ye sufficiely well developed o use i a capial equieme sysem. ccodig o he asle Commiee o akig Supevisio (999a 999b) ad may scholas (see Jackso Nickell ad Peaudi 999) impoa issues such as he coec shape of he loss disibuio have o bee esolved ad he sho spa of hisoical daa makes i impossible o popely validae cedi isk models. Fuhemoe ohe isk facos such as opeaioal isk have o bee adequaely sudied. he basic aio esablished i he Capial ccod migh also povide a eeded hedge agais opeaioal ad ohe isks. he poblems egadig he implemeaio of ieal models fo cedi isk egulaoy capial is mioed i a emegig couy coe. Moeove i is likely ha some of he poblems ae magified. Fo eample model assumpios boh i ems of sucue ad paamees ae likely o be moe usable ad echical ad huma esouces ae likely o be moe cosaied. Faced wih his ealiy ou obecives i he eecise below ae moe modes. Namely we coside ha such models migh be employed as a check o see whehe cue egulaios mach i boad ems implied heoeical levels. Hee ou coce is wih he oal amou of povisios ad capial available o a isiuio o o he fiacial sysem as a whole. We do o coside fo eample how his capial is disibued acoss he loa pofolio. I his way we do o addess quesios of efficiecy bu ahe quesios of oveall pudeial sadads. ohe possible use of cedi isk models is i supevisio. Capial equiemes i geia deped o he CMLS 4 aig ha he Supeiedecy of Fiacial Isiuios assigs o each isiuio. Supevisos i geia ae isiuios bewee 4 he acoym CMLS sads fo Capial sses Maageme aigs Liquidiy ad Sesiiviy which ae he si ses of vaiables ha supevisos eamie whe deemiig hei classificaio. 7
ad 5 based amog ohe higs o he level of isk of hei asses. his aig aslaes io a lowe o highe capial equieme sice each aig leads a diffee muliplie o be applied o he global capial equieme. easoable obecive is he ha cedi isk models may help supevisos quaify he cedi isk of isiuios ad pehaps become a eplici pa of hei (CMLS) aigs decisios. I developig a cedi isk model i is ecessay o measue o wha degee divesificaio educes isolvecy isk. Divesificaio cao compleely educe pofolio isk whe cedi oucomes ae posiively coelaed. Cedi bueau ifomaio ca eveal he ecoomy wide coelaio bewee he defaul isk of loas based o hei chaaceisics heeby discoveig he elaioship bewee divesificaio ad isk ad also ifom us abou he aue of cedi isk i momes of cisis. Cedi bueau ifomaio ca play a impoa ole i measuig (a) he isk of diffee ypes of loas ad (b) he isk of each bak s pofolio i ode o deemie he pope level of povisioig ad capial equieme. he fis sep i ou ivesigaio will be he developme of a mehodology ha esimaes he vaiace of he eu o bakig pofolios usig he CDSF ifomaio. We use his ifomaio o sudy loa oucomes based o debo vaiables calculae he vaiace of loa eus ad calculae he covaiace bewee loas wih diffee chaaceisics. hese ae he used o paameeize a fucio ha esimaes he vaiace of he eus of bakig pofolios i he geie sysem. 6. Calculaig Povisios as a Fucio of Loa Classificaio I ode o measue he ecoomic cos of cedi deeioaio we assume ha he value of a loa depeds o is classificaio. he povisios should eflec he diffeece bewee is balace shee value ad is ecoomic value so ha he loa s e balace is equal o is ecoomic value. his diffeece should eflec amog ohe higs he epeced loss due o cedi isk. he classificaio (o sae ) is a umbe bewee ad N. We assume ha a loa wih a balace of ad classificaio s has a ecoomic value of dollas whee 0 V s. We also add he sae 0 fo he case i which he loa is paid i full befoe he ed of he e peiod ad N is he sae i which he loa becomes iecoveable i he e peiod. V sice a loa ha is paid i full will yield is eie balace. We assume 0 ha whe a loa becomes iecoveable ha is value is zeo 5. hus V N 0 he loa s value i ay give peiod mus be equal o is pese epeced value i he followig peiod. I he followig peiod hee is some pobabiliy ha he loa will eihe become iecoveable o ha i will be compleely paid. hee is also some pobabiliy ha V s 5 his assumpio is o as esicive as i appeas. he followig aalysis ca be applied o ay loa povided ha i is fis decomposed io wo pas: a pa ha is ecoveed i he case of liquidaio ad a pa ha is o. he pa ha is ecoveed will eai is full value o mae wha is he classificaio of he loa. 8
i will eai he same classificaio o ha i will chage o ay oe of he ohe classificaios. We assume ha hese pobabiliies deped o he cue classificaio of he loa. We ca use hese pobabiliies o deive a value of he loa fo each classificaio i he fom developed by Cye Davidso ad hompso (96). Defie q( s) as he pobabiliy ha a loa i classificaio will chage o classificaio s. I he e peiod he loa will accue iees so ha is balace o payme will be R imes is cue value ( R > ) povided ha he loa is i classificaio o. I geia if a loa is i classificaio 3 o wose i geeally does o accue iees. If i does he bak mus se aside he eie amou of accued iees as povisios as is ecommeded by ieaioal sadads (asle Commiee o akig Supevisio 999c). I is ecessay o discou fuue cash flows i ode o eflec hei pese value. We defie he discou faco as β ad assume ha 0 < β <. If we kew wih ceaiy ha a loa wih a cue balace of i pesos would be i classificaio s i he e peiod he is pese value would be β RV s if i begis he peiod i classificaio o ad i β V s if i begis he peiod i classificaio 3-5. If a loa is paid i he e peiod i will yield R i pesos epeseig a pese value of β Ri pesos. If he loa becomes iecoveable i he e peiod he we assume ha is value is zeo as saed above. he esicio ha a loa s cue value is equal o he pese epeced value i he e peiod gives he followig epessios: 6 V β R q( s) Vs fo (.) ad s 0 5 V β q( s) Vs Rq( 0) fo 345 (.) s If we kow β ad R ad esimae he mai of elemes q ( s) he i is possible solve his se of 5 equaios fo he 5 ukow elemes: V... 5. veagig ove he fifee-moh peiod we obaied he followig asiio mai. 9
able : Mohly asiio Pobabiliies fo loas by classificaio Febuay 998 o pil 999 Classificaio a he ed of he moh 0 (paid) 3 4 5 6 (iecoveable) Classificaio a he begiig of he moh 54% 97% 6% 0% 0% 0% 00% 60% 43% 58% 68% 03% 08% 00% 3 50% 74% 4% 640% 9% 04% 00% 4 9% 7% 06% 3% 833% 9% 00% 5 00% % 0% 0% 03% 94% 3% I ode o pefom he calculaio idicaed i equaio (.) we assumed R o be equal o.0 which is appoimaely oe plus he aveage mohly iees ae i geia ove he eleva peiod. We assumed β o be equal o sice he aveage mohly deposi.005 ae i geia is appoimaely 0.5%. Wih hese assumpios we acquied a esimae of he veco V of loa values i each of he five classificaios. Povisios fo loas wih classificaio s should be equal o V of he balace as show i he able below. s able : simaed Values fo Loa Classificaios Classifica io Defiiio Value Implied Povisio Cue Miimum Povisio Nomal 99% % % Poeial Risk 9% 9% 5% 3 Subsadad 77% 3% 5% 4 Doubful 63% 37% 50% 5 Loss 40% 60% 00% oal fo he fiacial sysem 4.6 billio 6. billio 0
I ca be see ha he levels of povisio fo classificaios -3 ae close o hose implied by he model. he figues sugges howeve ha povisioig equiemes fo caegoy could be igheed wheeas fo 4 ad 5 hey ae oo sic. Loas aed as 5 seem o have some value eve hough he caegoy is defied as loss. his is because a small popoio of hese loas eveually epay. he oal miimum level of acual povisios fo he eie fiacial sysem is above he level ha is implied by he model. his suggess ha o a global basis he povisios of he geie fiacial sysem ae sufficie. Howeve we oe ha he esuls imply ha cue povisioig levels may be oo low fo caegoy ad oo high fo caegoies 4 ad 5. I ohe wods he model suggess ha i migh be appopiae o ale he disibuio of povisioig equiemes somewha acoss he diffee caegoies bu a he same ime suggess ha cue povisioig equiemes i aggegae epese a vey cosevaive appoach o coveig epeced cedi losses. he same ime we mus of couse emembe he limiaios of he model discussed above i dawig sog policy coclusios fom hese esuls. 7. simaig he vaiace of pofolio eus usig he CDSF he same model of loa value used o calculae he adequae level of povisios ca also be used o esimae he vaiace of pofolio eus. he vaiace of a pofolio eu ca give us a oio of he value a isk. wo impoa buildig blocks i ou calculaio of pofolio eu vaiace ae he vaiace of idividual loa eus ad he covaiace of eus bewee diffee loas. We defie he balace of loa as fo...n he vaiace of he eu as a pece of is value of loa as ad he covaiace of he eu of loa wih he eu of loa as. Wih his oaio we obseve ha he vaiace of he eu of he loa pofolio is: P N P : (3.) { } I ode o esimae P i is fis ecessay o esimae pais of loas ad. ad fo all loas ad all I ode o do his we divide loas io goups ad assume ha hei saisical popeies ae homogeeous wihi each goup. We assume ha loas of he same seco ad classificaio fom a goup. Fo eample all of he loas i classificaio 3 i he agiculual seco fom a goup. I each peiod he pobabiliies of chagig o each possible classificaio ae ideical fo all loas wihi each goup. Ou assumpio will
allow us o epess ad as fucios of hei seco ad classificaio ad esimae hem usig ecoomy-wide daa. Fis we oe ha if loa i classificaio ad seco has he pobabiliy q ( s) of edig i each of he seve possible classificaios s he he mea ad vaiace of is eu ae he followig: S s S q s q ( s) ( s) R V R V V s V s (4.) his gives a epessio fo he vaiace of a loa i ay goup ha depeds o is pobabiliies of asiio q ( s) ad he values of loas i each classificaio V s. I ode o apply i we use he values V s developed i he pevious secio ad we esimae q ( s) fo all secos ad all classificaios ad s usig daa fom he eie sample peiod. 6 I ode o esimae he covaiace of loa eus we model idividual loa eus as he sum of wo adom compoes: a goup compoe ad a idividual compoe. he eu of loa i peiod is: ( ) z (5.) whee ( ) is he goup compoe i peiod ad z is a zeo-mea compoe which is idepedely disibued fo each idividual. Ude he assumpio ha idividual compoes ae idepede he covaiace bewee he eus of loas ad a i ay peiod is he followig: ( ( ) ( )) Cov (6.) I ohe wods he covaiace bewee loa eus is equal o he covaiace of he goup compoe of each loa s eu. I he case whee ad : ( ( )) Va (7.) 6 I he fuue we will allow hese values o vay by seco so ha he value of a loa depeds o boh is seco ad is classificaio. We will he ecalculae he paamees wih he values V s.
I ode o esimae he covaiace bewee he goup compoes we calculae he aveage eu fo each goup i each ime peiod. We defie he goup aveage fo loas i seco classificaio ad peiod as ( ). Fo he goup compisig loas i seco ad classificaio he goup aveage a ime is equal o he followig: R S ( ) q s Vs V ( ) (8.) s Wih he elemes ( ) we ca esimae he vaiace ad covaiace of goup compoes ove ime. 7 I ppedi we obai he followig esimae fo usig daa fom peiods... whee loas ad ae i diffee goups i.e. ad/o : ˆ ( ) ( ) ( ) ( ) (9.) I ppedi we deive he followig equaio fo he covaiace of wo loas (i ad k) i he same goup (whee ad ) whee is he umbe of loas i he goup: ˆ ( ) ( ) ˆ 8 (0.) Havig deived a esimae fo he vaiaces of he eus of all loas ad he covaiace of all possible pais of loas i is possible o calculae he vaiace of ay loa pofolio. 7a. Daa he daa ha we use comes fom he Ceal de Deudoes daabase. We use all loas fom he eie fiacial sysem i he fifee mohs bewee Febuay 998 ad pil 999. hee wee appoimaely 4.5 millio loas i each moh of his peiod. We calculaed he asiio maices usig he daa fom successive peiods. 7 he pocess of deivig he covaiace (o coelaio) bewee loa eus usig he vaiace ad covaiace of goup aveage eus is kow i he cedi isk lieaue as evese-egieeig ad is quie widely used. 8 he secod em o he igh had side coecs fo he fac ha i a fiie sample we would epec he goup aveage eu o vay eve whe hee is o covaiace bewee loa eus (see ppedi ). 3
I ou eseach we will use he followig ifomaio fo each debo a each fiacial isiuio:. he amou of he deb. he picipal aciviy of he debo 3. he classificaio of he debo 4. he collaeal of he debo 7b. Paamees s oed i he ealie aalysis he vaiaces of aveage eus of diffee goups ad he covaiace bewee he eus of diffee goups ae impoa paamees i ou esimaio of loa pofolio vaiace. Hee we pese some of he esimaed paamees. hey show which idusy goups had moe volaile eus duig he peiod fom which we ook he daa ad also he coelaio bewee idusy aveage eus. able 3: Volailiy of Idusy veage Reus fo Loas wih Nomal Classificaio Idusy Sadad Deviaio of Mohly Reu giculue ad Fishig 0.85% Miig 0.09% Maufacuig ad Uiliies 0.3% Cosucio 0.% Commecial 0.7% Sevices 0.43% Pesoal loas 0.4% 4
able 4: Coelaio bewee Idusy veage Reus fo Loas wih Nomal Classificaio Idusy giculue ad Fishig Miig Maufacuig ad Uiliies Cosucio Commecial Sevices Pesoal loas giculue ad Fishig - 30.3% 98.7% 4.0% 89.6% 6.7% 90.7% Miig - 3.6% -5.6% 40.9% -9.0% 6.8% Maufacuig ad Uiliies - -5.9% 86.0%.5% 89.7% Cosucio - 3.9% -0.8% 3.7% Commecial - -8.% 87.6% Sevices - -8.6% Pesoal loas - able 3 shows ha some idusies have moe volaile loa eus ha ohes do. y fa he lages level of aveage eu volailiy coespods o he giculue ad Fishig Idusy whose aveage loa eus had a mohly volailiy equal o 0.85%. he ohe eeme we oe ha miig has a vey low volailiy of eus. his accods wih subsaial aecdoal evidece fom he bakig seco. I geeal agiculue is cosideed oe of he mos isky secos give he combiaio of small ofe family-led busiesses climaic isks ad volaile agiculual pices. lhough he miig seco has also suffeed fom eeme pice volailiy i is chaaceized by lage compaies may wih foeig capial able 4 shows he coelaio of idusy aveage eus. 5 of he umbes i he able ae posiive suggesig ha hee may be facos ha affec he pefomace of all loas i he ecoomy. Ideed i is clea ha mos secos ae cyclical wih pesoal loas maufacuig ad uiliies commecial loas agiculue ad fishig showig high posiive coelaios. Cosucio ad loas i he sevice seco appea o be he ecepio ehibiig egaive coelaios wih he ohe goup. he sigifica posiive coelaios sugges ha baks will be limied i he ee o which hey ca shele hemselves fom egaive ecoomic codiios wih divesificaio acoss idusies alhough his will deped o paicula baks pofolios. s meioed befoe he vaiaces ad covaiace ideally would have bee esimaed usig a much loge seies of daa. Sice ou daa spas oly 4 mohs i is aual o be coceed abou he sabiliy of he paamees. I paicula i migh be ha he vey high coelaios foud bewee he aveage eus of giculue ad Fishig loas ad Maufacuig ad Uiliy loas is a esul of paicula shocks ove he sample peiod ad 5
o a log u sucual pheomeo. We will oly be able o coec his poblem i a few yeas whe we have a loge sample peiod. 8. Implici Capial Requiemes s discussed i he ioducio hee ae some seious esicios i usig pofolio cedi isk models o acually esablish capial equieme egulaios boh i ems of he heoy i he calibaio of ay model wih available daa. Neveheless we cosideed i a ieesig eecise o esimae wha capial equiemes would be implied by he vaiace ad covaiace esimaes. I he above we have avoided makig assumpios abou he shape of he loss disibuio so sicly speakig i is o possible o cove he vaiace esimaed i he pevious secio io a peceile of he loss disibuio. Neveheless fo he sake of makig a compaiso bewee ou esuls ad ou eisig sysem of capial equiemes we will assume a implied capial equieme equal o 3 imes he esimaed volailiy ad wa ha i is ecessay o iepe ou esuls wih cauio. Naually if cedi loss disibuios ae omal he his will accod o he 99.9h peceile of he disibuio. mployig his cieio he followig ae aveage implici capial equiemes fo diffee ypes of fiacial isiuios: able 6: Implied Capial Requiemes fo Diffee ypes of Fiacial Isiuios ype of Fiacial Isiuio Implied Capial Requieme asle Requieme 9 geie veage Capial Requieme 0 veage Capial Level Medium Sized Reail 6.8% 6.6% 3.5% 9.0% aks Lage Reail aks 6.9% 5.6% 0.%.9% Small Reail aks 7.8% 6.9% 6.% 4.7% Pivaized aks 7.9% 5.0% 0.0% 5.5% Naioal Public aks 8.0% 5.5% 8.3% 3.7% Lage Wholesale ad Ivesme aks 8.% 4.7% 7.5% 4.4% 9 he asle ased equieme was calculaed usig he 8% capial o asses aio ad he asle Capial ccod s isk weighs. 0 he geie Capial Requieme is deived fom he fomula.5%*k*w*ir. K epeses he faco deived fom he supeviso s CMLS aig of he fiacial isiuio W epese he aveage (aslesyle) isk weigh of he asses ad IR is he isk idicao deived fom he iees ae of loas i he isiuio s pofolio. 6
Small ad Medium Wholesale ad Ivesme aks Ohe Fiacial Isiuios Povicial ad Muicipal Public aks 9.8% 7.0% 3.7% 49.4% 0.6% 7.6% 3.4% 40.4%.% 5.8%.9%.6% hid he geie capial equiemes ae i geeal highe ha hose of he implied levels (he ecepio beig lage wholesale baks). I some cases he acual geie equiemes ae subsaially highe ha he implied levels icludig eail baks ad ohe fiacial isiuios (o-baks). I he case of eail baks his gives some suppo fo he beefi of divesificaio of loa pofolios. O he ohe had lage wholesale baks have lowe acual equiemes because pobably because i geeal hey have a combiaio of good CMLS aigs ad low loa iees aes. he implied capial equieme is slighly highe ha he acual equieme pobably because hese baks led i geeal o low volailiy secos ad hee is o beefi fo his i cue egulaios. hese esuls sugges ha fuhe wok is usified i aempig o see how efiemes o cue egulaios migh esul i a fie coespodece bewee acual equiemes ad cedi isk of diffee ypes of fiacial isiuios. Howeve i is also woh oig ha he acual capial of he baks is sigificaly highe ha boh he implied level of capial give by he model ad he geie egulaios. I appeas he ha baks ae o aveage moe cosevaive wih espec o capial levels ha boh he heoeical capial equiemes ad he geie egulaios would sugges. he fial coclusio is he ha cue capial levels give sigifica comfo wih espec o esimaed cedi isk i he geie fiacial sysem. 9. Coclusios he obecive of his pape was o use he eesive cedi bueau daa of he Ceal ak i ode o evaluae povisios ad capial equiemes i he geie fiacial sysem. lhough hee ae some limiaios o he use of his ifomaio fo cedi isk models - he daabase was o oigially ieded fo his - we wee able o develop a simple model of loa valuaio ad pofolio eu vaiace ad use he cedi bueau daa o calibae ha model. We agued ha i heoy povisioig equiemes ad capial equiemes ca be defied wih espec o a sigle disibuio (he disibuio of poeial cedi losses) bu while povisios should eflec epeced losses capial equiemes should eflec uepeced losses elaive o some oleace value. 7
Usig his appoach ad he cedi bueau daa acual povisioig equiemes wee foud o be close (bu o eceed) implied levels bu ha hee was a agume o efie he equiemes acoss diffee caegoies. We also foud ha implied capial levels geeally eceed he asle miimum ecommedaio of 8% of asses a isk suggesig ha asle equiemes eed o be sice i he coe of a emegig ecoomy such as geia. Howeve we also foud ha implied capial equiemes wee i geeal lowe ha acual equiemes depedig o he ype of fiacial isiuio. We view his pape as a fis aemp o use a vey simple pofolio model of cedi isk ad cedi bueau daa o coside egulaoy capial equiemes. s discussed i he pevious secios hee ae may esicios ad healh waigs which should accompay his ype of aalysis. he heoeical assumpios ae sog ad he daa we have used is vey limied i ems of is ime-spa ec. he esuls aually eflec hese limiaios ad should be ead as suggesive ahe ha auhoiaive. Neveheless we coside his o be a eemely impoa poeial use of he eesive geia cedi bueau ad addiioal faco suppoig he policy of he Ceal ak o develop his eemely valuable esouce. 8
Refeeces asle Commiee o akig Supevisio (999a) Cosulaive Pape o a New Capial dequacy Famewok mimeo.} asle Commiee o akig Supevisio (999b) Cedi Risk Modelig Cue Pacices ad pplicaios mimeo. asle Commiee o akig Supevisio (999c) Soud Pacices fo Loa ccouig Cedi Risk Disclosue ad Relaed Maes mimeo. Cedi Suisse Fiacial Poducs (997) CediRisk Cedi Risk Maageme Famewok mimeo. Cye R.M. Davidso H.J. ad homso J.L. (96) simaio of he llowace fo Doubful ccous by Makov Chais i Maageme Sciece p.87-303 Diaz Julio (998) Cedi Ifomaio: Cocepual Issues ad a Descipio of he geie Case mimeo. Gupo Geg M. Fige Chisophe C. ad haia M. (997) Cedi Meics echical Docume Moga Guaay us Co. New Yok Jackso Paicia Nickell Pamela ad Peaudi William (999) Cedi Risk Modellig Fiacial Sabiliy Review Jue p. 94-0 Roisezvi lfedo. (997) Los isiuos de Ifomació Cediicia e geia. Ieal Memo CR 9
0 ppedi : he Covaiace of Idividual Loa Reus I his secio we will show ha he equaio give i (9.) is a ubiased esimao of he covaiace. (9.) saed he followig ( ) ( ) ( ) ( ) ˆ Defie ( ) ( ) [ ] ad ( ) ( ). he ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) his is equal o: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) sice he epeced values of he ohe coss poducs ae equal o zeo. his meas ha
( ) ( ) ( ) ( ) ˆ ppedi : he Covaiace of he eus of loas i he same goup quaio (0.) saed he esimae of he covaiace bewee he eus of loas i he same goup o be: ( ) ( ) ˆ ˆ whee is he umbe of loas i goup. We will ow show his o be a ubiased esimao of. Defie ( ) ( ) [ ] ad ( ) ( ) ad oe ha ad give ha he loas ae i he same goup. he { } ( ) ( ) ( ) [ ] ˆ ˆ I is possible o wie ( ) ( ) ( ) ( ) ( ) [ ] ( ) [ ] ( ) ( ) ( ) ) ( ) ( hus
( ) ( ) ( ) [ ] [ ] ˆ ˆ ˆ ˆ