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Comptroller of the Currency. Administrator of National Banks. Managing Model Risk in Retail Scoring Dennis Glennon Credit Risk Analysis Division Office of the Comptroller of the Currency September 28, 2012 - PowerPoint PPT Presentation

Comptroller of the CurrencyAdministrator of National Banks

Managing Model Risk in Retail Scoring

Dennis Glennon

Credit Risk Analysis DivisionOffice of the Comptroller of the Currency

September 28, 2012

The opinions expressed in this paper are those of the authors and do not necessarily reflect those of the Office of the Comptroller of the Currency. All errors are the responsibilities of the authors.

FilenameFilename2 Agenda Introduction to Model Risk What is it? Why is it relevant?

Managing Model RiskOverview of Sound Model Development and Validation Procedures

Emerging Issues Related to Model Risk2Filename3 Models Risk: What is it?Model Risk Potential for adverse consequences from decisions based on incorrect or misused model outputsModel errors that produce inaccurate outputsModel may be used incorrectly or inappropriately (i.e., using a model outside the environment for which it was designed).

Model risk emerges from the process used to develop models for measuring credit risk.

The process introduces a secondary loss exposure beyond that of credit risk alone

e.g., poor underwriting decisions based on erroneous models or overly broad interpretations of model results.

3Filename4 Model Risk: What is it?Credit Risk: The risk to earnings or capital from an obligor's failure to meet the terms of any contract with the bank or otherwise fails to perform as agreed.

A conceptually distinct exposure to loss.

There are many reasons for poor model-based results including:

Poor modeling (i.e., inadequate understanding of the business)Poor model selection (i.e., overfitting)Inadequate understanding of model useChanging conditions in the market

4Filename5Managing Model RiskThe goal of model-risk analysis is to isolate the effect of a bank's choice of risk-management strategies from those associated with incorrect or misused model output.

Model Validation is an essential component of a sound model-risk management process. Validate at time of model development/implementationOngoing monitoringRe-validate

5Filename6 Model RiskModel validation can be costly.

However, using unvalidated models to underwrite, price, and/or manage risk is potentially an unsafe and unsound practice.

The best defense against model risk is the implementation of formal, prudent, and comprehensive model-validation procedures.

6Filename7Sound modeling practices

In many cases, there are generally accepted methods of building and validating models.

These methods incorporate procedures developed in the finance, statistics, econometrics, and information theory literature.

Although these methods are valid, they may not be appropriate in all applications.

A model selected for its ability to discriminate between high and low risk may perform poorly at predicting the likelihood of default.7Model Risk: Sound Modeling PracticesFilename8Two primary modeling objectives

Classification: The model is used to rank credits by their expected relative performance

Prediction: The model is used to accurately predict the probability of the outcome

Modelers typically have one of these objectives in mind when developing and validating their models 8Models as Decision ToolsFilename9 9 01y Score (quintiles)y1020408060010010305070900102040608010030705090 Score (quintiles)9753111652117411951543[0.1][0.08][0.45][0.44][0.67][0.92][0.3][0.5][0.7][0.9][#B / (#G + #B)][bad rate][bad rate]obs. bad (B) - y=1obs. good (G) - y=0 Model 2 Model 1Model Selection: Which model is better?Filename 10A comparison of models: visual summary

Reliable and AccurateReliable, but not AccurateModels as Decision ToolsOdds: 33:1Bad %: 3.0%Score: 253Odds: 12.2:1Bad %: 7.6%Odds: 33:1Bad %: 3.0%Filename1011Illustrative Example

ln(20/1) = 3.0bad rate = 5%ln(4/1) = 1.4bad rate = 20%Filename1112The model design should reflect how the model will be used.

As such, the choices of:

sample designmodeling techniquevalidation procedures

should reflect the intended purpose for which the model will ultimately be used.

To effectively manage model risk, the right tools must be used.

12Models as Decision ToolsFilename13Models are developed for different purposes i.e., classification or prediction. As such, the choices of:

sample designmodeling techniquevalidation procedures

are driven by the intended purpose for which the model will ultimately be used. 13Models as Decision ToolsFilename14 Model Validation The classification objective is the weaker of two conditions.

There are well-developed methods outlined in the literature and accepted by the industry that are used to assess the validity of models developed under that objective.

In practice, we see:DevelopmentKS / Gini used as the primary model selection toolThese evaluated on the development, hold out, and out-of-time samplesValidation KS / KSStability test (e.g., PSI, characteristic analysis, etc.)Backtesting analysis14Filename15 Model ValidationAlmost all scoring models generate KS values that reject the null that the distribution of good accounts is equal to the distribution of bads.

KS is also used to identify a specific model with the maximum separation across alternative models.

In practice, however, the difference between the maxKS and those of alternative models is never tested using statistical methods (although there are tests outlined in the literature e.g., Krzanowski and Hand, 2011).

More importantly, once a model is selected, few modelers apply a statistical test to determine if the KS has change significantly over time to conclude the model is no longer working as expected.

15Filename16 Model ValidationThe test that have been developed, however, tend to be sensitive to sample size. Given the size of development and validation samples, very small changes may be statistically significant.

OPEN ISSUE 1: Are there tests banks can use to test for statistical significance that are not overly sensitive to sample size.

16Filename17 Model ValidationPredictive models are developed under a model accuracy objective.

As a result, a goodness-of-fit test is required for model selection.

Common performance measures used to evaluate predictive models:

Interval TestChi-Square TestHosmer-Lemeshow (H-L) Test

Unfortunately, the goodness-of-fit tests assume defaults are independent events. If the events are dependent, the tests will reject the null too frequently.17Filename18 Model ValidationThe Vasicek Test is an alternative test of accuracy that allows for dependence.

The Vasicek Test is designed to capture the effect of dependence on the size of the confidence bands.

Formula used to derive the confidence bands

where Vint is the width of the interval; ~ N(0,1); Z.95=1.64; and correlation.

18

Filename 19Vasicek Test: An Example Vasicek Test AnalysisSegmentAccountsEstimated PDActual PDVasicek Upper Bound 95% CI = 0.15 = 0.05 = 0.015110000.000000.002000.0000030.000000.000000.00005210000.000010.000000.0000580.000040.000030.00024310000.000080.000000.0003230.000230.000150.00062410000.000310.001000.0012720.000870.000590.00141510000.001020.004000.0039570.002650.001830.00299610000.003130.008000.0114660.007600.005360.00659710000.010030.019000.0335410.022300.016180.01620810000.037670.063000.1078770.073920.056050.04948910000.187980.267000.3938360.297710.245380.212201010000.759280.549000.9271030.864250.819190.78578Filename1920 Model Validation: Vasicek TestIf is too high the bands are too wide: too many models would pass the test

is not known and has to be estimated. For point-in-time based models, can be very smallFor through-the-cycle based models, can be large

In practice, we often see models fail the interval/Chi-square test, but pass the Vasicek test (especially when samples are large).

Open Issue 2: How do we resolve the inconsistency? 20Filename21Sensitivity of Validation Test to Sample SizeAccuracy tests tend to reject models thatdiscriminate well consistent with the expectations of the LOB

Measurement can be so precise that even a small, non-relevant difference in point estimates can be considered statistically significant.

21Filename22 Illustrative Example22

Filename23 Illustrative Example23

Filename24 Illustrative Example24

Filename25 Interval Tests with Large SamplesConclusion:Statistical difference: significantEconomic difference: insignificant

Solutions?Reduce the number observations using a sample: less powerful testRedefine the testInterval testFocus on capital25Filename26 Interval Tests with Large Samples26(5)(4)-1%+1%0 (1)(2)(3)Filename27 Interval TestRestate the null as an interval defined over an economically acceptable range

If the CI1- around the point estimate is within the in interval, conclude no economically significant difference

May want to reformulate the interval test in terms of an acceptable economic bias in the calculation of regulatory capital

Open Issue 3: How do we reconcile business and statistical significance?27Filename28ConclusionActive management of model risk

Sound model development, implementation, and use of models are vital elements, andRigorous model validation is critical to effective model risk management.

Model Risk should be managed like other risksIdentify the sourceManage it properly

28FilenameChart15.79118266494.72295322165.44802963985.02585225995.10473261754.19268046294.78415284154.03069453514.41884060783.80666248984.07584109073.45946628983.73289633952.89591193833.38777436132.37954613413.04452243772.02814824732.701361213