CFP conference 2016 - London Challenges For Measuring Lifetime PDs On Retail Portfolios Vivien BRUNEL September 20 th, 2016 Disclaimer: this presentation reflects the opinions of the author and not the one of his employer. Neither Société Générale nor the author may be held responsible for the use which may be made of the information contained therein.
Setting modeling standards
MAIN PRINCIPLES IFRS 9 phase 2 Risk management based Build upon the existing frameworks (monitoring, regulatory, ) Accounting should not change the risk management and monitoring practices, but should improve them Manage the interplay between accounting, regulatory and risk management processes Simplicity Avoid black box effects Leverage business knowledge Avoid full automatic framework, preference for auditability and understanding of the provision variations Make sure that the framework will be displayed and will evolve conveniently Materiality, proportionality A reference method displayed on the most significant entities in terms of exposure or credit risk A simplified approach for less significant entity which data collection and qualification is not the same level Comparability / benchmarking with peers Working groups are now structured across boarders Audit firms are starting to settle their standards
PD MODELING The market standard has not emerged yet Risk indicator for the transfer criteria (score, risk class, 1Y or lifetime PD, current or past payments in arrear) Tolerence on the initial recognition date (granting vs. first behavioral score) Lifetime PD measurement (link with the regulatory framework and the stress testing framework) Open options Which quantification framework? Scores? Migrations? Observed defaults? Statistical method for estimation: cohort vs. duration Forward-looking calibration methodology: multiplicative factor, systemic factor, default rate econometrics IFRS9 PDs shall include Position in the economic cycle and forecasts Forecast horizon (3 to 5 Y) Beyond the forecast horizon: extrapolation from available data Historical default rate TD historique Foreseeable Projections future pertinentes Default rate Taux de Défaut TD Moyen PD PIT 1Y TD (t-1,t) t-1 t 1Y 2Y 3Y 4Y 5Y Time Temps
LOSS RATE MODELING Challenges Estimate a loss rate at contract level Include discounting Coherence of loss rates in stages 1 and 2 with those of stage 3 Coherence between the IFRS loss rate and the LGD Comparison with the regulatory requirements Margins of prudence Regulatory LGD IFRS 9 Data quality, downturn, volatility No specific margin of prudence Robustness required Recovery costs Included Not included Cycle effects Downturn current condition and supportable and reasonable forecast Discount rate Contract rate Contract rate
EXPOSURE MODELING What s new? Drawings over full lifetime for in bonis exposures (differs from the regulatory CCF) Real amortization profile, either contractual or behavioral, including prepayments Ideal target Balance sheet part Real amortization profile including prepayments How to include forward-looking? constant prepayment rate vs. factor (econometric) model Off-balance sheet part Drawings up to maturity / default Consistency with regulatory CCF regarding the last 12 months before default Difficult to embed forward-looking Alternative option Duration model
Possible approaches for PD measurement
PD MODELING - SCORECARDS Scorecards are used for many purposes (granting, risk management), but are not commonly used for loan loss provisions Depending on the purpose, scores are different: granting scores, behavioral scores, attrition scores Scorecards are built at segment level Scorecard models can capture all factors if properly calibrated (fit real risk factors at segment level) and segmented. The link between scores and PDs is not straightforward Macroeconomic information is rarely considered in scorecard modeling Segmentation in scorebands would require a tremendous amount of data Scores are not suited for PD measurement over than 1 year. Another approach is needed for a dynamic model on PDs
PD MODELING ROLL RATES Roll rates Measure the percentage of financial assets that roll from one stage of delinquency time (days past due or unpaid amount) to the next within a given period of time Example: Roll rate calculation Initial portfolio: 500 revolving products equally distributed between 5 stages (performing, ]0;30] days past due, ]30; 60], ]60;90], D) Observation period: one month Roll rate can be account-based or balance-based Macroeconomic conditions are difficult to embed in roll rate modeling The calibration is essentially backward looking Predictions are short term Initial stage \ Final stage In Bonis Bucket 1 ]0:30j] Bucket 2 ]30:60j] Bucket 3 ]60:90j] Default In Bonis 80% 20% 0% 0% 0% Bucket 1 ]0:30j] Bucket 2 ]30:60j] Bucket 3 ]60:90j] 10% 80% 10% 0% 0% 0% 10% 60% 30% 0% 0% 0% 5% 60% 35% Default 0% 0% 0% 0% 100%* How to read the table: - At date 0, 100 contracts are in bucket 2 ([30:60 days past due[) - 1 month later, those contracts have migrated: 60 contracts remain in bucket 2: migradon rate from bucket 2 to bucket 2 equals to 60/100 = 60% 10 contracts go to bucket 1: migradon rate from bucket 2 to bucket 1 equals to 10/100 = 10% 30 contracts go to bucket 1: migradon rate from bucket 2 to bucket 1 equals to 30/100 = 30% *Default is considered as an absorbing stage
PD MODELING MARKOV MATRIX MODELS Matrix models are dynamic models by definition Constructed at the segment or portfolio level; mimics the formalism usually implemented on wholesale clients Risk categories are difficult to build in a normalized / uniform framework across the bank (product / client specificities, local businesses) External risk categories (credit bureau scores such as FICO for instance) don t exist everywhere Each cell of the matrix represents the migration rate from a particular risk category to another one Same technical framework as for corporates: a 12-month forecast is determined by applying the distribution of oneyear historical loss rates to the current distribution of outstanding loans Calibration is based either on cohorts or durations Many studies emphasize the comparative advantage of calibrating matrices based on durations This formalism is quite heavy to implement and there is an assumption of time homogeneity and markovianity Non time homogenous matrices can be calibrated based on the Aalen-Johansen estimator but require a lot of data Forward-looking adjustment of the matrices is done by a one factor (or more) deformation of the TTC matrices
PD MODELING VINTAGE ANALYSIS Vintage analysis goal Based on vintage criteria, the loss performance of the segment is tracked over time. Default rates are decomposed Vintage quality Maturation Exogenous factor (macroeconomic?) Vintage analysis technique Annual loss rates are analyzed with exponential smoothing techniques Vintage models can account for management strategies and exogenous factors by optimally adjusting parameters within the exponential smoothing algorithm Vintage models can be further segmented to reflect more granular levels of risk such as delinquent/non-delinquent and bankrupt / non-bankrupt populations Vintage models can be non parametric
PD MODELING SURVIVAL ANALYSIS Survival analysis models such as Cox s hazard model is dynamic and less complex than matrix models Segmentation is the key element of the model. Based on a duration model, we calibrate directly the default rate for any horizon. Dynamic aspects are embedded into the PD term structure PIT forward-looking components can be accounted for through the inclusion of covariates Implementation details Covariates can be time dependant (economic factors) and vintage dependant (factors that enter the score) Calibration of the model should account for the treatment of the misspecification error Alternative implementation proposal Segments are based on risk and age on book classes and calibration is done of PD curves is done on each segment The only adjustment is done with economic covariates to make the provision PIT forward-looking For retail exposures, it is frequent that economic cycle effects are non significant
PD MODELING - SUMMARY Modeling approach Pros Cons Scorecards Roll rates Matrix Vintage Cox s hazard model Based on real risk/behavioural factors Use test Market standard Fits the retail credit business model Use test Same technical framework as the corporate framework Easy to estimate lifetime PDs Separate effects (vintage quality, maturation, exogeneous) Easy to include macroeconomic effects and/or forward-looking Ability to include the quality of future production Direct estimation of PD curves dynamic model Account for non homogenous features Natural inclusion of covariates Static and short term approach (1 year maximum) Difficult to link with the macroeconomic factors No explicit link with macroeconomic factors Very short term predictions Unduly complex Does not cope with pathdependence Are vintages the main drivers of losses in stage 2? Portfolio model: the vintage is not the very risk factor at loan level Calibration may be complex if covariates are not only linked to the time dimension
CONCLUSION Retail portfolios are very high default portfolios. The calibration model must leverage on this property Scores are short term predictors and matrices seem unduly complex Survival models seem to make consensus in the industry, but calibration norms are still lacking. Naïve calibration is dangerous and the model should account for some specific features of retail portfolios, such as cure rates.