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estimated with PD, LGD, and EAD parameters calibrated withthe same characteristics (eg 12 months of losses) as thoseproposed in the Revised Framework. For the case of thecountry analyzed, it is shown that reserves built by the systemat the time of analysis accounted for approximately half of theestimated expected losses under these criteria and were lessrisk-sensitive. To address this issue a specific reserverequirement based on system-wide estimates of PD, LGD, andEAD was introduced.It is also shown that the use of system-wide parametersrepresents a useful benchmarking tool for the validation ofIRB models. IRB model estimations of PD calculated by abank seeking model approval are compared to system-wideestimations of PD. A detailed set of conclusions is drawn onthe IRB model proposal and its capacity to considersystem-wide explanatory variables of PD.An additional application is to measure the relevance of usingeither point-in-time (PIT) model estimates as opposed tothrough-the-cycle (TTC) models. The analysis of the structureof the model through time indicates the dependency of theaggregate risk of the system to a common set of explanatoryvariables and provides valuable insight in terms of systemvulnerabilities. By using both types of models, it is also shownhow system-wide PIT estimations of PD consistentlyunderestimate and overestimate the observed default rateswhen PIT models are estimated in respectively lower andhigher risk segments of the economic cycle.Finally, a set of conclusions is drawn from individual bank riskpricing practices, as interest rate charging policies canindividually be compared to expected loss estimations; thusallowing for risk-return analyses both across banks and withinbank portfolios. For the case of the credit card portfolio of thecountry analyzed, it is concluded that there exists clear pricedifferentiation across banks, generally associated with the riskprofile of the population, while it is not the case that pricingpractices of all institutions differentiate risk across their ownclientele.FSI Award – 2010 Winning Paper5

3.System-wide information and PD, LGD andEAD modelsModels of PD, LGD, and EAD are estimated by banks withinformation that reflects payment experience within the bank.These parameters tend to describe individual bank experienceand often show different explanatory factors when comparedto other banks’ models.In order to convey a system-wide dimension to parametersand identify if there exists common risk factors across banks,three sources of information were collected:1.Individual credit card statements that describe loan-leveldata information related to outstanding balance, interestrate, actual payments, minimum required payment, anddate of payment. This information is designed todescribe the payment behaviour of borrowers, identifyrecovery in subsequent periods after default and allowthe identification of the exposure at the time of default.2.Credit bureau information that consists of individualcredit records, including information such as the numberof loans the borrower had with other banks in theanalyzed period, its performance and the time elapsedsince the borrower first received a loan in the system.3.Social housing institute information which collectspayroll deductions from workers and describesborrowers’ employment history and current incomelevel.The ten largest institutions, accounting for 97% of total creditcards in the system, were selected to participate in theexercise. A random panel data sample of the system wasdesigned considering two dimensions:(i)Point-in-time dimensionThe information was structured to span a 25-month intervaldivided into two 12-month intervals and a reference point. Thefirst 12-month interval (historical period) gives information6FSI Award – 2010 Winning Paper

about the borrower’s behaviour, based on the three sources ofinformation mentioned above, for the twelve months precedingthe reference point. The twelve months after the referencepoint (performance period) are designed to identify individualdefault rates. This structure allows the association of borrowercharacteristics and default.(ii)Time series dimensionTo gain insight into the stability of the model through arelevant part of the cycle, 12 windows of 25 months ofinformation were extracted. The 12 reference points selectedfor each window were April 2006 to March 2007 spanning athree year period of time starting in April 2005 and ending inMarch 2008.Random samples were taken from the universe of loansavailable in the system as registered in the credit bureau foreach of the 12 reference points and the size of the samplewas determined to allow an estimation error of a PDparameter of 40 basis points with a 99% confidence.7Default is defined based on the definition of Basel II whichstates that a loan has defaulted if either one or both of thefollowing events have taken place: (1) the bank considers thatthe obligor is unlikely to pay its credit obligations to thebanking group in full, without recourse by the bank to actionssuch as realizing security (if held); and (2) the obligor is pastdue more than 90 days on any material credit obligation to thebanking group.7The formula used to determine the simple size of the credit card portfoliois: n N z 2 / 2 P (1 P )(N 1)e 2 z 2 / 2P (1 P )FSI Award – 2010 Winning Paper.7

PD modelCategorical data techniques such as logistic regression haveincreasingly been used in models of prediction of default andthis approach is proposed for the estimation of the model ofsystem-wide PD.8Let x i' be a vector of p independent variables, yi denotes thevalue of a dichotomous outcome variable, and i 1,2,3, ,N.Furthermore, assume that the outcome variable has beencoded as 0 or 1, representing the absence or the presence ofdefault, respectively. To fit the logistic regression modelrequires the estimation of the vector ' ( 0 , 1, . , p ) .Let the conditional probability that the outcome is present bedenoted by P (Y 1 X ' ) ( x ' ) . The logit of the multiplelogistic regression model is given by the equationg ( x ' ) 0 1x1 2 x 2 . p x p , in which case the logistic'regression model is ( x ) eg(x )''1 eg(x ). LGD modelLGD is the credit loss incurred if an obligor defaults and isdependent on the characteristics of the loan. Losses areinfluenced by the presence of collateral and when no collateralexists the cash flows that the borrower pays after defaultdetermine the LGD of the loan.The model proposed to estimate LGD for the credit cardportfolio analyzed is to account for the cash flows that occurthree months after default and compare them to the maximumoutstanding balance of the loan after the moment of default.88Hosmer and Lemeshow (1995).FSI Award – 2010 Winning Paper

The maximum outstanding balance is used in order toconsider the revolving nature of credit card loans, and hencethe possibility of balance increases due to line dispositions inthe period of default. Following this definition, LGD can beexpressed as:t3 Borrower PaymentsiLGD 1 i t defaultMAX Bal t default , Bal t default 1 , Bal t default 2 , Bal t default 3 Where Bal i is the outstanding balance of the credit card attime “i” and tdefault is the time of default of the loan.EAD modelEAD estimates the percentage of exposure the bank mightlose if the borrower defaults. The estimation of EAD becomeshighly relevant in revolving instruments such as credit cardsand hence it is necessary to include an estimation of the valueof the exposure that the borrower will have at the time ofdefault in order to obtain an appropriate estimate of theexpected loss. Commonly used methods of estimation for thisparameter9 are focused in metrics that associate theincrements in the balance between a specific date of referenceand the time of default. The model proposed in this documentconsists of estimating an exposure at default factor thatreflects the multiple of the outstanding balance at the momentof default to the outstanding balance at the reference point(EAD factor).Considering that the credit limit use at the reference point dateis a candidate to explain significant differences in the EADfactor, a simple statistical association between both variablesis proposed as follows:9Engelmann and Rauhmeier (2006).FSI Award – 2010 Winning Paper9

EAD factor f (balance at reference point date / credit limit atreference point date)Where,EAD factor balance at default / balance at reference pointdate.4.Empirical resultsPD modelThe independent variables used to build the PD model wereconstructed from the data set mentioned before and wereselected according to their explanatory power. For anexhaustive list of variables analyzed see Annex 1.The PD model contains the following five variables:1.X1: number of consecutive periods, up to the referencepoint, in which the cardholder has not paid its minimumcontractual payment obligation;2.X2: number of periods in which the cardholder has notcovered the minimum payment in the last 6 months.3.X3: payments made by the cardholder as a proportionof the outstanding balance of the credit card at thereference point;4.X4: total outstanding balance as a proportion of thecredit limit at the reference point; and5.X5: number of months elapsed since the issuance of thecredit card by the bank.10FSI Award – 2010 Winning Paper

Table 1System-wide PD explanatory variablesExplanatory variablesInterceptCoefficient–2.970***X1Current non-payment0.673***X2Historical non-payment0.469***X3Percentage of payment–1.022***X4Credit limit use–1.151***X5Maturity–0.007***Note: Significance level *** 0.001, ** 0.01, * 0.05 (performed with standardWald test).It is important to note that all relevant variables are associatedwith the characteristics of the borrower behaviour and creditcard use.LGD modelThe estimation of LGD considered all the credit cards thatdefaulted in the performance period and the reference point.Table 2 shows the average amount recovered by the banks inthe three-month period after default.FSI Award – 2010 Winning Paper11

Table 2Cash flow recovery of outstanding balance 3 monthsafter default as percentage of maximum outstandingbalance after default% of 1%0.7%80%–89%1%0.4%90%–99%1%0.5% 100%9%9.2%LGD81%The final LGD estimate for the systemic credit card portfoliois 81%.EAD modelThe association between the EAD factor and credit limit use isapparent, as illustrated in Graph 1.12FSI Award – 2010 Winning Paper

Graph 1EAD factor and credit limit use30Factor lanceT0/CreditLineEAD is therefore a function of the credit limit use of individualborrowers where low credit limit use is associated to high EADfactors. The resulting function is: Outstandin g Balance at reference point EAD factor Credit limit at reference point 0.5784Once the function is defined, adjustment factors are estimatedand summarized.FSI Award – 2010 Winning Paper13

Table 3EAD factors as a function of credit limit use% USECredit limituseFitted %–100%95%103%100%100% 100%1Mid–pointbThe curve was fitted by OLS by transforming the equation: y cx . Thesignificance level of the b parameter (t-test) is .0001.14FSI Award – 2010 Winning Paper

5.Model applications5.1Credit card portfolio reservesInternational accounting standard principles have for a longtime indicated that credit losses are to be recognized only ifthere is objective evidence of impairment as a result of a lossevent.10The applicable rule for the country analyzed in this documentestimates reserves as a function of the number of past duepayments owed by the borrower at the time of analysis.Table 4Credit card reserve requirement10Number of periods past due% Reserves00.5%110%245%365%475%580%685%790%895%9 or more100%IASB (2009).FSI Award – 2010 Winning Paper15

While the reserve methodology is easy to implement andreflects more reserves when there is more evidence of loandeterioration, as a prudential requirement, it shows thefollowing limitations:1.reserves are not calibrated to cover expected losses of12 months;2.all relevant available credit information is not consideredto differentiate risk among individual borrowers;3.loss estimations are not based on prospective analysis;4.the amount of reserves does not consider exposure atdefault adjustments.Total loan loss reserves were estimated using the requirementdescribed in Table 4 and contrasted to actual credit cardportfolio write-offs for the 12-month period following theestimation.16FSI Award – 2010 Winning Paper

Table 5Reserve requirement sufficiency measured in months12-month1write-offsReservesat start of12-month1period%Write-offs /ReservesMonths ofcoverageBank 12,5771,045246.51%4.9Bank 211,3975,198219.26%5.5Bank 36,6504,624143.83%8.3Bank 4629212296.69%4.0Bank 5397212187.36%6.4Bank 62,2061,401157.44%7.6Bank 74,0011,070373.86%3.2Bank 8534475112.39%10.7Bank 81.12%6.6Bank 10Credit CardSystemNote: In what follows Bank 1, 2, .,10 represent the same institution.1In millions.Table 5 shows that reserves were on average sufficient tocover 6.6 months of actual write-offs. The results also illustratethe heterogeneity that the regime generates across banks interms of the number of months that the allowance covers. Thislast fact may lead the regulator to consider banks that complywith the regime as equally equipped to cover losses even ifthere was significant variance among them.FSI Award – 2010 Winning Paper17

In order to test the exposure of the system, the loan lossdistribution of the analyzed portfolio was estimated by usingsystem-wide PD, LGD, and EAD and the IRB capital formulasset in the Revised Framework (Basel II).Graph 2Loan loss distribution and capitaland reserve requirementReserves9.31%FREQUEN CYExpected Loss18.42%Capital Requirement Reserves(Standard Approach)17.31%Capital Requirement Reserves(IRB approach)36.54%% Assets8% risk weigthed Assets18.12 % risk weigthed AssetsGraph 2 makes evident that the regime of reserves along withthe Basel I capital standard for the credit card loan portfolioanalyzed were insufficient to cover losses measured under theBasel II approach.System-wide models of PD, LGD, and EAD can be furtherused to estimate individual banks’ expected losses by feedingcorresponding client information on PD and EAD equations.This procedure results in estimates of individual banks’expected losses and capital estimations illustrated in Table 6.18FSI Award – 2010 Winning Paper

Table 6Individual banks’ capital and reserve m(Systemwide modelwide modelapproach inapproach)IRBformulas)%Reserves(Table k 18.45%8%17.63%17.65%Bank 212.17%8%17.57%17.82%Bank 315.84%8%30.21%23.90%Bank 421.95%8%75.48%10.52%Bank 58.58%8%23.87%19.06%Bank 69.66%8%19.11%19.08%Bank 78.73%8%14.52%16.85%Bank 810.06%8%16.62%17.93%Bank 98.10%8%13.70%13.79%Bank 1019.98%8%60.19%16.21%9.31%8%18.42%18.12%Credit CardSystemThe comparison of both regimes shows that the formerreserve and capital regime were also insufficient to coverexpected losses for each institution in the system.System-wide models of PD, LGD, and EAD were introduced inthe analyzed country as a minimum reserve requirement(Annex 2) to address these issues and set a homogeneoustime frame for loss coverage. These requirements allowed theFSI Award – 2010 Winning Paper19

regulator to equip the system with a homogeneous regime ofreserves fitted to sustain 12 months of expected losses andpromoted incentives for banks to develop their own IRBmodels and to actively manage the risk of their portfolios dueto the fact that the regulatory cost of individual loans is morerisk sensitive.5.2System-wide PD dependency on idiosyncratic andcyclical factorsThe credit card portfolio risk exposure of the analyzed countryappears to be subject to systemic risk. In order to test thehypothesis of the

winning FSI Award paper for 2010. This award, given every two years at the time of the International Conference of Banking Supervisors, was established to encourage thought and research on issues relevant to banking supervisors globally. In 2010, nine papers were received from central banks and supervisory authorities in eight countries.