Vision 2014: Advanced-techniques-for-expected-loss-modeling

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Advanced techniques for expected loss modeling

Danilo Clemente Coelho BV Financial Services

Guilherme Barreto Fernandes Experian Brazil

#vision2014

2 © 2014 Experian Information Solutions, Inc. All rights reserved. Experian Public.

Agenda

Overview Banco Votorantim

Overview payroll loans in Brazilian market

Motivation

Technical details:

► PD model

► LGD model

Concluding remarks


Banco Votorantim

Payroll loan concepts and portfolio


Banco Votorantim is one of the largest

privately-held Brazilian banks in total assets…

10 largest banks – Total Assets (R$B)¹

111120

131

163475

725

779

859

Votorantim BTG Pactual

Safra

HSBC Santander

BNDES

Bradesco

CEF Itaú 1,011

Banco do Brasil 1,179

National privately-held

Foreign

State-owned

Shareholder

50% Total

10th

Banco Votorantim: one of the leading banks in Brazil



Payroll loans

7th largest player in the payroll loan market

Focus on INSS (retirees and pensioners)

Managed loan portfolio (R$B)

1.5

Dec/1

2

Off-

balance

-7.0%

On-

balance

Dec/1

3

7.6

6.3

1.3

Sept/1

3

8.2

6.6

9.7

7.2

2.5 -16.5%

-4.8%

∆Dec13

/Sept13

Portfolio of payroll loans in Banco Votorantim


Government regulations

Three types of payroll loans

► Private sector employees

► Government workers

► Retirees and pensioners

Long-term loans

Collateral: turns future income as a guarantee

Low spreads

Default characteristics idiosyncratic risk such as demission

Collection

► Recovery based on “clean credit lines”

Payroll loans main characteristics


Credit losses forecast

1. Build a model that knows when (and not only if) the client will default

2. How much we could recover to minimize losses

Challenge Forecast profitability of the product


PD Model

Cox proportional hazard model

Default curve calibration


Better usage:

Better prediction on 12-month window: Is default rate rising when compared to past vintages?

Better pricing solution: PD curve adjusted to term

Early indicator on default: Earlier vintages can be used in modeling process

PD Model: Concepts

Time to default

Loan accounts

PD 20%

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Situation 1

Observation period = 12 months

PD 20%

Default

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Situation 2


Survival analysis

𝑺𝒊 (𝒕) = 𝑺𝟎(𝒕)𝒆𝒙𝒑(𝒙′𝒊𝜷)

Surv

ival

Time

𝜆𝑖 (𝑡) = 𝜆0(𝑡) ∙ 𝛼(𝑥′𝑖𝛽)

𝜆𝐶𝑜𝑥(𝑡) = 𝑓 𝐾𝑀0 ∙ 𝑒𝑥𝑝(𝑥′𝑖𝛽)

Kaplan-Meier estimate

Baseline hazard

Proportional factor

Cox Proportional Hazard Model 𝜆0(𝑡) Baseline hazard: describes the shape of the log-survival curve

Proportional factor: incorporates the individual’s covariates shifting the survival curve up/downwards according to one’s risk

𝑒𝑥𝑝(𝑥′𝑖𝛽)

𝜆0(𝑡) Baseline hazard: Needed for PD point estimation for any time t

Proportional factor: Ranks the individuals according to risk profile

𝑒𝑥𝑝(𝑥′𝑖𝛽) (𝑥𝑖)

Application: Score = Probability of default before time t: 1-S(t)


Estimation Payment behavior

Term and conditions

Demographics

Total indebtness

Market delinquency

Credit demand

Modeling process and performance measures

Variable selection

Multicollinearity

Outliers / leverages

Transformations

Variable stability

0%

10%

20%

30%

40%

50%

60%

KS

KS per vintage

Development

43,62

Out-of-sample

42,32

Out-of-time

41,41


Cumulated default rate C

um

ula

ted d

efa

ult r

ate

C

um

ula

ted d

efa

ult r

ate

Month in performance window

Expected default per

risk bucket


risk bucket

Observed default per

risk bucket

High accuracy in

low risk buskets

Low accuracy in

high risk buckets


Risk bucket calibration

Cum

ula

ted h

aza

rd

Months in performance window

𝜆 𝑡 = −𝑆′(𝑡)

1 − 𝑆(𝑡)=𝑓(𝑡)

𝐹(𝑡)

Observed hazard function per risk bucket PD per homogenous groups (risk buckets)

𝜆(𝑡|𝑥) = 𝜆0(𝑡) ∙ 𝑒𝑥𝑝(𝑥′𝛽)

PD

Credit scoring

HG

3

HG

4

HG

5

HG

7

HG

1

HG

2

HG

6

Different hazard function per risk bucket

Separate calibration per risk bucket k (Sk(t))

K risk buckets ordering PD per credit scoring range


Credit scoring obtained from the model developed:

Credit scoring of the individual is given by:

The score creates seven risk buckets. For each, a different non-parametric baseline is estimated:

The calibrated PD model is given by:

Calibration methodology

𝑆 𝑡|𝑥 = 𝑆0 𝑡𝑒𝑥𝑝(𝑥′𝛽)

𝑆𝑐𝑜𝑟𝑒 𝑥 = 𝑃(𝐷 = 1|𝑡 = 12, 𝑥) = 1 − 𝑆 12 = 1 − 𝑆0 12𝑒𝑥𝑝(𝑥′𝛽)

𝑆0𝑘 𝑡 ⇒ 𝐾𝑎𝑝𝑙𝑎𝑛 − 𝑀𝑒𝑖𝑒𝑟 𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑖𝑜𝑛 𝑝𝑒𝑟 ℎ𝑜𝑚𝑜𝑔𝑒𝑛𝑜𝑢𝑠 𝑔𝑟𝑜𝑢𝑝 𝑘

𝑆∗ 𝑡|𝑥 = 𝑆0𝑘 𝑡 𝑒𝑥𝑝(𝑥

′𝛽)



risk bucket

Calibrated PD per risk

bucket


risk bucket

PD curve after calibration C

um

ula

ted d

efa

ult r

ate

Month in performance window

Cum

ula

ted d

efa

ult r

ate


risk bucket High accuracy in

low risk buskets

High accuracy in

high risk buckets


LGD Model

Tobit Model

Logistic regression comparison

Recovery curve calibration


Default 1 2 3 4

Time

Valu

e

Va

lor p

rese

nte

EAD

=(Recovery – costs)

EAD: Exposure at default

NPV: Net present value

LGD definition and calculation

EAD + NPV( Costs ) – NPV( Recovery )

EAD LGD =

LGD


𝑦 ∗= 𝛽′𝑋 + 𝜀 𝑦 = 𝑚𝑎𝑥 0, 𝑦 ∗

𝑙𝑛𝐿 = −1

2ln 2𝜋 + ln 𝜎2 +

(𝑦 − 𝛽′𝑋 )2

𝜎2𝑦>0

+ 𝑙𝑛 1 − 𝑁(𝛽′𝑋 )

𝜎𝑦=0

Incorporates the

concentration on

LGD = 0

Tobit model

0%

10%

20%

30%

40%

50%

60%

70%

80%

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

Dis

trib

uti

on

LGD


60%

65%

70%

75%

80%

85%

90%

95%

100%

105%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

LG

D

Workout period

Observed LGD curve by vintage

Payroll loan: LGD curves

Earlier default

vintages: lower

recovery

LGD workout:

12-month

Enough default vintages for modeling

Take into account new default characteristics

LGD curve is not stable on 12-month workout


Model performance

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

5 10 15 20 25 30 35 40

LG

D12

LGD estimated x observed – Development sample

Spearman correlation:

Development

sample:0.497

Validation sample:0.504

Estimated Observed

Spearman correlation

Correlation measure based on ranks

Asymmetry has low impact on interpretation

Score must order LGD, not predict point estimates


Response variable

► Event: LGD over 100%

► Non-event: LGD under 100%

Results:

Tobit model vs. logistic regression

Similar results according to these measures

KS Spearman Corr.

Tobit 39.8% 49.9%

Logistic 40.4% 49.7%


Response variable



Results:

► Database divided into three groups:

1. 1/3 lowest scores

2. 1/3 middle scores

3. 1/3 highest scores


LGD12 Tobit

Logistic 1 2 3 Total

1 61.1% 71% 61%

2 66.1% 77.6% 85.4% 78%

3 82.6% 88.5% 88%

Total 61% 78% 88%


Response variable



Results:

► Observed LGD in each group:

1. 1/3 lowest scores: 61%

2. 1/3 middle scores: 78%

3. 1/3 highest scores: 88%


Prediction

Logistic Tobit Observed LGD Closest to group

2 middle 1 low 66.1% 1 low

1 low 2 middle 71% 2 middle

3 high 2 middle 82.6% 2 middle

2 middle 3 high 85.4% 3 high


Homogenous grouping: 8

Polynomial function extrapolation

Average R2 of 97%

Calibration to 24 months workout window

0%

20%

40%

60%

80%

100%

120%

1 3 5 7 9 11 13 15 17 19 21 23

LG

D

GH8

31% 0%

20%

40%

60%

80%

100%

120%

1 3 5 7 9 11 13 15 17 19 21 23

GH7

40%

LG

D

0%

20%

40%

60%

80%

100%

120%

1 3 5 7 9 11 13 15 17 19 21 23

GH6

48%

0%

20%

40%

60%

80%

100%

120%

1 3 5 7 9 11 13 15 17 19 21 23

GH5

55%

0%

20%

40%

60%

80%

100%

120%

1 3 5 7 9 11 13 15 17 19 21 23

GH4

61%

Workout

LG

D

0%

20%

40%

60%

80%

100%

120%

1 3 5 7 9 11 13 15 17 19 21 23

GH3

69%

0%

20%

40%

60%

80%

100%

120%

1 3 5 7 9 11 13 15 17 19 21 23

Workout

GH2

78%

Workout

0%

20%

40%

60%

80%

100%

120%

1 3 5 7 9 11 13 15 17 19 21 23

GH1

85%


Concluding remarks


Advanced models, as Tobit and Cox regression, not only achieve regulatory demands, but also give a more precise and useful information for business management

Survival PD Model:

► Extends performance window

► Allow the use of several vintages (captures up-to-date characteristics)

Concluding remarks


Tobit model for LGD and recovery curve calibration:

► Outperforms logistic regression on high losses

► Simple interpretation of parameters

● Linear relation

Benefits:

► Going further in analytics techniques adds value to business allowing broader credit management tools

► PD model: Pricing and expected cash flow according to term

► LGD model: Expected cash flow is useful in provisioning and collection

Concluding remarks


For additional information, please contact:

[email protected]

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Vision 2014: Advanced-techniques-for-expected-loss-modeling