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”
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.