A Survey of Issues in Consumer Credit Risk

Presented by: Musa Malwandla, Mercy Marimo, Thabiso Twala

AGENDA

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SURVEY OF THE CONSUMER CREDIT RISK LANDSCAPE

ACTUARIAL TECHNIQUES IN CONSUMER CREDIT RISK

WIDER TOPICS IN CONSUMER CREDIT RISK

Survey of the Landscape

• Credit Scoring

• Impairment Analysis

• Capital Requirements

3

Credi t R i sk in a Nutshel l

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Credit Loss [ECL]

Probability of Default

[PD]

Exposure Given

Default [EAD]

Loss Given Default [LGD]

The loss to be

incurred over

some horizon

The likelihood of

moving into default

over some horizon

(analogous to 𝑛𝑞𝑥)

The loan balance

at the point of

default

The proportion of

the principal-at-

risk that is lost

DEN

SITY

PORTFOLIO LOSS

Portfolio Loss Distribution

VaR

(α)

Base

l E[L]

"Unexpected Loss"

IFRS9

E[L]

5

Credit Scoring

6

Credi t Scor ing

Purpose:

• Assessing the risk of default

Inputs:

• Demographic data, e.g., age, income

• Behavioural data, e.g., delinquency, utilisation

• Economic data, e.g., interest rate, GDP

Uses:

• Application scoring

• Impairment analysis

• Capital analysis

• Credit collections

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Risk Group 1Risk Group 2

Risk Group 3

Risk Group 4

Risk Group 5

OB

SER

VED

PD

MODEL PD

Credit Scoring Model

Credi t Scor ing

Main techniques:

• Logistic regression

• Decision trees

Measures of success:

• Goodness of fit (e.g., Hosmer-Lemeshow test)

• Discriminatory power (e.g., Gini statistic)

Complications:

• Dealing with varying time horizons

• Dealing with time-varying covariates

Some literature:

• Calibration problem: Crook, Hamilton and Thomas (1992)

• Modelling with macroeconomic variables: Malwandla (2016)

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DEFA

ULT

RA

TE

CALENDAR TIME

Modif ied Logist ic Regression

default rate log-logistic

DEFA

ULT

RA

TE

CALENDAR TIME

Standard Logist ic Regression

default rate logistic

Credi t Scor ing

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Population

Credit Utilisation < 20%

Age < 25 Age >=25

Credit Utilisation >= 20%

Delinquent on Other Loans =

'Yes'

In Default on Other Loans =

'Yes'

In Default on Other Loans =

'No'

Delinquent on Other Loans =

'No'

Number of Months Since

Delinquent <= 6

Number of Months Since

Delinquent > 6

RG2: PD=2.0% RG1: PD=1.5%

RG6: PD=12% RG5: PD=8.0% RG4: PD=5% RG3: PD=3.0%

Impairment Provisions

10

Impai rment P rovis ions

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Purpose:

•Estimating the credit impairment provision for IFRS 9 published accounts

•Concerned with estimating the mean of the credit loss distribution

Three stages of IFRS 9 impairments:

•Stage 1 [“insignificant” deterioration]: 1-year EL

•Stage 2 [“significant” deterioration]: lifetime EL

•Stage 3 [default]: lifetime EL

Analytical complications:

Modelling with variable horizon

Modelling with macroeconomic variables

Capital Requirements

12

Capi ta l Requi rements

Purpose:

• Setting the capital requirement

• Concerned with estimating the tail of the credit loss distribution

Basel III:

• Expected Loss: 𝐸 𝐿 = 𝑃𝐷 × 𝐸𝐴𝐷 × 𝐿𝐺𝐷• Unexpected Loss: U𝐿 𝛼 ≈ 𝐹−1 𝛼 × 𝐸𝐴𝐷 × 𝐿𝐺𝐷 − 𝐸 𝐿

Basel-Vasicek framework:

• 𝑃𝐷 follows a Vasicek distribution

• 𝐸𝐴𝐷 and 𝐿𝐺𝐷 are assumed to be constant

• Risk is measured on a through-the-cycle basis

Point-in-time vs through-the-cycle:

• Point-in-time – more ‘purist’ and forward-looking

• Through-the-cycle: more stable, better planning, macroprudential

Some literature:

• Modelling risk on PiT vs. TTC basis: Malwandla (2016)

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DEFA

ULT

RA

TE

TIME

Point- in-T ime PD

lower (95% CI) upper (95% CI) portfolio default rate

DEFA

ULT

RA

TE

TIME

Through-the-Cycle PD

lower (95% CI) upper (95% CI) portfolio default rate

Re-der iv ing the Basel -Vas icek F ramework

Given:

…a portfolio of 𝑛 loans…

…𝐷𝑖 is Bernoulli random variable indicating default on loan 𝑖…

… 𝑝𝑖 𝐸 is the probability of default on loan 𝑖…

… and 𝐸 is the only systemic risk variable.

We are interested in the distribution of 𝑃 =1

𝑛σ𝑖=1𝑛 𝐷𝑖

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We need an assumpt ion…

All loans are homogenous in risk:

𝑝𝑖 𝐸 = 𝑝 𝐸 .

This produces a scaled compound binomial

distribution for 𝑃:

𝐹𝑝 𝑥 = ∞−∞𝐵𝑛,𝑝 𝑒 𝑛𝑥 𝑔𝐸 𝑒 𝑑𝑒.

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And another…

The portfolio is infinitely large:

𝑛 → ∞.

By the Law of Large Numbers, this produces:

𝑃 =1

𝑛

𝑖=1

𝑛

𝐷𝑖 → 𝑝 𝐸 .

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And one more…

The systemic risk is normally distributed:

𝐸~𝑁 0, 𝜎2 .

This produces the Vasicek distribution:

𝐹𝑝 𝑥 = ФФ−1 𝑥 −Ф−1 ҧ𝑝

𝜎,

where 𝜎 is the volatility of the system ≡ systemic risk

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Capi ta l Requi rement as a Quant i le o f the Dis t r ibut ion

The capital requirement is given by:

Q 𝛼 ≈ 𝐹−1 𝛼 × 𝐸𝐴𝐷 × 𝐿𝐺𝐷

for:

𝐹−1 𝛼 = 𝛷𝜌

1 − 𝜌𝛷−1 𝛼 +

1

1 − 𝜌Ф−1 𝑃𝐷

where:

• 𝜌 =𝜎

1+𝜎is termed the asset correlation coefficient

• 𝛼 is the chosen capital level (typically 99.9%)

• 𝑃𝐷, 𝐸𝐴𝐷 and 𝐿𝐺𝐷 are portfolio averages

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Basel-Vas icek in P ract ice

Banks determine their own PD, EAD and LGD.

Basel framework provides 𝜌 (which measure systemic risk)

for the given class of loans:

𝜌 = ൞

15% 𝑓𝑜𝑟 𝑚𝑜𝑟𝑡𝑔𝑎𝑔𝑒4% 𝑓𝑜𝑟 𝑟𝑒𝑣𝑜𝑙𝑣𝑖𝑛𝑔

𝑓 𝑃𝐷 𝑜𝑡ℎ𝑒𝑟 𝑟𝑒𝑡𝑎𝑖𝑙 𝑒𝑥𝑝𝑜𝑠𝑢𝑟𝑒𝑠

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The Seven Deadly

Assumptions

The portfolio is infinitely large.

The portfolio is homogenous.

The exposure at default is constant and known.

Loss given default is non-random and known.

The systemic risk factor is normally distributed.

The systemic risk factor is cyclical and not subject to structural discontinuities.

The Basel III parameters are relevant to the portfolio being modelled.

20

The Large Homogenous Por t fo l io (LHP) Assumpt ion

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0,1

%

0,4

%

0,7

%

1,0

%

1,3

%

1,6

%

1,9

%

2,2

%

2,5

%

2,8

%

3,1

%

3,4

%

3,7

%

4,0

%

4,3

%

4,6

%

4,9

%

5,2

%

5,5

%

5,8

%

6,1

%

6,4

%

6,7

%

7,0

%

7,3

%

7,6

%

7,9

%

8,2

%

8,5

%

8,8

%

9,1

%

9,4

%

9,7

%

10,0

%

DEN

SIT

Y

DEFAULT RATE

LHP Assumption (n = 100)

Empirical (n = 100) LHP (n = 100)

0,1

%

0,4

%

0,7

%

1,0

%

1,3

%

1,6

%

1,9

%

2,2

%

2,5

%

2,8

%

3,1

%

3,4

%

3,7

%

4,0

%

4,3

%

4,6

%

4,9

%

5,2

%

5,5

%

5,8

%

6,1

%

6,4

%

6,7

%

7,0

%

7,3

%

7,6

%

7,9

%

8,2

%

8,5

%

8,8

%

9,1

%

9,4

%

9,7

%

10,0

%

DEN

SIT

Y

DEFAULT RATE

LHP Assumption (n = 500)

Empirical (n = 500) LHP (n = 500)

0,1

%

0,4

%

0,7

%

1,0

%

1,3

%

1,6

%

1,9

%

2,2

%

2,5

%

2,8

%

3,1

%

3,4

%

3,7

%

4,0

%

4,3

%

4,6

%

4,9

%

5,2

%

5,5

%

5,8

%

6,1

%

6,4

%

6,7

%

7,0

%

7,3

%

7,6

%

7,9

%

8,2

%

8,5

%

8,8

%

9,1

%

9,4

%

9,7

%

10,0

%

DEN

SIT

Y

DEFAULT RATE

LHP Assumption (n = 1,000)

Empirical (n = 1000) LHP (n = 1000)

0,1

%

0,4

%

0,7

%

1,0

%

1,3

%

1,6

%

1,9

%

2,2

%

2,5

%

2,8

%

3,1

%

3,4

%

3,7

%

4,0

%

4,3

%

4,6

%

4,9

%

5,2

%

5,5

%

5,8

%

6,1

%

6,4

%

6,7

%

7,0

%

7,3

%

7,6

%

7,9

%

8,2

%

8,5

%

8,8

%

9,1

%

9,4

%

9,7

%

10,0

%

DEN

SIT

Y

DEFAULT RATE

LHP Assumption (n = 25,000)

Empirical (n = 25000) LHP (n = 25000)

Actuarial Techniques in Consumer Credit Risk

• Exogenous Maturity Vintage

• Survival Analysis

• Threshold Regression

22

Exogenous Maturity Vintage

23

EMV: Overv iew

Rationale:

• Decompose credit risk experience along three dimensions:

• Maturity/age

• Vintage/cohort

• Exogenous/period

Typical model:

• Model form: 𝑝 𝐸 = 𝛷 𝛼 +𝑀𝑡−𝑠 + 𝐸𝑡 + 𝑉𝑠

• Exogenous component 𝐸𝑡 modelled via time series

Analytical challenges:

• Problem: identifiability, Yang (2006), Fu (2008)

• Solution: substituting vintage with behavioural score, Malwandla

(e.2020)

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EMV: Components

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DEFA

ULT

RIS

K

BEHAVIOURAL RISK SCORE

Origination (Behavioural) Component

DEFA

ULT

RIS

K

ACCOUNT MATURITY

Matur i ty Component

DEFA

ULT

RIS

K

PERIOD (CALENDAR TIME)

Exogenous Component

Exogenous Effect Macroeconomic Fit

DEFA

ULT

RA

TE

OBSERVATION DATE (CALENDAR TIME)

Model Accuracy

Actual PD Predicted PD

EMV: for Capi ta l Requi rements

The exogenous component is the true measure of systemic risk.

A universal formula for the asset correlation coefficient (Malwandla, e.2020):

• Allows us to model binary outcome with macroeconomic data.

• Produces net formula for asset correlation coefficient:

𝜌 =𝜎2 1− 𝑟2

1+𝜎2 1− 𝑟2(vs. 𝜌 = ൞

15% 𝑓𝑜𝑟 𝑚𝑜𝑟𝑡𝑔𝑎𝑔𝑒4% 𝑓𝑜𝑟 𝑟𝑒𝑣𝑜𝑙𝑣𝑖𝑛𝑔

𝑓 𝑃𝐷 𝑜𝑡ℎ𝑒𝑟 𝑟𝑒𝑡𝑎𝑖𝑙 𝑒𝑥𝑝𝑜𝑠𝑢𝑟𝑒𝑠for Basel)

Point-in-time vs. through-the-cycle:

• In point-in-time model, we will model the exogenous component: 𝑟2 > 0

• In a through-the-cycle model, we ignore the exogenous component: 𝑟2 = 0

Factors influencing the asset correlation coefficient:

• The level of systemic volatility

• How much the volatility influences the portfolio default rate

• How well the systemic volatility can be modelled using macroeconomic data

• How well the macroeconomic data ca be forecasted

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0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0%

10

%

20

%

30

%

40

%

50

%

60

%

70

%

80

%

90

%

10

0%

r=

ρ

Broader Perspect ive: Through - the-Cycle vs . Po int - in-T ime

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DEFA

ULT

RA

TE

OBSERVATION DATE (CALENDAR TIME)

Point- in-T ime Confidence Interval

Default Rate Predicted PD CI Lower Bound CI Upper Bound

DEFA

ULT

RA

TE

OBSERVATION DATE (CALENDAR TIME)

Through-the-Cycle Confidence Interval

Default Rate Predicted PD CI Lower Bound CI Upper Bound

𝑝 𝐸 = 𝛷 𝛼 +𝑀𝑡−𝑠 + 𝐸𝑡 + 𝑉𝑠 𝑝 𝐸 = 𝛷 𝛼 +𝑀𝑡−𝑠 + 𝑉𝑠

𝜌 =𝜎2 1 − 𝑟2

1 + 𝜎2 1 − 𝑟2𝜌 =

𝜎2

1 + 𝜎2

Broader Perspect ive: Forward-Looking Through-the-Cycle

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DEFA

ULT

RA

TE

OBSERVATION DATE (CALENDAR TIME)

Forward-Looking Through-the-Cycle Confidence Interval

History Case 1 Case 2 Case 3 Historical Low. CI. Historical Up. CI. Prospective Low. CI. Prospective Up. CI.

Rates at 6%

GeneralisedProportional

Hazard Model

29

General i sed PH: Overv iew

Purposes:• Modelling survival data with time-varying covariates

• Decompose data into three components:

• Survival time

• Behavioural risk

• Calendar time

Typical model:• Gaussian: ℎ𝑗,𝑠 𝑡 = 𝛷 𝑏𝑡 + 𝜑𝑗,𝑠 + 𝑒𝑠• Coxian: ℎ𝑗,𝑠 𝑡 = 𝛷 𝑏𝑡 + 𝑒𝑠

𝜑𝑗,𝑠

Uses:• IFRS 9 impairment PD modelling

• General survival analysis

Some literature:• LGD modelling with survival analysis: Marimo, Chimedza (2017)

• Cross-Sectional Survival Analysis: Marimo, Malwandla, Breed (2017)

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General i sed PH: I l lus t ra t ion

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HA

ZA

RD

RA

TE

SURVIVAL TIME

Fixed Baseline: Baseline Variable Baseline: Baseline + Macroeconomic Index Final Hazard: Baseline + Macroeconomic Index + Behavioural

Threshold Regression Model

32

TRM: Overv iew

Purpose:

• Modelling the waiting time until a process breaches a threshold

• In credit risk modelling:

• Modelling the time until a consumer’s net income drops

below a default threshold.

• Analogous to Merton/Black default model: waiting time until

assets drop below liability.

Interesting properties:

• When underlying process is stochastic, waiting time is Inverse

Gaussian.

• Inverse Gaussian produces a Vasicek distribution for PD.

• Can thus be used for economic capital modelling.

(TRM) 𝛷𝜌𝛷−1 𝛼 −𝐷𝐷𝑠

1−𝜌vs. 𝛷

𝜌𝛷−1 𝛼 +𝛷−1 ҧ𝑝

1−𝜌(Basel II)

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HA

ZA

RD

RA

TE

SURVIVAL TIME

Modelling Survival Time

actual_default mig_default

TRM: Sav ings P rocess

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CO

NSU

MER

SA

VIN

GS (

OR

FIR

M’S

ASSETS

)

SURVIVAL TIME

Account 1 Account 2 Account 3 Account 4 Account 5 Threshold

“Time to Default”

Model: 𝑆𝑗 𝑡 = 𝜇𝑗 + 𝜎 𝜌𝐸 𝑡 + 1 − 𝜌𝜀𝑗 𝑡

Prob. of Default: PD = 𝑃 𝑆𝑗 𝑇 < 𝐾

Model drift using customer data: 𝜇𝑗 = 𝛼 + σ𝑙 𝛽𝑙𝑋𝑙

“In

itia

l Dis

tan

ce

to

D

efa

ult”

Wider Topics in Consumer Credit Risk

• Profit Scoring

• Economic Value

• Data Science

35

AGENDA

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SOME HISTORY AND

INITIAL SOLUTIONS WITH

THEIR LIMITATIONSALTERNATIVE SOLUTIONS PRELIMINARY RESULTS

Some His tory…

Fischer’s work (±1940s) on classifying flower species was the

catalyst needed to automate the credit granting process

• Application scoring

• Behavioural scoring

All the above techniques used in the loan granting have loan

default as the primary target!

Default alone is not enough to fully encompass the risk/reward a

client poses

It is now time for the next stage of the evolution – PROFIT

SCORING!

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Credi t P ro f i t Scor ing: Rat ionale

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Credit Loss

Probability of Default

Exposure at Default

Loss Given Default

• Variations in EAD and LGD also have material influence.

• Profit scoring focuses on estimating economic value (or profitability) instead of merely tracking the

default risk

• Profit scoring is a better tool as it better aligns with business objectives

• Risk-adjusted return considerations

• market share, etc

Prof i t Scor ing: Rat ionale

• Several views of the customer would ideally need to be created:

• contract level views

• product level views

• bundled views

• holistic views

• A key advantage of this approach is that it allows the bank to:

• cherry pick customers (Incl. cross-selling)

• identify highly profitable customers, and enhance the relationships

• It's an important metric as it costs less to keep an existing customer than

it does to acquire new ones, so increasing the value of your existing

customers is a great way to drive growth.

• This view better facilitates tactical and strategic pricing and acquisition

decisions. Due to the multidimensional view of the customer, the

profitability model should drive the decision to grant credit.

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Prof i t Scor ing: P re l iminary Resul t s

• Profit scoring has received some attention recently, mostly from an

academic perspective.

• Serrano-Cinca & Gutiérrez-Nieto (2016) found that “a lender selecting

loans by applying a profit scoring system using multivariate regression

outperforms the results obtained by using a traditional credit scoring

system, based on logistic regression”.

• Others have found the use of Machine Learning methods have further

improved the solutions to the profit scoring problem

• There are significant challenges in building these type of models:

• Price influences profitability (and arguably default risk), and

profitability should influence price (chicken and egg situation!)

• Reliable data is hard to find (particularly for holistic views)

• Model risk is particularly high!

• Twala (e.2020) implements the ideas discussed in retail portfolios.

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Concluding Remarks

41

Areas of Fur ther Research

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• Resolving the Other Deadly Assumptions

• Development Finance

• Economic (Embedded) Value for banks

• Cross-Portfolio Aggregation

• Unification within Credit Risk• Unification across Risk Types

Economic Value

PV of NIM

Lifetime EL

Cost of Capital

Economic Capital

Free Capital

“Value of in-Force” “Adjusted Net Worth”

QUESTIONS?malwandla@live.co.za

mercy.dzikiti@gmail.com

t.o.twala@gmail.com

The views and opinions mentioned in this presentation do not necessarily constitute the views,

opinions, processes, risks, systems, strategies of any persons, organisations and/or companies that

might have been mentioned (directly or indirectly) in this presentation. This presentation is not meant

to give any advice in any way. All material used or referenced, is assumed to have been for fair use.