Financial Stability Institute

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1 Fnancal Sably Insue FSI Award 21 Wnnng Paper Regulaory use of sysem-wde esmaons of PD, LGD and EAD Jesus Alan Elzondo Flores Tana Lemus Basualdo Ana Regna Qunana Sordo Comsón Naconal Bancara y de Valores, Mexco Sepember 21 JEL classfcaon: G21, G28

2 The vews expressed n hs paper are hose of her auhors and no necessarly he vews of he Fnancal Sably Insue or he Bank for Inernaonal Selemens. Copes of publcaons are avalable from: Fnancal Sably Insue Bank for Inernaonal Selemens CH-42 Basel, Swzerland E-mal: fs@bs.org Tel: Fax: and Ths publcaon s avalable on he BIS webse Fnancal Sably Insue 21. Bank for Inernaonal Selemens. All rghs reserved. Bref excerps may be reproduced or ranslaed provded he source s ced. ISSN

3 Foreword The Fnancal Sably Insue s pleased o presen he wnnng FSI Award paper for 21. Ths award, gven every wo years a he me of he Inernaonal Conference of Bankng Supervsors, was esablshed o encourage hough and research on ssues relevan o bankng supervsors globally. In 21, nne papers were receved from cenral banks and supervsory auhores n egh counres. A jury of hghly qualfed ndvduals read all of he papers and chose he wnner. The group was chared by Mr Jame Caruana, General Manager of he Bank for Inernaonal Selemens. I also ncluded Mrs Ruh de Krvoy, former Presden of he Cenral Bank of Venezuela; Mr Nck LePan, former Supernenden of Fnancal Insuons, Canada; Mr Charles Freeland, former Depuy Secreary General of he Basel Commee on Bankng Supervson; and Mr Sefan Waler, Secreary General of he Basel Commee on Bankng Supervson. The jury members and he FSI are pleased o announce ha he paper auhored by Mr Jesus Alan Elzondo Flores, Ms Tana Lemus Basualdo and Ms Ana Regna Qunana Sordo of he Mexcan Comsón Naconal Bancara y de Valores has been chosen as he wnner of he 21 FSI Award. In he paper, he auhors se ou an example of how o use a prudenal ool ypcally amed a copng wh he solvency of ndvdual banks o deal wh he measuremen of sysemc rsk. Congraulaons o our hree wnners, as well as o he auhors of he oher papers submed for consderaon. Ther neres n analysng and poenally mprovng supervsory mehods provdes a rue servce o he supervsory communy. Josef Tošovský Charman Fnancal Sably Insue Sepember 21 FSI Award 21 Wnnng Paper

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5 Conens Foreword Inroducon Sysem-wde PD, LGD and EAD Sysem-wde nformaon and PD, LGD and EAD models Emprcal resuls Model applcaons Cred card porfolo reserves Sysem-wde PD dependency on dosyncrac and cyclcal facors Bank IRB model comparson o sysem-wde model esmaes Rsk reurn analyss of he cred card porfolo Dfferences n pon-n-me PIT) models and hrough-he-cycle TTC) esmaons Conclusons Annex 1: Explanaory varables Annex 2: Reserve requremen rule Bblography FSI Award 21 Wnnng Paper

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7 1. Inroducon The objecve of prudenal regulaon has for a long me been he solvency of ndvdual enes and hence a vas range of prudenal ools were developed o address hs prory. Mos recenly, due o he perod of fnancal sress and he falure of seemngly solven nsuons, he nernaonal supervsory communy has expanded he relevance of prudenal ools n promong he sably of he fnancal sysem as a whole n addon o ndvdual nsuons. In hs sense he Basel Commee has concluded ha he ssue of sysemc rsk s probably he mos mporan and mos dffcul one confroned by he nernaonal regulaory communy and ha progress requres, among oher hngs, a combnaon of beer regulaon and he ncluson of a macro perspecve no prudenal ools. 1 Wh hs n mnd, he am of hs paper s o exend he use of a prudenal ool ypcally used o cope wh he solvency of ndvdual nsuons n order o esmae rsk parameers ha measure sysemc rsk. Ths objecve s acheved by esmang sysem-wde Probably of Defaul PD), Loss Gven Defaul LGD), and Exposure a Defaul EAD) parameers for a real porfolo wh nformaon ha s represenave of he sysem, boh cross-seconally and for a relevan par of he economc cycle. Ths paper nends o generae a prudenal ool ha ) encompasses boh mcro and macro prudenal supervson concerns and ) sheds lgh on he adequacy of banks ndvdual reserves and her suffcency o cover sysemc expeced losses. The ool also seeks o dsenangle he naure of exposure of he sysem o rsk, n erms of s dependency on sysemc facors, as opposed o dosyncrac ones. 1 Caruana 21). FSI Award 21 Wnnng Paper 1

8 The paper draws srongly from he recommendaons o enhance he reslence of he fnancal sysem ssued by he Basel Commee n December Parcularly, on he loan loss provsonng prncples hghlghed by he documen, n whch, among ohers, s proposed o: ) use robus and sound mehodologes ha reflec expeced cred losses n he banks exsng loan porfolo over he lfe of he porfolo and ) he ncorporaon of a broader range of avalable cred nformaon han he one presenly ncluded n he ncurred loss model o acheve early denfcaon and recognon of losses. In hs paper, he second secon defnes wha s undersood by sysem-wde PD, LGD, and EAD and examnes he relevance of s use as a regulaory ool. The hrd secon explans he models used o esmae sysem-wde parameers and he nformaon used n hem. The fourh secon provdes emprcal resuls. The fnal secon provdes praccal applcaons of he regulaory ool for boh mcro and macroprudenal dmensons. 2. Sysem-wde PD, LGD and EAD In June 26, he Basel Commee ssued he Revsed Framework on Inernaonal Convergence of Capal Measuremen and Capal Sandards Basel II), 3 whch ook no accoun new developmens n he measuremen and managemen of bankng rsks for hose nsuons ha oped o use he nernal rangs-based IRB) approach. In hs approach, nsuons are allowed o use her own nernal measures for key drvers of cred rsk as prmary npus o he 2 3 Basel 29). Basel 26). 2 FSI Award 21 Wnnng Paper

9 capal calculaon. These measures requre he esmaon of he followng parameers 4 ha descrbe he exposure of he porfolo: 5 ) probably of defaul PD), whch gves he average percenage of oblgors ha defaul n a rang grade n he course of one year; ) exposure a defaul EAD), whch gves an esmae of he ousandng amoun drawn amouns plus lkely fuure draw-downs of ye unused lnes) n case he borrower defauls; and ) loss gven defaul LGD), whch gves he percenage of exposure he bank mgh lose f he borrower defauls. These rsk measures are convered no rsk weghs and regulaory capal requremens by means of rsk wegh formulas specfed by he Basel Commee. The parameers menoned above are amed a descrbng he exposure of he bank o s own cred rsk. However, he esmaon of hese parameers can be escalaed o consder sysem-wde nformaon. The nerpreaon of hese parameers gans a broader dmenson snce explanaory rsk facors reflec he poenal exposure of he sysem o a common rsk and can be analyzed n wo complemenary dmensons ha offer valuable nsgh no sysemc vulnerables e cross-seconal and hrough me). On he cross-seconal dmenson s acknowledged ha a shock hng one nsuon can spread o oher nsuons ha are nerconneced; hus, such shock can become a sysemc hrea. Ths fnancal shock may be orgnaed from a common exposure across he sysem. 4 5 Real exposures. Basel 25). FSI Award 21 Wnnng Paper 3

10 Whle he use of sysem-wde esmaons of PD, LGD, and EAD may no shed lgh on he ner-lnkages among nsuons, appears o be a useful dagnosc ool for deecng a common exposure o a rsk facor across he sysem. 6 The lne of nvesgaon ha s proposed separaes he analyss of sysem-wde PD no wo dfferen branches. On he one hand, we analyze varables assocaed wh ndvdual borrower behavour; hus such varables are no nfluenced or under drec conrol of fnancal nsuons. Examples of hese varables are paymen behavour or cred lm use. On he oher hand, he varables assocaed wh dosyncrac facors ndvdual nsuon) such as collecon and orgnaon pracces followed by specfc nsuons. The hypohess s ha, f sysem-wde PDs are explaned by varables relaed o he behavour of ndvdual borrowers and no sgnfcan mpac s borne by dosyncrac facors, no only s he sysem exposed o a common rsk exposure bu, as long as explanaory facors are dependen on he economc cycle, s also exposed o cycle dynamcs. In hs sense, he procyclcal dmenson of sysemc rsk relaes o how aggregae rsk evolves over me and s dependency on he economc cycle. In order o es f he sysem s exposed o he me dmenson varan of sysemc rsk, sysem-wde PDs are correlaed o aggregae varables relaed o he economc cycle and s sgnfcance s sascally esed. Furher applcaons of sysem-wde PD, LGD, and EAD as a regulaory ool are presened. As menoned before, he Revsed Framework on Inernaonal Convergence of Capal Measuremen and Capal Sandards proposes he esmaon of capal assumng ha expeced losses are consued and 6 However once hese parameers are esmaed, hey can be furher used n subsequen research o explore ner-lnkages among nsuons usng a framework o assess sysemc fnancal sably as defned by Segovano and Goodhar 29). 4 FSI Award 21 Wnnng Paper

11 esmaed wh PD, LGD, and EAD parameers calbraed wh he same characerscs eg 12 monhs of losses) as hose proposed n he Revsed Framework. For he case of he counry analyzed, s shown ha reserves bul by he sysem a he me of analyss accouned for approxmaely half of he esmaed expeced losses under hese crera and were less rsk-sensve. To address hs ssue a specfc reserve requremen based on sysem-wde esmaes of PD, LGD, and EAD was nroduced. I s also shown ha he use of sysem-wde parameers represens a useful benchmarkng ool for he valdaon of IRB models. IRB model esmaons of PD calculaed by a bank seekng model approval are compared o sysem-wde esmaons of PD. A dealed se of conclusons s drawn on he IRB model proposal and s capacy o consder sysem-wde explanaory varables of PD. An addonal applcaon s o measure he relevance of usng eher pon-n-me PIT) model esmaes as opposed o hrough-he-cycle TTC) models. The analyss of he srucure of he model hrough me ndcaes he dependency of he aggregae rsk of he sysem o a common se of explanaory varables and provdes valuable nsgh n erms of sysem vulnerables. By usng boh ypes of models, s also shown how sysem-wde PIT esmaons of PD conssenly underesmae and overesmae he observed defaul raes when PIT models are esmaed n respecvely lower and hgher rsk segmens of he economc cycle. Fnally, a se of conclusons s drawn from ndvdual bank rsk prcng pracces, as neres rae chargng polces can ndvdually be compared o expeced loss esmaons; hus allowng for rsk-reurn analyses boh across banks and whn bank porfolos. For he case of he cred card porfolo of he counry analyzed, s concluded ha here exss clear prce dfferenaon across banks, generally assocaed wh he rsk profle of he populaon, whle s no he case ha prcng pracces of all nsuons dfferenae rsk across her own clenele. FSI Award 21 Wnnng Paper 5

12 3. Sysem-wde nformaon and PD, LGD and EAD models Models of PD, LGD, and EAD are esmaed by banks wh nformaon ha reflecs paymen experence whn he bank. These parameers end o descrbe ndvdual bank experence and ofen show dfferen explanaory facors when compared o oher banks models. In order o convey a sysem-wde dmenson o parameers and denfy f here exss common rsk facors across banks, hree sources of nformaon were colleced: 1. Indvdual cred card saemens ha descrbe loan-level daa nformaon relaed o ousandng balance, neres rae, acual paymens, mnmum requred paymen, and dae of paymen. Ths nformaon s desgned o descrbe he paymen behavour of borrowers, denfy recovery n subsequen perods afer defaul and allow he denfcaon of he exposure a he me of defaul. 2. Cred bureau nformaon ha consss of ndvdual cred records, ncludng nformaon such as he number of loans he borrower had wh oher banks n he analyzed perod, s performance and he me elapsed snce he borrower frs receved a loan n he sysem. 3. Socal housng nsue nformaon whch collecs payroll deducons from workers and descrbes borrowers employmen hsory and curren ncome level. The en larges nsuons, accounng for 97% of oal cred cards n he sysem, were seleced o parcpae n he exercse. A random panel daa sample of he sysem was desgned consderng wo dmensons: ) Pon-n-me dmenson The nformaon was srucured o span a 25-monh nerval dvded no wo 12-monh nervals and a reference pon. The frs 12-monh nerval hsorcal perod) gves nformaon 6 FSI Award 21 Wnnng Paper

13 abou he borrower s behavour, based on he hree sources of nformaon menoned above, for he welve monhs precedng he reference pon. The welve monhs afer he reference pon performance perod) are desgned o denfy ndvdual defaul raes. Ths srucure allows he assocaon of borrower characerscs and defaul. ) Tme seres dmenson To gan nsgh no he sably of he model hrough a relevan par of he cycle, 12 wndows of 25 monhs of nformaon were exraced. The 12 reference pons seleced for each wndow were Aprl 26 o March 27 spannng a hree year perod of me sarng n Aprl 25 and endng n March 28. Random samples were aken from he unverse of loans avalable n he sysem as regsered n he cred bureau for each of he 12 reference pons and he sze of he sample was deermned o allow an esmaon error of a PD parameer of 4 bass pons wh a 99% confdence. 7 Defaul s defned based on he defnon of Basel II whch saes ha a loan has defauled f eher one or boh of he followng evens have aken place: 1) he bank consders ha he oblgor s unlkely o pay s cred oblgaons o he bankng group n full, whou recourse by he bank o acons such as realzng secury f held); and 2) he oblgor s pas due more han 9 days on any maeral cred oblgaon o he bankng group. 7 The formula used o deermne he smple sze of he cred card porfolo 2 Nz s: α / 2 P1 P) n =. 2 2 N 1) e + zα / 2 P1 P) FSI Award 21 Wnnng Paper 7

14 PD model Caegorcal daa echnques such as logsc regresson have ncreasngly been used n models of predcon of defaul and hs approach s proposed for he esmaon of he model of sysem-wde PD. 8 ' Le x be a vecor of p ndependen varables, y denoes he value of a dchoomous oucome varable, and = 1,2,3,,N. Furhermore, assume ha he oucome varable has been coded as or 1, represenng he absence or he presence of defaul, respecvely. To f he logsc regresson model ' requres he esmaon of he vecor β = β, β,..., β ). 1 p Le he condonal probably ha he oucome s presen be ' ' denoed by P Y = 1 X ) = π x ). The log of he mulple logsc regresson model s gven by he equaon g x ' ) = β β x β x... β, n whch case he logsc regresson model s p x p ' g x ) ' e π x ) =. ' g x ) 1 e LGD model LGD s he cred loss ncurred f an oblgor defauls and s dependen on he characerscs of he loan. Losses are nfluenced by he presence of collaeral and when no collaeral exss he cash flows ha he borrower pays afer defaul deermne he LGD of he loan. The model proposed o esmae LGD for he cred card porfolo analyzed s o accoun for he cash flows ha occur hree monhs afer defaul and compare hem o he maxmum ousandng balance of he loan afer he momen of defaul. 8 Hosmer and Lemeshow 1995). 8 FSI Award 21 Wnnng Paper

15 The maxmum ousandng balance s used n order o consder he revolvng naure of cred card loans, and hence he possbly of balance ncreases due o lne dsposons n he perod of defaul. Followng hs defnon, LGD can be expressed as: LGD = 1 MAX = 3 defaul { Bal, Bal, Bal, Bal } defaul Borrower Paymens defaul + 1 defaul + 2 defaul + 3 Where Bal s he ousandng balance of he cred card a me and defaul s he me of defaul of he loan. EAD model EAD esmaes he percenage of exposure he bank mgh lose f he borrower defauls. The esmaon of EAD becomes hghly relevan n revolvng nsrumens such as cred cards and hence s necessary o nclude an esmaon of he value of he exposure ha he borrower wll have a he me of defaul n order o oban an approprae esmae of he expeced loss. Commonly used mehods of esmaon for hs parameer 9 are focused n mercs ha assocae he ncremens n he balance beween a specfc dae of reference and he me of defaul. The model proposed n hs documen consss of esmang an exposure a defaul facor ha reflecs he mulple of he ousandng balance a he momen of defaul o he ousandng balance a he reference pon EAD facor). Consderng ha he cred lm use a he reference pon dae s a canddae o explan sgnfcan dfferences n he EAD facor, a smple sascal assocaon beween boh varables s proposed as follows: 9 Engelmann and Rauhmeer 26). FSI Award 21 Wnnng Paper 9

16 EAD facor = f balance a reference pon dae / cred lm a reference pon dae) Where, EAD facor = balance a defaul / balance a reference pon dae. 4. Emprcal resuls PD model The ndependen varables used o buld he PD model were consruced from he daa se menoned before and were seleced accordng o her explanaory power. For an exhausve ls of varables analyzed see Annex 1. The PD model conans he followng fve varables: 1. X1: number of consecuve perods, up o he reference pon, n whch he cardholder has no pad s mnmum conracual paymen oblgaon; 2. X2: number of perods n whch he cardholder has no covered he mnmum paymen n he las 6 monhs. 3. X3: paymens made by he cardholder as a proporon of he ousandng balance of he cred card a he reference pon; 4. X4: oal ousandng balance as a proporon of he cred lm a he reference pon; and 5. X5: number of monhs elapsed snce he ssuance of he cred card by he bank. 1 FSI Award 21 Wnnng Paper

17 Table 1 Sysem-wde PD explanaory varables Explanaory varables Coeffcen Inercep 2.97*** X1 Curren non-paymen.673*** X2 Hsorcal non-paymen.469*** X3 Percenage of paymen 1.22*** X4 Cred lm use 1.151*** X5 Maury.7*** Noe: Sgnfcance level ***.1, **.1, *.5 performed wh sandard Wald es). I s mporan o noe ha all relevan varables are assocaed wh he characerscs of he borrower behavour and cred card use. LGD model The esmaon of LGD consdered all he cred cards ha defauled n he performance perod and he reference pon. Table 2 shows he average amoun recovered by he banks n he hree-monh perod afer defaul. FSI Award 21 Wnnng Paper 11

18 Table 2 Cash flow recovery of ousandng balance 3 monhs afer defaul as percenage of maxmum ousandng balance afer defaul % of Recovery Inerval Frequency % % Recovered % 9% 6%.4% 1% 19% 1% 1.6% 2% 29% 8% 2.% 3% 39% 4% 1.5% 4% 49% 3% 1.2% 5% 59% 2% 1.1% 6% 69% 1%.7% 7% 79% 1%.7% 8% 89% 1%.4% 9% 99% 1%.5% > 1% 9% 9.2% LGD 81% The fnal LGD esmae for he sysemc cred card porfolo s 81%. EAD model The assocaon beween he EAD facor and cred lm use s apparen, as llusraed n Graph FSI Award 21 Wnnng Paper

19 Graph 1 EAD facor and cred lm use 3 25 Facor = EAD/BalanceT % 5% 1% 15% 2% 25% 3% BalanceT/CredLne EAD s herefore a funcon of he cred lm use of ndvdual borrowers where low cred lm use s assocaed o hgh EAD facors. The resulng funcon s: Ousandng Balance a reference pon EAD facor = Cred lm a reference pon.5784 Once he funcon s defned, adjusmen facors are esmaed and summarzed. FSI Award 21 Wnnng Paper 13

20 Table 3 EAD facors as a funcon of cred lm use % USE Cred lm use Md pon Fed curve 1 % 1% 5% 566% 1% 2% 15% 3% 2% 3% 25% 223% 3% 4% 35% 184% 4% 5% 45% 159% 5% 6% 55% 141% 6% 7% 65% 128% 7% 8% 75% 118% 8% 9% 85% 11% 9% 1% 95% 13% >=1% 1% 1% 1 The curve was fed by OLS by ransformng he equaon: y = cx b. The sgnfcance level of he b parameer -es) s FSI Award 21 Wnnng Paper

21 5. Model applcaons 5.1 Cred card porfolo reserves Inernaonal accounng sandard prncples have for a long me ndcaed ha cred losses are o be recognzed only f here s objecve evdence of mparmen as a resul of a loss even. 1 The applcable rule for he counry analyzed n hs documen esmaes reserves as a funcon of he number of pas due paymens owed by he borrower a he me of analyss. Table 4 Cred card reserve requremen Number of perods pas due % Reserves.5% 1 1% 2 45% 3 65% 4 75% 5 8% 6 85% 7 9% 8 95% 9 or more 1% 1 IASB 29). FSI Award 21 Wnnng Paper 15

22 Whle he reserve mehodology s easy o mplemen and reflecs more reserves when here s more evdence of loan deeroraon, as a prudenal requremen, shows he followng lmaons: 1. reserves are no calbraed o cover expeced losses of 12 monhs; 2. all relevan avalable cred nformaon s no consdered o dfferenae rsk among ndvdual borrowers; 3. loss esmaons are no based on prospecve analyss; 4. he amoun of reserves does no consder exposure a defaul adjusmens. Toal loan loss reserves were esmaed usng he requremen descrbed n Table 4 and conrased o acual cred card porfolo wre-offs for he 12-monh perod followng he esmaon. 16 FSI Award 21 Wnnng Paper

23 Table 5 Reserve requremen suffcency measured n monhs 12-monh wre-offs 1 Reserves a sar of 12-monh perod 1 % Wre-offs / Reserves Monhs of coverage Bank 1 2,577 1, % 4.9 Bank 2 11,397 5, % 5.5 Bank 3 6,65 4, % 8.3 Bank % 4. Bank % 6.4 Bank 6 2,26 1, % 7.6 Bank 7 4,1 1, % 3.2 Bank % 1.7 Bank 9 9,392 6, % 8.4 Bank % 7.6 Cred Card Sysem 38,326 21, % 6.6 Noe: In wha follows Bank 1, 2,..,1 represen he same nsuon. 1 In mllons. Table 5 shows ha reserves were on average suffcen o cover 6.6 monhs of acual wre-offs. The resuls also llusrae he heerogeney ha he regme generaes across banks n erms of he number of monhs ha he allowance covers. Ths las fac may lead he regulaor o consder banks ha comply wh he regme as equally equpped o cover losses even f here was sgnfcan varance among hem. FSI Award 21 Wnnng Paper 17

24 In order o es he exposure of he sysem, he loan loss dsrbuon of he analyzed porfolo was esmaed by usng sysem-wde PD, LGD, and EAD and he IRB capal formulas se n he Revsed Framework Basel II). Graph 2 Loan loss dsrbuon and capal and reserve requremen Reserves 9.31% F R E Q U E N C Y Expeced Loss 18.42% Capal Requremen + Reserves Sandard Approach) 17.31% Capal Requremen + Reserves IRB approach) 36.54% 8% rsk weghed Asses % rsk weghed Asses % Asses Graph 2 makes evden ha he regme of reserves along wh he Basel I capal sandard for he cred card loan porfolo analyzed were nsuffcen o cover losses measured under he Basel II approach. Sysem-wde models of PD, LGD, and EAD can be furher used o esmae ndvdual banks expeced losses by feedng correspondng clen nformaon on PD and EAD equaons. Ths procedure resuls n esmaes of ndvdual banks expeced losses and capal esmaons llusraed n Table FSI Award 21 Wnnng Paper

25 Table 6 Indvdual banks capal and reserve requremens % Reserves Table 4 approach) % Capal Requremen Sandard approach) % Expeced Loss Sysemwde model approach) % Capal Requremen Sysemwde model approach n IRB formulas) Bank % 8% 17.63% 17.65% Bank % 8% 17.57% 17.82% Bank % 8% 3.21% 23.9% Bank % 8% 75.48% 1.52% Bank % 8% 23.87% 19.6% Bank % 8% 19.11% 19.8% Bank % 8% 14.52% 16.85% Bank 8 1.6% 8% 16.62% 17.93% Bank 9 8.1% 8% 13.7% 13.79% Bank % 8% 6.19% 16.21% Cred Card Sysem 9.31% 8% 18.42% 18.12% The comparson of boh regmes shows ha he former reserve and capal regme were also nsuffcen o cover expeced losses for each nsuon n he sysem. Sysem-wde models of PD, LGD, and EAD were nroduced n he analyzed counry as a mnmum reserve requremen Annex 2) o address hese ssues and se a homogeneous me frame for loss coverage. These requremens allowed he FSI Award 21 Wnnng Paper 19

26 regulaor o equp he sysem wh a homogeneous regme of reserves fed o susan 12 monhs of expeced losses and promoed ncenves for banks o develop her own IRB models and o acvely manage he rsk of her porfolos due o he fac ha he regulaory cos of ndvdual loans s more rsk sensve. 5.2 Sysem-wde PD dependency on dosyncrac and cyclcal facors The cred card porfolo rsk exposure of he analyzed counry appears o be subjec o sysemc rsk. In order o es he hypohess of he exsence of sysemc rsk exposure, PD, LGD and EAD models were renforced wh a new se of explanaory varables relaed o bank dosyncrac rsk and bank exposure o cycle dynamcs o deec boh poenal cross-seconal and procyclcal sysemc rsk exposure. ) Cross-seconal dmenson Explanaory varables of he PD model presened n secon 4 were shown o be dependen on facors relaed o ndvdual borrower characerscs and paymen behavour. In order o es he hypohess of cross-seconal sysemc rsk due o a common exposure, he proposed nex sep conssed of esng f banks were a sgnfcan explanaory varable n he deermnaon of sysem-wde PD. For hs purpose, bank porfolos were sgnalled wh a dummy varable ha assocaed each loan o he correspondng bank, and hese dummy varables were esed for her sgnfcance n he fnal PD model. 2 FSI Award 21 Wnnng Paper

27 Table 7 PD model ncludng bank dummy varables Explanaory varables Coeffcen Inercep 2.826** Curren non-paymen.675** Hsorcal non-paymen.486** Percenage of paymen.9** Cred lm use 1.63** Maury 1.8** Dummy bank 9.54* Dummy bank 1.575** Noe: Sgnfcance level ***.1, **.1, *.5 performed wh Wald Tes). Table 7 shows he resulng esmaes for qualave varables descrbng banks parcpang n he sysem and resuls ndcae ha banks are no a sgnfcan facor n explanng sysem-wde PD wh he excepon of Bank 1 whch corresponds o an nsuon ha was closng s cred card busness a he me of analyss. I s nerpreed ha he rsk borne by he sysem s mosly explaned by ndvdual borrower behavour no maer n whch bank he clen s locaed, meanng ha here s no sgnfcan nfluence of dosyncrac facors such as beer collecon pracces from banks ha mgh mgae he rsk of he cred card porfolo. I s mporan o underlne ha he absence of explanaory power of bank varables does no mply ha here s a smlar level of exposure across hem, bu ha correspondng PD of each bank s dependen on he same facors of paymen behavour of he clenele. Ths means ha f he PD s FSI Award 21 Wnnng Paper 21

28 dfferen among hem s mosly explaned by he fac ha he clenele behavour reflecs more rsk. Ths would mply ha he exposure s more dependen on exogenous raher han endogenous facors or bank-conrolled facors) whch would n he end resul n a hgher vulnerably of he sysem o a common rsk exposure. In order o es furher hs hypohess, PD models were bul for each parcpang bank usng he correspondng daabases. As expeced, all he seleced varables of he model were sgnfcan for all banks and concden wh sysem-wde esmaes of PD. 22 FSI Award 21 Wnnng Paper

29 Table 8 Indvdual bank PD model esmaes Inercep Curren Non- Paymen Hsorcal Non- Paymen Percenage of paymen Cred Lm Use Maury ROC Bank ***.47***.596*** 1.324*** 1.14***.17***.848 Bank ***.677***.522***.646*** 1.583***.8***.834 Bank ***.59***.428***.625*** 1.14***.5***.796 Bank 4.98***.711***.45***.743***.725***.43***.796 Bank ***.553***.499*** 1.339*** 1.676***.76***.841 Bank ***.63***.536*** 1.84***.761***.11***.844 Bank ***.643***.563***.829*** 1.864***.4***.877 Bank ***.515***.529*** 1.4*** 1.85***.7***.844 Bank ***.57***.629***.565***.856***.6***.855 Bank ***.597***.351***.273***.764***.48***.767 Noe: Sgnfcance level ***.1, **.1, *.5. FSI Award 21 Wnnng Paper 23

30 ) Tme or procyclcal dmenson On he oher hand, as menoned before, he procyclcal dmenson of sysemc rsk relaes o how aggregae rsk evolves over me and s dependency on he economc cycle. Even hough he me seres used for he exercse was for a lmed par of he cycle, covers a relevan par of. Bllons 1,2 1, Graph 3 Compound annual growh rae CAGR) of bank porfolos Commercal CGAR = 8.19% Consumer CGAR = 29.46% Morgage CGAR = 2.48% - Mar-4 Mar-5 Mar-6 Mar-7 Mar-8 Mar-9 24 FSI Award 21 Wnnng Paper

31 Graph 4 Consumer cred pas due loan rao Delnquency Index Pas Due Loans / Toal Balance ) of consumer loans porfolo 13% 12% 11% 1% 9% 8% 7% 6% 5% 4% 3.2% 3% 2% 2.6% 1% % 1.3% Dec-4 Dec-5 Dec-6 Dec-7 Dec-8 Dec-9 8.8% 4.9% 4.5% Cred Cards Consumer Cred Oher** Graphs 3 and 4 llusrae he srong perod of growh of consumer cred porfolos durng he perod under revew whch was mached o an ncreasng deeroraon rae of he cred card porfolo. The effec of hgher levels of leverage across households resuled n deerorang cred qualy, no only for newly orgnaed loans, whch showed less experence n handlng cred, bu also for cusomers ha were already n he porfolo and ncreased her ndebedness by conracng new cred cards offered by compeors. FSI Award 21 Wnnng Paper 25

32 Graph 5 Household ndebedness Creds per Person by Cred Type D E F M A M J J A S O N D E F M A M J 27 J A S O N 1. Bank cred cards lef axs) Morgage rgh axs) Car rgh axs) 9, MXN pesos Monhly Average Deb-Capacy per Debor Sample) 8, 7, 6, 5, 4, 3, 2, 1, Number of Cred Cards Dec. 25 Nov FSI Award 21 Wnnng Paper

33 In order o es he me dmenson exposure o sysemc rsk and consderng he relave me seres lmaons of daa, wo me seres of daa were bul and added o he panel daa sample ha refleced dfferen aspecs of he economc cycle. On he one hand, he ncrease of compeon ha was approxmaed by he number of nsuons operang n he sysem. On he oher hand he relave experence of he sysem n managng deb, measured by he average age of borrowers exraced from he cred bureau daabase. Graph 6 Number of nsuons offerng cred card loans 18 Number of Insuons 2% 17 18% % 14% Defaul rae 14 12% 13 1% Number of Insuons Defaul rae FSI Award 21 Wnnng Paper 27

34 Graph 7 Average number of monhs of he populaon n each me observaon n he panel daa sample 15 Maury Cred Bureau 2% 1 18% % 14% 85 12% 8 1% Defaul rae Maury Bureau Defaul rae The hypohess of procyclcal behavour s esed by esmang he sgnfcance of hese varables n explanng sysemc PD. Table 9 Average age of populaon n he cred bureau Explanaory varables Coeffcen Inercep.874** X1 Curren non-paymen.682*** X2 Hsorcal non-paymen.495*** X3 Percenage of paymen 1.8*** X4 Cred lm use.951*** X5 Maury.1*** Maury bureau.37*** Noe: Sgnfcance level ***.1, **.1, * FSI Award 21 Wnnng Paper

35 Table 1 Number of nsuons offerng cred card loans Explanaory varables Coeffcen Inercep 3.76*** X1 Curren non-paymen.685*** X2 Hsorcal non-paymen.492*** X3 Percenage of paymen 1.11*** X4 Cred lm use.936*** X5 Maury.11*** Number of nsuons.82*** Noe: Sgnfcance level ***.1, **.1, *.5. Tables 9 and 1 provde evdence of sgnfcan correlaon of hese varables wh sysemc PD showng dependence on varables ha reflec relevan aspecs of he cycle. Even hough evdence s no conclusve as only one par of he cycle s consdered for analyss, hs lne of nvesgaon offers room for furher work as he denfcaon of sgnfcan varables may shed fuure lgh on early warnng mechansms of rsk buld-up n he sysem. 5.3 Bank IRB model comparson o sysem-wde model esmaes The analyzed counry has mplemened he Basel II capal framework, allowng banks o use IRB models o esmae capal requremens. Banks ha op o follow hs approach have o documen her model and are subjec o approval for use. An nernal model developed by a bank ha parcpaes n cred card busness has been subjec o he approval process FSI Award 21 Wnnng Paper 29

36 durng he perod of analyss. Emprcal esmaes of ndvdual PDs are obaned from he bank s model and hese can be conrased o sysem-wde models of PD esmaes for he same group of borrowers. The objecve of he comparson s o analyze wheher IRB model esmaes consder rsk facors ha showed o be relevan n he sysem-wde esmaon of PD and herefore shed lgh on he adequacy of he IRB model. Graph 8 IRB model PD esmaes as compared o PD esmaes usng he sysem-wde model IRB 5.% 4.5% 4.% 3.5% 3.% 2.5% 2.% 1.5% 1.%.5%.%.% 1.% 2.% 3.% 4.% 5.% Sysem wde PD Model PD esmaes from he IRB model proposed by he bank show a endency o esmae lower PDs han sysem-wde model esmaes. Addonally, a paern of lnear esmaons s observed for he IRB model ha mgh reveal less sensvy o relevan rsk facors. In order o analyze hese dscrepances, a sample of loans ha shows a consan bank IRB model PD.76%) s colleced from he daabase and furher compared. 3 FSI Award 21 Wnnng Paper

37 The comparson hs me uses wo relevan varables ha dfferenae rsk across clens, e clen ndebedness and paymen behavour. Graph 9 Bank s IRB esmaes and sysem-wde model of PD esmaes for dfferen ndebedness levels 14% 12% 1% PD 8% 6% 4% 2% % % 2% 4% 6% 8% 1% PD_Sysem_Model PD_IRB %Indebness Level FSI Award 21 Wnnng Paper 31

38 Graph 1 Bank s IRB esmaes and sysemc PD esmaes for dfferen paymen behavour characerscs PD 14% 12% 1% 8% 6% 4% 2% % % 2% 4% 6% 8% 1% PD_Sysem_Model PD_IRB Paymen Behavor The bank IRB model shows null sensvy o ndvdual borrower ndebedness and paymen behavour characerscs and hence provdes mporan evdence for he regulaor o furher analyze he srucure of he model durng he auhorzaon process of he IRB model for he correspondng bank. 5.4 Rsk reurn analyss of he cred card porfolo Sysem-wde PD, LGD, and EAD models were used o calculae expeced losses for he en parcpang banks. Smlarly, neres raes charged o clens ha were par of he panel daa sample exraced from he sysem were aggregaed for he same banks o map n a rsk-reurn axs he profably of her producs. 32 FSI Award 21 Wnnng Paper

39 Graph 11 Rsk reurn map of cred card porfolo 6% Preco excesvo 5% 4 1 Spread over nerbank rae 4% 3% 2% % % % 1% 2% 3% 4% 5% 6% Expeced Loss Graph 11 shows ha an adequae rsk-reurn orderng across banks exsed n he marke snce hgher expeced losses were assocaed wh hgher neres raes. In order o learn he sraeges ha led o hs orderng, he populaon of banks was dvded no hee groups accordng o her marke sraeges as measured by he profle of her clens. The hree groups denfed were: ) banks ha opened access o new cusomers; ) banks ha ganed marke share by offerng cheaper producs o clens served by oher banks; and ) banks ha remaned servng a sable populaon of borrowers. FSI Award 21 Wnnng Paper 33

40 Graph 12 Bank sraeges as llusraed by borrowers age n he sysem and n he bank Banks n he frs group Banks 4, 1 and 5) end o be characerzed by a younger cred bureau average age populaon, hgher expeced losses and hgher neres raes. Banks n he second group Banks 1, 2, 3, 6 and 8) are characerzed by a populaon of borrowers ha s no new o he sysem e a longer lfe n he cred bureau) bu presen recen experence nsde he nsuon and lower neres raes. Fnally he hrd group Bank 7 and 9) s from banks ha serve a populaon of clens wh longer experence boh n he sysem and n he bank. Ineres raes were hgher and expeced losses lower. Rank orderng across banks n erms of rsk s an mporan feaure for he sysem. However, s equally mporan for he sysem o observe rsk prcng sraeges whn he nsuons 34 FSI Award 21 Wnnng Paper

41 ha consder ndvdual borrower s rsk and hence ransm adequae neres raes o clens. In order o es he hypohess of rsk prcng dfferenaon, ndvdual clen PD esmaes were assocaed wh correspondng neres raes charged. Graph 13 Ex ane PD esmaes and neres raes Non Defauled* Defauled* Ineres rae Spread) 1% 4.% % of Cred Cards 8% 6% 4% 2% % [%-5%) [5%-1%) [1%-2%) [2%-3%) [3%-4%) [4%-5%) [5%-1%] Ex ane probably of defaul 32.5% 25.% Spread over nerbank rae A.1 ncrease n he PD parameer s refleced on average on an ncrease n he spread over he nerbank rae of 16.6 bass pons. Even hough he sysem conssenly shows approprae prce dfferenaon eg hgher ex ane PDs show hgher neres raes) when he es s repeaed for ndvdual banks, hs concluson does no always sand rue. FSI Award 21 Wnnng Paper 35

42 Table 11 Rae sensvy o PD Slope of neres rae Spread) Bank Bank Bank 3.1 Bank Bank 5.11 Bank 6.45 Bank 7.1 Bank 8.41 Bank Bank 1.53 Prce dfferenaon can be furher analyzed accordng o he facors ha have a larger nfluence on rsk. As documened n secon 4, he varable ha reflecs he paymen made by he ndvdual as a proporon of he ousandng balance shows approprae rsk dfferenaon; however, no sgnfcan dfference n neres rae s observed. 36 FSI Award 21 Wnnng Paper

43 Graph 14 Rsk prce dfferenaon across he sysem accordng o clen s percenage of paymen Non defauled* Defauled* Ineres rae Spread) 1% 52% % of Cred Cards 8% 6% 4% 2% % [%-1%) [1%-2%) [2%-4%) [4%-6%) [6%-8%) [8%-1%] >1% 36% 2% Spread over nerbank rae Percenage of Paymen Smlarly he degree of ndebedness of he borrower was shown o be a relevan rsk facor; alhough no sgnfcan dfference n cred card neres rae s observed. Graph 15 Clen ndebedness rsk prce dfferenaon across he sysem Non Defauled* Defauled* Ineres rae Spread) 1% 52.% % of Cred Cards 8% 6% 4% 2% % [%-1%) [1%-2%) [2%-4%) [4%-6%) [6%-8%) [8%-1%] >1% 36.% 2.% Spread over nerbank rae Cred Lm Use FSI Award 21 Wnnng Paper 37

44 The nroducon of reserve requremens ha reflec drec exposure o sysem-wde varables s expeced o generae regulaory ncenves for banks o sar rsk prcng sraeges among nsuons ha wll promoe more compeon n he sysem. The analyss presened resuled n benefs o he regulaor snce generaed relevan dscussons wh banks on prcng sraeges, rsk managemen capaces and broader opcs relaed o compeveness n he cred card busness. 5.5 Dfferences n pon-n-me PIT) models and hrough-he-cycle TTC) esmaons Models for PD esmaon can be calculaed wh nformaon from one perod one 25-monh wndow of me) as pon-nme PIT) esmaes or, n lne wh he Revsed Framework, hrough-he-cycle TTC) by consderng nformaon from a longer perod. TTC sysems are expeced o esmae more sable PDs over he cycle. In order o es he dfferences n PIT and TTC models for he porfolo analyzed, wo addonal models were esmaed by usng separae daa from wo dfferen reference daes Aprl 26 and February 27). 38 FSI Award 21 Wnnng Paper

45 Table 12 PIT and TTC model esmaes Model esmaon usng only nformaon from Aprl 26 Explanaory varables Coeffcen Wald Confdence Level 95%) Inercep 3.386** Curren non-paymen.682** Hsorcal non-paymen.541** Percenage of paymen.245* Cred lm use 1.277** Maury.9**.12.6 Model esmaon usng only nformaon from February 27 Explanaory varables Coeffcen Wald Confdence Level 95%) Inercep 2.395** Curren non-paymen.797** Hsorcal non-paymen.487** Percenage of paymen.724** Cred lm use 1.94** Maury.14** Noe: Sgnfcance level ***.1, **.1, *.5 performed wh Wald Tes). FSI Award 21 Wnnng Paper 39

46 Table 12 con) PIT and TTC model esmaes Model esmaon usng all wndows proposed model) Explanaory varables Coeffcen Wald Confdence Level 95%) Inercep 2.97** Curren non-paymen.673** Hsorcal non-paymen.469** Percenage of paymen 1.22** Cred lm use 1.151** Maury.7**.8.7 Noe: Sgnfcance level ***.1, **.1, *.5 performed wh Wald Tes). Evdence from he esmaons of PIT and TTC models suggess ha no only explanaory varables are he same across banks as suggesed n secon 5.2, bu hey also concde n dfferen segmens of he analyzed cycle. Coeffcens for he varables ncluded n he TTC model are sgnfcan for he PIT models and do no dffer sgnfcanly among hem. The nercep parameer shows a sgnfcan dfference across he cycle, whch suggess ha he PD level changed over me whle s srucure remaned he same. PD esmaes were obaned for each of he hree models and hen compared o acual defaul frequences. 4 FSI Award 21 Wnnng Paper

47 Graph 16 Aprl 26 pon n me PD esmaon 2.% 18.% 16.% 14.% 12.% 1.% 8.% 6.% Defaul Rae PD_264 Graph 17 March 27 pon n me PD esmaon 2.% 18.% 16.% 14.% 12.% 1.% 8.% 6.% Defaul Rae PD_272 FSI Award 21 Wnnng Paper 41

48 Graph 18 TTC PD esmaon 2.% 18.% 16.% 14.% 12.% 1.% 8.% 6.% Defaul Rae PD_Model The evdence suggess ha PDs are underesmaed when models are bul on he lower par of he cycle, whle he oppose s rue when s done on he hghes par of he cycle. I s acknowledged here ha he comparson of PD forecass s no oally conclusve as he TTC model s used o forecas he frequences of defaul used for s own esmaon. However, he evdence shown from PIT esmaes usng conrasng daa ses allows he concluson ha TTC esmaes are beer sued o provde more sable forecass of PD and are less dependen on he economc cycle. 6. Conclusons The dagnoss of sysemc rsk exposure has never been more mporan n he nernaonal regulaory agenda o proec fnancal sysems from desablzng evens. There exss oday mporan effors o address hs rsk and he presen documen nends o add o hs lne of work. 42 FSI Award 21 Wnnng Paper

49 Regulaory auhores are prvleged n erms of sysem-wde oversgh and are n a srong poson o develop he capaces o measure and dagnose sysemc rsk exposure. Ths paper proposes o esmae a mcroprudenal ool PD, LGD, and EAD) wh sysem-wde nformaon and s shown o offer relevan nformaon on sysemc rsk exposure and hence serves a macroprudenal purpose. I was concluded ha he rsk borne by he sysem s mosly explaned by ndvdual borrower behavour no maer n whch bank he clen s locaed. Ths means ha here s no sgnfcan nfluence of dosyncrac facors, such as beer collecon pracces from banks, ha mgh mgae he rsk of he cred card porfolo. Thus, s observed ha he sysem s exposed o a common rsk exposure. Even hough evdence s no conclusve as only one par of he cycle s consdered for he analyss, sgnfcan cycle varables were shown o nfluence he behavour of PD hrough me, whch may shed fuure lgh on early warnng mechansms of rsk buld-up n he sysem. The analyss presened resuled n a benef o he regulaor snce generaed sysem-wde parameers ha allowed he regulaor no only o equp he sysem wh more reserves o susan expeced losses, bu also o esablsh a homogeneous regme across banks ha covers a fxed me perod of expeced losses. Smlarly, resuls generaed relevan dscussons wh banks on prcng sraeges, rsk managemen capaces and broader opcs relaed o compeveness n he cred card busness. Ths approach s currenly beng promoed for oher real porfolos and wll be exended o commercal loan porfolos. Furher lnes of research are he developmen of ools ha explcly lnk macroeconomc and fnancal facors o rsk parameers, quanfyng he ner-lnkages among nsuons and he margnal conrbuon of sysemc rsk by ndvdual banks. FSI Award 21 Wnnng Paper 43

50 Annex 1: Explanaory varables The unverse of varables analyzed for he selecon of explanaory rsk facors for he PD fnal model s descrbed here. The npus o buld he varables are: PT, ) amoun of paymens made on me by he cardholder durng he perod ) o he cred card ) PA, ) amoun of addonal paymens made by he cardholder ) durng he perod ) o he cred card ) SP, ) s he oal ousandng balance of he cred card ) n perod ) PTO, ) oal amoun of paymens on me + addonal) made by he cardholder durng he perod ) o he cred card ) PM, ) s he mnmum paymen requred as a percenage of he balance due for he cred card ) n perod ) TI, ) s he annual neres rae for he cred card ) n perod ) LC, ) s he cred lm or cred lne approved n perod ) of he cred card ) 44 FSI Award 21 Wnnng Paper

51 Accoun Performance PGE_PAY_T: Percenage of paymen Paymens made by he cardholder as a proporon of he ousandng balance of he cred card a he reference pon. PT,) + PA,) SP,) PGE_PAY_3M Average of he percenages represenng he paymen of he ousandng balance for he las hree monhs also bul for 6, 9 and 12). = = 2 PT = = 2, ) SP + PA, ), ) FSI Award 21 Wnnng Paper 45

52 PGE_TOTALPAY_3M Percenage of perods n whch he borrower has pad all or more) of her balance whn he las hree monhs also bul for 6, 9 and 12). = = 2 SI PA, ) + PT, ) SP, ) ) 3 NUM_INC_PAY Number of ncreases n he percenage of paymen over he pas 12 monhs. PT, ) PT, 1) 11 1 ) = = IF > = SP, ) SP, PGE_MINAMOUNT_T Mnmum paymen requred as a percenage of he ousandng balance a me of reference. PM SP,),) 46 FSI Award 21 Wnnng Paper

53 AVRGE_ MINAMOUNT_3M Average of he mnmum paymen requred as a percenage of he balance of he las hree monhs also bul for 6, 9 and 12). = = = 2 = 2 PM, ) 3 SP, ) 3 NUM_INC_MINAMOUNT Number of ncreases n he mnmum paymen as a percenage of he balance) durng he pas 12 monhs. = PM,) PM, 1) IF > = 11 SP,) SP, 1 ) FSI Award 21 Wnnng Paper 47

54 NUM_DEC_MINAMOUNT Number of decreases n he mnmum paymen as a percenage of he balance) durng he pas 12 monhs. = = IF < = SP, ) SP, PM, ) PM 11 1 ), 1) SUM_NONPAY_3M Number of perods n whch he cardholder has no covered he mnmum paymen n he las hree monhs. = = 2 IF PT, ) + PA, ) < PM, ) ) MAX_NONPAY_3 Maxmum number of consecuve perods n whch he borrower has no pad he mnmum conracual paymen oblgaon n he las hree monhs. PT, ) + PA = = IF = 2 PT, 1) + PA, 1) < PM, ), ) < PM, ) y 1 48 FSI Award 21 Wnnng Paper

55 NONPAY_SA: Curren Non- Paymen ACT) Number of consecuve perods, up o he reference pon, n whch he cardholder has no pad s mnmum conracual paymen oblgaon. PT ) + PA = = IF = 11 PT 1) + PA 1) < PM ) ) < PM ) y 1 NONPAY_HIS: Hsorcal Non- Paymen HIS) Number of perods n whch he cardholder has no covered he mnmum paymen n he las sx monhs. = = 5 IF PT, ) + PA, ) < PM, ) ) NONPAY_HIS_12 Number of perods n whch he cardholder has no covered he mnmum paymen n he las 12 monhs. = = 11 IF PT, ) + PA, ) < PM, ) ),,,,,, FSI Award 21 Wnnng Paper 49

56 INC_NONPAY_12M Maxmum number of consecuve perods n whch he borrower dd no make he mnmum paymen requred on he las 12 monhs. = = 11 IF NONPAY _ SA _ T > NONPAY _ SA _ T 1 ) PER_MORE1MIN_12M Number of perods n whch he borrower has accumulaed over a perod whou makng he mnmum paymen n he las 12 monhs. = = IF = 11 PT 1) + PA 1) < PM ) PT ) + PA ) < PM ) y 1,,,,,, 5 FSI Award 21 Wnnng Paper

57 TIMES2NONPAY Number of mes ha he borrower dd no make he mnmum paymen on wo consecuve perods n he pas 12 monhs. = PT,) + PA,) < PM,)and IF PT, 1) + PA, 1) < PM, 1) and = 11 PT, 2) + PA, 2) < PM, 2) USE_LINE_T: Cred Lm Use Toal ousandng balance as a proporon of he cred lm a he reference pon. SP LC,, ) ) FSI Award 21 Wnnng Paper 51

58 AVRGE_USELINE_3M Average of he Cred Lm Use durng he las hree monhs also bul for 6, 9 and 12 monhs). = = = 2 = 2 SP, ) 3 LC, ) 3 MAX_USELINE_3M Maxmum Cred Lm Use n he las hree monhs also bul for 6, 9 and 12 monhs). max = SP, ) LC, ) = 2 52 FSI Award 21 Wnnng Paper

59 MAXINC_LIMIT Maxmum ncrease n he cred lm durng he las 12 monhs expressed as a percenage of he cred lm n he reference dae. max SP LC, ).) = = 11 ) PGE_OVERLIMIT_3M Percenage of perods n whch he borrower over-lm whn he las hree monhs also bul for 6, 9 and 12 monhs). = = 2 IF SP, 3 ) > LC, )) FSI Award 21 Wnnng Paper 53

60 PGE_ACTMAX_3M Percenage ha represens he balance on he reference dae from he maxmum balance due n he las hree monhs. SP, = max SP, ) ) = = 2 NUM_MAXBALANCE_6M Number of mes ha he balance was equal o he cred lm n he las sx monhs. = = 5 IF SP, ) = LC, )) 54 FSI Award 21 Wnnng Paper

61 PGE_ENDEBT_6M Percenage ha represens he balance on he dae of reference agans he average balance of he las sx monhs. SP = = 1 6, SP 6 =, ) ) PJE_ENDEU_1TRIM Percenage ha represens he balance on he las rmeser agans he average balance of he second rmeser. = = = = SP, ) 3 SP, ) 3 FSI Award 21 Wnnng Paper 55

62 INC_CONSEC_3M Number of consecuve ncreases n he balance durng he las hree monhs. = = 2 IF LC, ) > LC, 1)) DEC_CONSEC_3M Number of consecuve decreases n he balance durng he las hree monhs. = = 2 IF LC, ) < LC, 1)) INACUM_T Number of cumulave ncreases n he balance over he pas 12 monhs. = = 11 LC, ) > LC, 1) 56 FSI Award 21 Wnnng Paper

63 DECACUM_T Number of cumulave decreases n he balance durng he pas 12 monhs. = = 11 LC, ) < LC, 1) TEOMAT_T Theorecal erm monhs) n whch he borrower would cover he oal deb accordng o he mnmum paymen and he neres rae. ln PM,) ln 1 + PM TI,),) 12 TI,) 12 * SP,) FSI Award 21 Wnnng Paper 57

64 TEOMATPT_T Theorecal erm monhs) n whch he borrower would cover he oal deb accordng o he acual paymen made by he borrower and he neres rae. ln PT,) ln 1 + PT TI,),) 12 TI,) 12 * SP,) 58 FSI Award 21 Wnnng Paper

65 Cred Bureau Informaon AGE_T: MATURITY Number of monhs elapsed snce he openng of he cred card n he bank. T CC Open Dae ACCTS_MTG_T_SUM Number of morgages or fxed paymens ype cred ha he borrower had a he reference pon. Opened before he reference dae and no closed before he reference pon.) = = 12 H, ) FSI Award 21 Wnnng Paper 59

66 ACCTS_REV_T_SUM Number of revolvng accouns ha he borrower had a he reference pon. Opened before he reference dae and no closed before he reference pon.) = = 12 R, ) ACCTS_TOT_T_SUM Number of accouns ha he borrower had a he reference pon. Opened before he reference dae and no closed before he reference pon.) = = 12 H, ) + R, ) MTG_T_SUM Number of morgages a he reference pon. = = H, ) 6 FSI Award 21 Wnnng Paper

67 OPENED_MTG_HIST_SUM Number of morgages or fxed-paymen ype creds opened durng he perod of 12 monhs before he reference pon. = = 12 AH, ) OPENED_REV_HIST_SUM Number of revolvng accouns opened durng he perod of 12 monhs before he reference pon. = = 12 AR, ) OPENED_TOT_HIST_SUM Number of accouns opened durng he perod of 12 monhs before he reference pon. = = 12 AH, ) + AR, ) FSI Award 21 Wnnng Paper 61

68 CLOSED_MORT_HIST_SUM Number of morgages or fxed-paymen ype creds closed durng he perod of 12 monhs before he reference pon. = = 12 CH, ) CLOSED_REV_TOT_ACC Number of revolvng accouns closed durng he perod of 12 monhs before he reference pon. = = 12 CR, ) CLOSED_TOT_ACC_HIST Number of accouns closed durng he perod of 12 monhs before he reference pon. = = 12 CH, ) + CR, ) 62 FSI Award 21 Wnnng Paper

69 AGE_BUREAU_T Number of monhs elapsed snce he borrower opened hs/her frs cred n he fnancal sysem o he reference pon. Monhs snce he frs appearance n he Cred Bureau. T Dae of frs cred a CB PAST_DUE_HIST Indcaes f an accoun was pas due durng he perod of 12 monhs before he reference pon. SI PT, ) + PA, ) < PM, ),1,) FSI Award 21 Wnnng Paper 63

70 Employmen Behavour INCOME_LVL_T Income level a he dae of reference. SM = ) AVG_INCOME_6M Income average on he las sx monhs.. = = 5 SM 6, ) DAYS_PER_T Number of days ha he borrower worked n he las womonh perod snce he reference pon. DC = ) 64 FSI Award 21 Wnnng Paper

71 AVG_DAYS_6M Average over he las sx monhs of he number of days he borrower worked n a wo-monh perod. = = 5 DC 6, ) FSI Award 21 Wnnng Paper 65

72 Annex 2: Reserve requremen rule As of Sepember 29, all banks n he analyzed counry have o apply he formulas presened n he paper n order o esmae he amoun of reserves requred for her cred card porfolo. Insuons calculae provsons of he cred card porfolo, loan by loan, wh he nformaon correspondng o he las paymen perod known a he end of he monh. The oal amoun of reserves s he sum of he reserves of each cred, obaned as follows: R = PD LGD EAD Where: R PD = Amoun of reserves of he h cred. = Probably of defaul of he h cred. LGD = Loss gven defaul of he h cred EAD = Exposure a defaul of he h cred. Probably of Defaul If ACT < 4 hen PD = 1 [ ACT HIS.75MAT 1.217% PAY % USE 1+ e ] Else f ACT >= 4 hen PD = 1% 66 FSI Award 21 Wnnng Paper