Risk Quantification of Retail Credit: Current Practices and Future Challenges*

Transcription

1 Rsk Quantfcaton of Retal Credt: Current Practces and Future Challenges* Wllam W. Lang Anthony M. Santomero Federal Reserve Bank of Phladelpha *The vews expressed n ths paper are those of the authors and do not necessarly reflect those of the Federal Reserve Bank of Phladelpha or of the Federal Reserve System.

2 I. Introducton Ths paper examnes current practces at U.S. banks for quantfyng credt rsk and estmatng economc captal n retal portfolos. In addton, the paper examnes ssues facng banks and ther regulators n developng an nternal ratngs based (IRB) approach to settng captal requrements for retal exposures. Wthn the last decade, many large banks have made substantal strdes n ncorporatng quanttatve credt rsk models nto busness practces. Based largely on ndustry models (e.g. CredtMetrcs, Credt Rsk +, KMV Portfolo Manager), an ncreasng number of nsttutons use credt rsk models for rsk management, allocatng economc captal and measurng rsk-adjusted returns at the busness lne level. Developments n credt rsk modelng are nfluencng, and beng nfluenced by, the effort to reform the Basel Commttee s standards for regulatory captal Basel II. 2 A stated goal of ths reform effort s to create a captal standard that s more senstve to the rsk of an nsttuton. To acheve ths goal, the Basel Commttee proposes allowng banks wth suffcently sophstcated rsk measurement and management systems to use ther own nternal systems determnng key rsk parameters enterng nto the regulatory captal calculaton. Whle the general prncples of portfolo credt rsk modelng are equally applcable for commercal and retal portfolos, ndustry and regulatory resources devoted to advanced credt rsk models have largely concentrated on commercal loan portfolos. Thus, t s not altogether surprsng that the ntal Basel II consultatve paper n 999 on The term economc captal s defned here as the amount of captal allocated to a partcular actvty based on the actvty s margnal contrbuton to economc rsk. 2 Basel Commttee on Bankng Supervson (200a).

3 the reform of the captal standards contaned very lttle explct dscusson of the retal portfolo. Whle the current Basel II proposal contans more explct language dscussng the specal features assocated wth measurng retal credt rsk, t s clear that work n ths area s relatvely underdeveloped. Ths paper s an attempt to address ths mbalance, as much of t s devoted to a dscusson of the current state of bank practces for modelng retal credt rsk and the assocated calculaton of economc captal. In addton, t wll dscuss some of the key challenges n usng nternal models for settng regulatory captal requrements for retal exposures. Informaton for ths paper comes from a varety of sources ncludng dscussons wth bank rsk managers and modelers. Snce much of the data and methodology gathered are propretary, the paper dscusses general prncples behnd varous approaches and methodologes. II. Characterstcs of Retal Credts For the purposes of ths paper, the defnton of retal lendng s consstent wth the one used n the current Basel proposal. Retal loans nclude loans to ndvduals or households, ncludng credt card loans, mortgage loans, home equty lnes of credt, auto loans, and other consumer loans. The Basel II proposal also ncludes n ts defnton of retal exposures low value loans to small busnesses f those exposures are prmarly managed on a pooled bass. Retal loans are relatvely small value loans, and, wth economes of scale assocated wth nformaton gatherng and montorng of larger loans, lmted resources are devoted to analyzng the dosyncratc rsk of an ndvdual borrower or faclty. Retal lenders n 2

4 the U.S. typcally rely heavly on sophstcated statstcal models of borrower performance for approvng loans and generally track performance of those credts on a pool or segment bass. The prmary statstcal tool for makng retal credt decsons s credt scorng. The exstence of extensve credt bureau data n the U.S. allows lenders to use a wealth of readly avalable data on ndvduals to estmate bureau scorng models. In addton to standardzed bureau scorng models, banks often buy or develop customzed scorng models talored to the bank s own clent populaton. Many companes wth a suffcently large retal portfolo employ applcaton scorng models that allow an nsttuton to ncorporate addtonal nformaton collected durng the loan applcaton process. In addton to scorng customers at the tme of applcaton, scorng models are used n a dynamc way for managng accounts and for nternal bank analytcs. Many lenders obtan updated or refreshed bureau scores on a monthly bass and some use behavoral scores that factor n the borrower s performance on accounts wth the bank. Scorng on a dynamc bass s used for a wde varety of purposes ncludng credt lne changes, collectons and analyzng account proftablty. In summary, a central feature of the modern retal credt busness s the wde scale use of statstcal models for decson makng. Yet, despte ths extensve use of sophstcated statstcal tools for managng retal credt portfolos, ndustry efforts to model credt rsk loss dstrbutons are relatvely new and relatvely less developed than n the commercal lendng area. There are a number of lkely reasons for ths. Frst, the economes of scale n loan evaluaton and loan montorng create economc ncentves to devote a greater share of 3

5 lender resources to the evaluaton of dosyncratc rsk factors for large loans. Whle ths does not automatcally translate nto more resources devoted to modelng commercal portfolo losses, the greater effort and techncal expertse devoted to analyzng volatlty of ndvdual commercal loans helped spur the development of more sophstcated commercal portfolo rsk measurement systems. A second factor accountng for the more rapd development of commercal credt rsk models s the long hstory of ratng agency evaluatons for commercal frms wth publcly traded securtes. These agency ratngs, along wth the extensve data avalable for publcly traded frms, provde extremely useful benchmarks for the development of quantfcaton methods for commercal portfolos. As a result, most banks wth nternal credt rsk models benchmark ther nternal loan gradng systems to equvalent agency ratngs. 3 The extensve prcng data on publcly traded securtes also allowed modelers to more drectly ncorporate nnovatons n fnancal economcs, e.g., opton prcng models, nto ther credt rsk models. Whle these reasons help explan why credt rsk modelng developed more quckly n the commercal loan settng, there are also some sgnfcant advantages for credt modelers measurng rsk n retal portfolos. In partcular, the heavy relance n retal lendng on statstcal scorng models means that judgmental factors play a relatvely smaller role n the retal portfolo. In prncple, wth fewer judgmental factors enterng the evaluaton of ndvdual credts, retal portfolos should be more amenable to quanttatve rsk modelng. A key problem n commercal credt rsk modelng s estmatng the quanttatve rsk parameters assocated wth a partcular gradng system 3 See Carey and Treacy (998) for a detaled dscusson of bank nternal ratng systems. 4

6 and ensurng that loans are approprately graded. If loans are scored, then the quanttatve meanng of a partcular gradng system s more transparent. Nonetheless, current bank practce n modelng retal lendng rsk typcally concentrates on estmatng frst moments of performance,.e., expected losses and delnquency rates, rather than on modelng hgher moments of the loss dstrbuton. In part ths can be attrbutable to the tendency of busness managers to focus on expected proftablty rather than on measures of volatlty. In addton, many practtoners n the retal lendng area mstakenly beleve that the law of large numbers mples that the dstrbuton of retal outcomes wll show lttle varablty around the frst moments of the dstrbuton. From ths proposton they conclude that sgnfcant departures from expectatons are solely the result of model error or poorly desgned busness practces. Theoretcally, the law of large numbers mples that the dosyncratc components of ndvdual loan rsk wll be relatvely unmportant, but t does not mply that movements away from the mean generated by systematc rsk factors wll be small. The mportance of systematc factors n loss volatlty can only be determned by emprcal analyss. The vew that sgnfcant departures from expectatons are solely the result of model error or poorly desgned busness practces, a vew stll common among commercal lenders as well, can be descrbed as the banker vew of rsk. The banker vew emphaszes the endogenous components of credt rsk, n partcular the role of rsk management processes and controls n reducng that rsk. Ths contrasts wth the fnance vew that emphaszes the exogenous components of rsk resultng from underlyng stochastc processes affectng a chosen portfolo. The fnance vew stresses 5

7 the role of rsk management n accurately measurng rsks and ensurng that the company maxmzes ts objectves by choosng from the effcent rsk/reward set of opportuntes. Of course, there are endogenous and exogenous components to the loss volatlty of a gven portfolo of loans. Usng the performance statstcs from an nsttuton s nternal data provdes a method for mplctly ncorporatng the effect of endogenous busness processes on loss volatlty. III. Measurng Credt Rsk: Some Theoretcal Fundamentals In general, the credt rsk models for retal exposures currently n use at U.S. banks are based on a default-mode modelng approach, rather than a mark-to-market model. Therefore, for ease of exposton, we wll confne our dscusson to default-mode models n ths paper. Consder an ndvdual loan wth a gven probablty of default (PD), percentage loss gven default (LGD), and dollars of exposure at default (EAD), where all of the relevant parameters are measured over a one year tme horzon. The dollars of expected loss on the loan s then: EL = PD LGD EAD () Assumng ndependence among these parameters and a known EAD, then t s relatvely easy to show that the standard devaton (SD) of loss per dollar of exposure for ths loan s: 4 SD = ( σ LGD + PD σ ) = ( PD ( PD) LGD + PD σ PD LGD 2 LGD ) (2) SD s a stand-alone measure of rsk. 6

8 If we measure the standard devaton of losses for the portfolo, we get: SDP = j.5 ρ SD j SD j (3) where ρ j s the correlaton between asset and j. As s apparent, estmatng ths model requres estmates of the cross asset correlaton parameters. To determne the approprate level of economc captal for any loan portfolo requres establshng a relevant probablty threshold (e.g., 99.95% probablty that losses wll be less than captal wthn one year). To translate an estmate of SDP to economc captal requres some assumpton about the underlyng dstrbuton of losses (e.g. Normal, Beta, etc.) or, alternatvely, the use of stochastc smulaton methods to determne the tal of the dstrbuton. An mportant decson made early on n the Basel II process was the determnaton that the state of portfolo credt rsk modelng was nsuffcently developed for drect use n settng regulatory captal. In partcular, concern was expressed over the relablty of current methods of estmatng correlaton parameters and questons were rased about the ablty of external supervsors to valdate such estmates. Whle the Basel Commttee suggested that nternal portfolo models would eventually become the bass for settng regulatory captal, t proposed to move mmedately to a smplfed approach to the use of nternal ratngs n the determnaton of regulatory captal. The nternal ratngs based approach, or IRB, allows bank s to use ther nternal loan ratngs categores as a bass for settng regulatory captal. However, captal requrements are set based on rsk parameters estmated separately for each ratngs category. 4 For a more complete dscusson of measurng loan loss volatlty see Ong (998). 7

9 In a model of portfolo loss dstrbutons, the economc captal assocated wth a partcular asset (or a sub-portfolo of assets) depends on ts contrbuton to portfolo rsk, and n general ths contrbuton cannot be determned usng estmates of a sub-portfolo s stand-alone loss dstrbuton. 5 Stated dfferently, total economc captal wll generally be less than or equal to the sum of economc captal approprate for each asset or subportfolo on a stand-alone bass. However, there are classes of models whch are consstent wth an IRB or rskbucketng approach. In partcular, Gordy(2000) has shown that, for a class of one-factor models, portfolo economc captal wll equal the sum of stand-alone economc captal for ndvdual assets or sub-portfolos. The model underlyng the current Basel II s a specal case of the Gordy one-factor model and s based on a Merton model wth a sngle normally dstrbuted systematc rsk factor. Assume that a borrower has returns characterzed by: X = ρ Y + ρ ε (4) where Y s a systematc rsk factor, ρ s the correlaton of asset wth the systematc factor, and ε s an ndependent dosyncratc stochastc factor. We assume X s normally dstrbuted wth mean 0 and varance of. 6 Let π equal borrower 's uncondtonal probablty of default. Ths mples that borrower defaults when X < N - (π ). Portfolo losses, condtonal on Y, can be wrtten as: k L ( Y ) = λ LGD M (Y, ε, ρ ) = (5) 5 If the portfolo s suffcently granular then dosyncratc components of loss would not enter the calculaton. 6 Once a normal dstrbuton of returns s posted, assumng a standard normal s done wthout loss of generalty. 8

10 9 where λ are the dollars of exposure at default n asset and M ( ) s an ndcator varable takng on the value f the th asset defaults and 0 otherwse. To calculate the uncondtonal expected loss smply replace E M ( ) = π and LGD wth ts expected value. Borrow defaults whenever X falls below some unobserved threshold - N - (π ). Condtonal on Y, borrower defaults when: ( ) ) (6 / ) ( ) ( Y p N or N X ρ ρ ε π < < For a portfolo that s suffcently granular,.e., no ndvdual loan s large relatve to the portfolo, the actual loss rate gven the realzaton of Y wll asymptotcally approach the expected loss rate condtonal on Y: 7 ( ) ) (7 ] / ) ( [ ] [ ] [ ) ( k Y N N LGD E Y L E Y L ρ ρ π λ = = To calculate losses at a gven confdence level (e.g probablty L < K), substtute N - ( ν ) = Y where ν s the chosen confdence level. ( ) ) (8 ] / ) ( ) ( [ ] [ ) ( k N p N N LGD E Y L ρ ν ρ λ ν = = Note from the above equaton that, n ths one-factor model, the tal of the portfolo loss dstrbuton s lnear n the tal of the loss dstrbuton for each ndvdual asset. Smlarly, f there are sub-portfolos of loans wth dentcal rsk parameters ncludng a common asset correlaton, then the tal of the portfolo loss dstrbuton wll be lnear n 7 See Gordy ( 2000).

11 the tals of these homogenous sub-portfolos. Thus the model s compatble wth a rsk bucketng approach to settng economc captal. 8 Whle the one factor model s consstent wth a rsk bucketng approach, the sngle factor model s a very restrctve one. In short, portfolo dversfcaton effects are lkely to matter. The approach the Basel Commttee has taken s to ncorporate an ndustry average dversfcaton effect through the correlaton parameter enterng nto equaton (8). Regulators have used a combnaton of statstcal estmates based on ndustry data and comparsons wth current ndustry estmates of economc captal to set correlaton parameters. In effect, ths creates an average ndustry dversfcaton dscount factor at the product or sub-product level. In the current Basel II proposal, advanced IRB nsttutons wll provde own estmates for PD and LGD for a partcular nternal loan ratng (for commercal loans) or by homogenous pools of retal credts. The correlaton parameter s determned by regulators and banks cannot use ther own nternal estmates of asset correlatons wthn a loan ratng/pool category, across ratng/pool categores or across product types (e.g. correlaton between retal exposures and commercal exposures). Ths decson not to allow banks to use own estmates of correlatons s a drect outgrowth of the Basel Commttee s vew that exstng methods for estmatng dversfcaton effects for loan portfolos are unrelable. There s an alternatve ratonale for lmtng the scope of nternal estmates used n settng regulatory captal. An optmal regulatory captal model may not necessarly be 8 Typcally banks subtract expected losses from ther estmates of the tal of the loss dstrbuton when calculatng economc captal. However, wth the excepton of credt card portfolos, the current Basel II formulas use a verson of equaton (8). Basel II allows for captal requrements related to expected losses 0

12 dentcal to the best nternal rsk measurement model. Snce regulatory captal s enforced externally, an approprate regulatory model must be ether drectly verfable by supervsors or be suffcently ncentve compatble to produce statstcally unbased estmates from the regulated nsttuton. Estmates of frst moments of the loss dstrbuton (probablty of default, loss gven default, exposure at default) may be more easly verfable by thrd partes than estmates of hgher moments of the dstrbuton or estmates of asset correlatons. For example, f we are estmatng parameters from a normal dstrbuton confdence ntervals around the mean of the dstrbuton wll be functons of the second moment. And, confdence bands around the varance of the dstrbuton wll be functons of the fourth moment of the dstrbuton. In addton, estmates of volatlty wll depend very crtcally on the tmng of losses. Banks have a certan degree of flexblty n the tmng of loss recognton to smooth losses and potentally reduce estmates of loss rate volatlty. IV. The Rsk Bucketng Approach and Retal Exposures At frst glance, applyng the current IRB approach to retal exposures would seem relatvely smple. Snce nsttutons rely heavly on statstcal models of performance for both makng credt decsons and account management, t would seem relatvely easy to use those quanttatve estmates to supply the relevant rsk parameters for retal exposures. In partcular, the exstence of credt scorng would seem to provde a drect estmate of the probablty of default. 9 to be covered to a lmted extent by loan loss reserves [see Basel Commttee on Bankng Supervson (200b)]. 9 There are a wde varety of scorng models used for dfferent purposes (e.g. scorng for determnng optmum collecton strateges). For ease of exposton, the term scorng model s used here to refer to models commonly used for grantng credt or determnng the level of credt.

13 However, the converson of statstcal methods commonly used n managng a retal portfolo nto estmates relevant to calculatng economc captal s not trval. Two ssues seem of most relevance: estmaton of the probablty of default, and the determnaton of homogenous rsk pools the retal analog to commercal loan ratngs. Estmatng Default Probabltes Modern credt scorng models apply statstcal technques on the extensve data avalable on ndvdual borrowers to generate performance forecasts for varous types of retal loans. For example, many scorng models use logstc regresson to estmate the probablty of a loan becomng delnquent or chargng off. The output of these models s a drect probablty estmate of delnquency or default. However, there are certan dffcultes n drectly usng these estmates as the PD n an economc captal model. Frst, the probablty estmate s typcally not a one-year ahead probablty. The typcal methodology s to estmate a two-year ahead delnquency probablty based on four years of data. 0 Snce scorng models are generally not duraton models, the forecasted probabltes cannot be adjusted smply to accommodate a shorter tme horzon. More substantally, scorng models are generally bult as tools to rank order the performance characterstcs of the populaton, rather than tools to accurately forecast the frequency of partcular performance outcomes. Ths modelng objectve effects how the models are constructed, and mportantly effects the valdaton methods for assessng accuracy. 2

14 Scorng models are not true forecast models n that they typcally do not nclude the lkely state of the economc envronment over the forecast perod. For example, scorng models based on logstc regresson technques typcally do not nclude actual or predcted values of relevant economc factors among the regressors. Thus, the models are a true forecast only f the best predcton of the path of the economy over the next two years s the economy s path over the pror two year perod. The absence of predcted economc varables does not mply that scorng models produce an uncondtonal probablty of default -- theoretcally the relevant nput for PD n the one-factor model of equaton (8). Instead, the probablty estmate s the probablty of default condtonal on a replcaton of recent economc hstory. Whle numerc scores are generated to produce the same probablty of default over dfferent tme perods, a borrower wth dentcal characterstcs wll have a dfferent score dependng on when the scorng model s estmated. As credt scorng models are typcally developed as methods to rank order potental borrowers, the most common method for testng the accuracy of a scorng model s the Kolmogorov-Smrnov Goodness-of-Ft Test (K-S Statstc). The K-S statstc essentally measures whether the performance of lower scored borrowers s substantally worse than the performance of those wth hgher scores. A model may perform very well usng the K-S statstc whle producng large predcton errors for any gven score band. For example, f the actual performance of borrowers unformly shfts n a worse or better drecton, the K-S statstc wll not deterorate. 0 Scorng models generally produce probabltes of varous stages of delnquency up to and ncludng default. For ease of exposton, we refer to the output of the scorng model as a probablty of default estmate. 3

15 The relance on the rank orderng propertes of a credt scorng model reflects the busness methods used for managng rsk n retal portfolos. Hstorcally, the retal market was characterzed by lenders makng offers of credt at a sngle nterest rate and then ether acceptng or rejectng borrowers based on an assessment of lkely performance. Lenders needed only to establsh a sngle margn separatng the two pools of accepted and rejected applcants. The probabltes of performance for non-margnal applcants would affect actual earnngs results, but generally would not effect the decson to extend credt for applcants well above or well below the credt score cutoff. Probablty estmates would stll be crtcal for makng decsons about margnal borrowers. However, a retal lender s approach to handlng predcton error uncertanty was typcally to rely on montorng actual performance and adjustng relevant score cutoffs based on recent performance hstory. Ths approach to rsk management determned when scorng models needed to be reestmated. Generally, a credt scorng model was only reestmated f ts rank orderng propertes deterorated, but t was not typcally dscarded f t rank orders properly but substantally msforecasts the condtonal probablty of default. To some extent, ths explans the reluctance of credt rsk modelers to use drectly the probablty estmates derved from credt scorng models as PD s n ther economc captal models. There have been and contnue to be substantal market changes takng place that wll lkely lead to mproved drect estmates of probablty of default usng scorng models n the near future. Among other factors, the revoluton n nformaton and communcatons technology has led to much greater degrees of rsk-based prcng and targeted marketng 4

16 n retal lendng. In ths envronment, a greater premum s placed on a lender s ablty to accurately dfferentate the credt qualty of borrowers and to understand the contrbutons of partcular sub-portfolos to the overall level of rsk. Ths nevtably leads to a greater emphass on scorng models for predctng proftablty outcomes of partcular busness decsons rather than merely establshng reject/accept cut-offs. Accurate forecasts of proftablty requre mprovements n methodologes for more accurate forecasts of actual default frequences. Whle there are weaknesses n usng the drect probablty estmates derved from scorng models, the rank orderng propertes of scorng models can be an mportant nput nto estmates of the probablty of default, nonetheless. Some banks use nternal data to estmate the ex post one-year ahead default behavor usng credt scores and other rsk factors, such as loan seasonng, delnquency status, loan-to-value ratos, as condtonng varables. However, two related emprcal ssues arse when usng ths approach to estmate PD: Should models use orgnaton or refreshed scores? Should recent hstory be weghed more heavly n the analyss? Refreshed scores represent the most up-to-date nformaton about borrower qualty and therefore provde the most approprate predctor of performance of the partcular loans n the portfolo. 2 However, refreshed scores wll be sgnfcantly affected by the A lender compares any gan from ncreasng prce dscrmnaton to the costs of the ncreased nformaton necessary for more fnely dfferentatng potental borrowers. 2 Theoretcally, refreshed scores could be a worse short-run predctor of performance snce the models do not nclude optmal predctons of future economc factors. However, emprcally the varatons n ndvdual characterstcs should generally domnate varatons generated by msforecasts of future economc factors. Moreover, snce economc factors tend to be hghly autoregressve, the mplct economc predctons n the refreshed score should be ether dentcal (scorng model estmated over the same perod) or better (scorng model estmated over more recent perod) than the predctons mplct n the orgnaton score. 5

17 state of the economy. That s, n a bad economc envronment all scores wll generally shft down for two reasons. Frst, t s more lkely that measured borrower characterstcs wll have deterorated (e.g. more late payments, hgher unemployment) durng economc downturns. Second, scores wll generally shft down for a gven set of ntal borrower characterstcs snce borrowers wth the same ntal condtons over the estmaton perod are more lkely to suffer smlar negatve economc shocks. Whle orgnaton scores wll not provde the optmum performance forecast over the next year, orgnaton scores wll reflect a smoother dstrbuton of cyclcal effects snce loans n the portfolo wll be orgnated at dfferent tme perods. In short, a model based on the most current nformaton about borrowers wll produce more accurate short-run loss predctons, but those predctons wll have a greater pro-cyclcal component. A second related ssue s the sample perod over whch the relatonshp should be estmated. A general way to thnk about ths ssue s whether recent observatons should receve greater weght n forecasts relatve to earler observatons. 3 A longer hstory would be an approprate estmate of the long run one year default probablty f the relatonshp between score and performance are statonary. However, f there are permanent shfts n the relatonshp, then greater weght should be gven to more recent hstory. 4 Moreover, greater weght should be gven to more recent hstory f the objectve of regulatory captal mnmums s to ensure adequate coverage for short-run rsks. Settng regulatory captal mnmums to cover short-run rsks produces a more pro- 3 At the extremes the alternatves are to estmate the relatonshp over a long perod of tme gvng each perod equal weght or to truncate the sample and only estmate the relatonshp over recent tme perods. 4 Km and Santomero (993) dscuss ths ssue n relatonshp to establshng loan loss reserve requrements. 6

18 captal requrement, and ths approach has been rejected by the Basel Commttee largely due to concerns over creatng an excessvely pro-cyclcal captal requrement. Resolvng ths ssue s an emprcal matter. Unfortunately, current practce n ths area s largely drven by data avalablty consderatons. In the past, most banks dd not make a systematc effort to mantan extensve nternal hstorcal data at the ndvdual account level. Whle account level data generally exsts n archved systems, retrevng the data and generatng consstent data elements s usually very costly for large banks. Ths problem s partcularly acute for nsttutons that have partcpated n multple mergers among banks wth ncompatble nformaton systems. One approach employed by many banks s to create an nternal hstorcal database from the hstorcal scores on ther own customers obtaned from the credt bureaus. In addton, some large nsttutons are undertakng major efforts to create consstent hstorcal nternal data seres. Whle ths s partly n response to the Basel II proposals, t s manly a recognton of the compettve value of mprovng nternal analytcs. One potental unntended benefcal externalty that may result from an IRB captal standard s that t wll produce relatvely consstent standards for data mantenance at large banks. Gong forward, ths could substantally reduce some of the dffcultes of creatng consstent hstorcal data when large nsttutons merge. Defnng Homogenous Rsk Pools 7

19 The Basel II rsk-bucketng approach requres that estmaton of PD and LGD be done for sub-portfolos of homogenous exposures. 5 For the commercal loan portfolo, the relevant sub-portfolos wll be nternal ratngs categores. 6 Whle the methods for groupng commercal loans nto nternal ratngs categores are not dentcal across bankng organzatons, there s a degree of consstency due to the typcal practce at large banks of mappng nternal loan grades to equvalent bond ratngs. There are no smlar benchmark crtera for groupng retal exposures by homogenous rsk characterstcs. At frst glance, the problem of creatng homogenous rsk pools for retal exposures appears to be relatvely smple. Snce retal lenders use farly standard quanttatve measures of credt qualty n managng a retal portfolo, t s relatvely straghtforward to group retal exposures by a set of objectve crtera. Ths contrasts wth the commercal loan process where subjectve and dosyncratc factors play a more sgnfcant role n ratng assgnment. However, whle bucketng loans usng objectve crtera s relatvely straght forward once crtera are establshed, there s no standard ndustry practce for settng crtera and no benchmark analogous to bond ratngs for commercal loans. Moreover, segments used for nternal bank management typcally span a wde spectrum of credt rsk. For example, credt card ssuers commonly track performance by segments defned by malng programs amed at a partcular clent base (e.g. student cards), by affnty card programs (e.g. unversty afflaton), or co-branded cards (e.g. arlne card). 5 In the Merton one-factor model economc captal for the portfolo s a weghted sum of the economc captal for ndvdual assets. One cannot substtute the average rsk parameter for a portfolo or subportfolo made up of non-homogenous assets. 6 The regulatory standards for advanced IRB nsttutons wll requre banks to have a mnmum number of ratngs categores. 8

20 Retal portfolo rsk managers do track nformaton on varous types of credt scores and other rsk metrcs, and ths nformaton s used n varous ways. However, there are no standard methods for groupng credts nto rsk buckets for analytcal purposes. For products wth a very large customer base, rsk bucketng could n prncple be done at a very fne level for measurng probablty of default. The two man constrants are ensurng adequate sample szes for estmaton and obtanng hstorcal data consstent wth the rsk segmentaton adopted. Usng the current Basel one-factor model to set requred captal wll create an ncentve for bank s to use more fnely defned rsk pools for calculatng captal. In the one factor model descrbed above, captal factors are concave n PD for gven LGD. Snce bank s are lkely to have estmates of PD on a much fner level then nformaton on LGD (nformaton on LGD s are generally not tracked at the account level), then overall requred captal wll be lower f PD s are estmated at a fner level of segmentaton. Thus, the one-factor model creates ncentves for bank s to generate relable nformaton at a more granular level. Note that ths s exactly opposte to the results from usng measures of volatlty. Snce the sum of sub-portfolo volatltes wll generally be greater than the volatlty of the entre portfolo, captal requrements based on volatlty measures wll be hgher the fner the degree of segmentaton. Thus, use of drect measures of hstorcal volatlty wthout correctng for dversfcaton effects (or more generally the effects of segment composton) could create dsncentves for measurng rsk parameters on more granular sub-portfolos. 9

21 V. Summary Current retal credt rsk modelng at U.S. bankng nsttutons has been relatvely slow n development and s characterzed by a wde dvergence n approaches. In addton, few banks have mantaned hstorcal databases wth consstent data to enable estmatng of detaled rsk characterstcs of the components of ther portfolo. Nevertheless, there are sgnfcant nherent advantages to credt rsk modelng n the retal area compared to modelng commercal loan portfolos. In partcular, the wde scale use of very sophstcated credt scorng models and the assocated extensve data mned to produce scores provdes excellent raw materal for sophstcated portfolo rsk measurement technques. Many nsttutons wth large retal portfolos are recognzng the value of credt rsk modelng for a wde varety of busness purposes ncludng allocaton of economc captal. Ths recognton, along wth the desre to qualfy as advanced IRB banks n the Basel II framework, s generatng substantal efforts to mprove retal banks nformaton systems and modelng sophstcaton. It s lkely, gven the nherent advantages of quanttatve tools for credt rsk modelng of retal exposures, that advances n ths feld wll move rapdly and that the drecton wll be toward portfolo modelng based on measurng performance characterstcs for detaled segments of the retal portfolo. 20

22 References Gordy, Mchael (2000). Credt VaR Models and Rsk-Bucket Captal Rules: A Reconclaton, Proceedngs of the 36th Annual Federal Reserve Bank of Chcago Conference on Bank Structure and Competton, 2000, Basel Commttee on Bankng Supervson (200a). The New Basel Captal Accord, Consultatve Paper, January. Basel Commttee on Bankng Supervson (200b), IRB Treatment of Expected Losses and Future Margn Income, July. Km, D. and A. M. Santomero (993). Forecastng Requred Loan Loss Reserves, Journal of Economcs and Busness, Vol. 45(3-4), Ong, Mchael K. (999). Internal Credt Rsk Models: Captal Allocaton Models and Performance Measurement, (London: Rsk Books). Treacy, Wllam and Mark Carey (998). Credt Rsk Ratng at Large U.S. Banks, Federal Reserve Bulletn 84,