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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.

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Agenda

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

Managing Model Risk Overview of Sound Model Development and

Validation Procedures

Emerging Issues Related to Model Risk

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Models Risk: What is it?

Model Risk – Potential for adverse consequences from decisions based on incorrect or misused model outputs Model errors that produce inaccurate outputs Model 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.

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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 use Changing conditions in the market

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Managing Model Risk

The 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/implementation Ongoing monitoring Re-validate

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Model Risk

Model 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.

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Sound 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.

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Model Risk: Sound Modeling Practices

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Two 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 8

Models as Decision Tools

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0

1

y

Score (quintiles)

y

1

020 40 80600 10010 30 50 70 900

10 20 40 60 80 10030 7050 90

Score (quintiles)

9 7 5 3 1 11 6 5 2 1

1 7 4 1195 1 5 43

[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 1

Model Selection: Which model is better?

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A comparison of models: visual summary

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320 300 280 260 240 225

development log odds

actual log odds

score

log(

odds

)

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309 289 269 249 229 209

actual log odds

development log odds

Reliable and AccurateReliable, but not Accurate

Models as Decision Tools

Odds: 33:1Bad %: 3.0%

Score: 253

Odds: 12.2:1Bad %: 7.6%

Odds: 33:1Bad %: 3.0%

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Illustrative Example

Risk-Rating Model

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644 653 665 675 684 693 706 715 725 739 753

Score Bands

ln(g

ood/

bad)

Development (K-S = 32.1)

Validation (K-S = 34.3)

ln(20/1) = 3.0bad rate = 5%

ln(4/1) = 1.4bad rate = 20%

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The model design should reflect how the model will be used.

As such, the choices of: sample design modeling technique validation 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.

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Models as Decision Tools

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Models are developed for different purposes – i.e., classification or prediction. As such, the choices of:

sample design modeling technique validation procedures

are driven by the intended purpose for which the model will ultimately be used.

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Models as Decision Tools

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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: Development

KS / Gini used as the primary model selection tool These evaluated on the development, hold out,

and out-of-time samples Validation

KS / ΔKS Stability test (e.g., PSI, characteristic analysis,

etc.) Backtesting analysis 14

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Model Validation

Almost 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.

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Model Validation

The 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.

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Model Validation

Predictive 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 Test Chi-Square Test Hosmer-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. 17

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Model Validation

The 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 ρ – correlation.

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)1(

)( 95.1 ZPD

Vint

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Vasicek Test: An Example

Vasicek Test Analysis

Segment Accounts Estimated PD Actual PD Vasicek Upper Bound

95% CI

ρ = 0.15 ρ = 0.05 ρ = 0.015

1 1000 0.00000 0.00200 0.000003 0.00000 0.00000 0.00005

2 1000 0.00001 0.00000 0.000058 0.00004 0.00003 0.00024

3 1000 0.00008 0.00000 0.000323 0.00023 0.00015 0.00062

4 1000 0.00031 0.00100 0.001272 0.00087 0.00059 0.00141

5 1000 0.00102 0.00400 0.003957 0.00265 0.00183 0.00299

6 1000 0.00313 0.00800 0.011466 0.00760 0.00536 0.00659

7 1000 0.01003 0.01900 0.033541 0.02230 0.01618 0.01620

8 1000 0.03767 0.06300 0.107877 0.07392 0.05605 0.04948

9 1000 0.18798 0.26700 0.393836 0.29771 0.24538 0.21220

10 1000 0.75928 0.54900 0.927103 0.86425 0.81919 0.78578

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Model Validation: Vasicek Test

If ρ is too high the bands are too wide: too many models would pass the test

ρ is not known and has to be estimated. For point-in-time based models, ρ can be very

small For through-the-cycle based models, ρ 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?

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Sensitivity of Validation Test to Sample Size

Accuracy tests tend to reject models that discriminate 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.

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Illustrative Example

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Default Rates

0.00

10.00

20.00

30.00

40.00

score range

def

ault

rat

e

actual 34.11 22.75 16.18 13.63 11.44 9.84 9.07 7.60 7.35 6.83 6.37 5.72 5.41 4.49 4.41 3.57 3.44 2.93 2.27 1.14

predicted 34.56 22.55 16.59 13.27 11.48 9.86 8.65 7.90 7.16 6.54 5.97 5.50 5.04 4.64 4.14 3.76 3.38 2.96 2.46 1.43

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

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Illustrative Example

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Default Rate p-values HL

Seg Default Non-Default Total Actual Predicted (cv - 5%)

1 4027 7780 11807 34.11 34.56 0.3039 1.0572 2 2992 10158 13150 22.75 22.55 0.5832 0.3011 3 1847 9568 11415 16.18 16.59 0.2390 1.3867 4 1184 7505 8689 13.63 13.27 0.3226 0.9787 5 878 6795 7673 11.44 11.48 0.9125 0.0121 6 1007 9223 10230 9.84 9.86 0.9459 0.0046 7 598 5996 6594 9.07 8.65 0.2250 1.4722 8 536 6512 7048 7.60 7.90 0.3506 0.8713 9 474 5973 6447 7.35 7.16 0.5541 0.3500

10 507 6913 7420 6.83 6.54 0.3124 1.0205 11 459 6752 7211 6.37 5.97 0.1516 2.0568 12 373 6150 6523 5.72 5.50 0.4357 0.6076 13 380 6647 7027 5.41 5.04 0.1562 2.0109 14 339 7214 7553 4.49 4.64 0.5354 0.3842 15 355 7698 8053 4.41 4.14 0.2238 1.4799 16 244 6584 6828 3.57 3.76 0.4094 0.6806 17 239 6712 6951 3.44 3.38 0.7819 0.0767 18 246 8145 8391 2.93 2.96 0.8712 0.0263 19 217 9360 9577 2.27 2.46 0.2296 1.4432 20 208 17978 18186 1.14 1.43 0.0010 10.8227

HL stat 27.0433 p-value 0.0782

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Illustrative Example

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p-values

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0.60

0.80

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score range

p

n-sample 3n-sample c-value

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Interval Tests with Large Samples

Conclusion: Statistical difference: significant Economic difference: insignificant

Solutions? Reduce the number observations using

a sample: less powerful test Redefine the test

Interval test Focus on capital

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Interval Tests with Large Samples

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(5)

(4)

-1% +1%0

(1)

(2)

(3)

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Interval Test

Restate the null as an interval defined over an economically acceptable range

If the CI1-α 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?

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Conclusion

Active management of model risk Sound model development, implementation, and use

of models are vital elements, and Rigorous model validation is critical to effective

model risk management.

Model Risk should be managed like other risks Identify the source Manage it properly

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