A Survey of Issues in Consumer Credit Risk Presented by: Musa - - PowerPoint PPT Presentation

A Survey of Issues in Consumer Credit Risk

Presented by: Musa Malwandla, Mercy Marimo, Thabiso Twala

AGENDA

ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

2

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

Credit Risk in a Nutshell

ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

4

Credit Loss [ECL] Probability

• f Default

[PD] Exposure Given Default [EAD] Loss Given Default [LGD]

The loss to be incurred over some horizon The likelihood of moving into default

• ver some horizon

(analogous to 𝑜𝑟𝑦) The loan balance at the point of default The proportion of the principal-at- risk that is lost

DENSITY PORTFOLIO LOSS

Portfolio Loss Distribution

VaR(α) Basel E[L] "Unexpected Loss" IFRS9 E[L]

5

Credit Scoring

6

Credit Scoring

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

ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

7 Risk Group 1 Risk Group 2 Risk Group 3 Risk Group 4 Risk Group 5 OBSERVED PD MODEL PD

Credit Scoring Model

Credit Scoring

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)

ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

8

DEFAULT RATE CALENDAR TIME

Modified Logistic Regression

default rate log-logistic DEFAULT RATE CALENDAR TIME

Standard Logistic Regression

default rate logistic

Credit Scoring

ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

9 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

Impairment Provisions

ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

11

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

Capital Requirements

Purpose:

• Setting the capital requirement
• Concerned with estimating the tail of the credit loss distribution

Basel III:

• Expected Loss: 𝐹 𝑀 = 𝑄𝐸 × 𝐹𝐵𝐸 × 𝑀𝐻𝐸
• Unexpected Loss: U𝑀 𝛽 ≈ 𝐺−1 𝛽 × 𝐹𝐵𝐸 × 𝑀𝐻𝐸 − 𝐹 𝑀

Basel-Vasicek framework:

• 𝑄𝐸 follows a Vasicek distribution
• 𝐹𝐵𝐸 and 𝑀𝐻𝐸 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)

ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

13

DEFAULT RATE TIME

Point-in-Time PD

lower (95% CI) upper (95% CI) portfolio default rate DEFAULT RATE TIME

Through-the-Cycle PD

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

Re-deriving the Basel-Vasicek Framework

Given: …a portfolio of 𝑜 loans… …𝐸𝑗 is Bernoulli random variable indicating default on loan 𝑗… … 𝑞𝑗 𝐹 is the probability of default on loan 𝑗… … and 𝐹 is the only systemic risk variable. We are interested in the distribution of 𝑄 =

1 𝑜 σ𝑗=1 𝑜

𝐸𝑗

ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

14

We need an assumption…

All loans are homogenous in risk: 𝑞𝑗 𝐹 = 𝑞 𝐹 . This produces a scaled compound binomial distribution for 𝑄: 𝐺

𝑞 𝑦 = ׬ −∞ ∞ 𝐶𝑜,𝑞 𝑓

𝑜𝑦 𝑕𝐹 𝑓 𝑒𝑓.

ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

15

And another…

The portfolio is infinitely large: 𝑜 → ∞. By the Law of Large Numbers, this produces: 𝑄 = 1 𝑜 ෍

𝑗=1 𝑜

𝐸𝑗 → 𝑞 𝐹 .

ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

16

And one more…

The systemic risk is normally distributed: 𝐹~𝑂 0, 𝜏2 . This produces the Vasicek distribution: 𝐺

𝑞 𝑦 = Ф Ф−1 𝑦 −Ф−1 ҧ 𝑞 𝜏

, where 𝜏 is the volatility of the system ≡ systemic risk

ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

17

Capital Requirement as a Quantile of the Distribution

The capital requirement is given by: Q 𝛽 ≈ 𝐺−1 𝛽 × 𝐹𝐵𝐸 × 𝑀𝐻𝐸 for: 𝐺−1 𝛽 = 𝛸 𝜍 1 − 𝜍 𝛸−1 𝛽 + 1 1 − 𝜍 Ф−1 𝑄𝐸 where:

• 𝜍 =

𝜏 1+𝜏 is termed the asset correlation coefficient

• 𝛽 is the chosen capital level (typically 99.9%)
• 𝑄𝐸, 𝐹𝐵𝐸 and 𝑀𝐻𝐸 are portfolio averages

ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

18

Basel-Vasicek in Practice

Banks determine their own PD, EAD and LGD. Basel framework provides 𝜍 (which measure systemic risk) for the given class of loans: 𝜍 = ൞ 15% 𝑔𝑝𝑠 𝑛𝑝𝑠𝑢𝑕𝑏𝑕𝑓 4% 𝑔𝑝𝑠 𝑠𝑓𝑤𝑝𝑚𝑤𝑗𝑜𝑕 𝑔 𝑄𝐸 𝑝𝑢ℎ𝑓𝑠 𝑠𝑓𝑢𝑏𝑗𝑚 𝑓𝑦𝑞𝑝𝑡𝑣𝑠𝑓𝑡

ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

19

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 Portfolio (LHP) Assumption

ACTUARI AL SOCI E TY 2019 CONV E NTI ON | 22 - 23 OCTOBER 2019

21

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% DENSITY 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% DENSITY 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% DENSITY 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% DENSITY 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: Overview

Rationale:

• Decompose credit risk experience along three dimensions:
• Maturity/age
• Vintage/cohort
• Exogenous/period

Typical model:

• Model form: 𝑞 𝐹 = 𝛸 𝛽 + 𝑁𝑢−𝑡 + 𝐹𝑢 + 𝑊

𝑡

• Exogenous component 𝐹𝑢 modelled via time series

Analytical challenges:

• Problem: identifiability, Yang (2006), Fu (2008)
• Solution: substituting vintage with behavioural score, Malwandla

(e.2020)

ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

24

EMV: Components

ACTUARI AL SOCI E TY 2019 CONV E NTI ON | 22 - 23 OCTOBER 2019

25

DEFAULT RISK BEHAVIOURAL RISK SCORE

Origination (Behavioural) Component

DEFAULT RISK ACCOUNT MATURITY

Maturity Component

DEFAULT RISK PERIOD (CALENDAR TIME)

Exogenous Component

Exogenous Effect Macroeconomic Fit DEFAULT RATE OBSERVATION DATE (CALENDAR TIME)

Model Accuracy

Actual PD Predicted PD

EMV: for Capital Requirements

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:

𝜍 =

𝜏2 1− 𝑠2 1+𝜏2 1− 𝑠2

(vs. 𝜍 = ൞ 15% 𝑔𝑝𝑠 𝑛𝑝𝑠𝑢𝑕𝑏𝑕𝑓 4% 𝑔𝑝𝑠 𝑠𝑓𝑤𝑝𝑚𝑤𝑗𝑜𝑕 𝑔 𝑄𝐸 𝑝𝑢ℎ𝑓𝑠 𝑠𝑓𝑢𝑏𝑗𝑚 𝑓𝑦𝑞𝑝𝑡𝑣𝑠𝑓𝑡 for Basel) Point-in-time vs. through-the-cycle:

• In point-in-time model, we will model the exogenous component: 𝑠2 > 0
• In a through-the-cycle model, we ignore the exogenous component: 𝑠2 = 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

ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

26

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% r= ρ

Broader Perspective: Through-the-Cycle vs. Point-in-Time

ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

27

DEFAULT RATE OBSERVATION DATE (CALENDAR TIME)

Point-in-Time Confidence Interval

Default Rate Predicted PD CI Lower Bound CI Upper Bound DEFAULT RATE OBSERVATION DATE (CALENDAR TIME)

Through-the-Cycle Confidence Interval

Default Rate Predicted PD CI Lower Bound CI Upper Bound

𝑞 𝐹 = 𝛸 𝛽 + 𝑁𝑢−𝑡 + 𝐹𝑢 + 𝑊

𝑡

𝑞 𝐹 = 𝛸 𝛽 + 𝑁𝑢−𝑡 + 𝑊

𝑡

𝜍 = 𝜏2 1 − 𝑠2 1 + 𝜏2 1 − 𝑠2 𝜍 = 𝜏2 1 + 𝜏2

Broader Perspective: Forward-Looking Through-the-Cycle

ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

28

DEFAULT RATE 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%

Generalised Proportional Hazard Model

29

Generalised PH: Overview

Purposes:

• Modelling survival data with time-varying covariates
• Decompose data into three components:
• Survival time
• Behavioural risk
• Calendar time

Typical model:

• Gaussian: ℎ𝑘,𝑡 𝑢 = 𝛸 𝑐𝑢 + 𝜒𝑘,𝑡 + 𝑓𝑡
• Coxian: ℎ𝑘,𝑡 𝑢 = 𝛸 𝑐𝑢 + 𝑓𝑡

𝜒𝑘,𝑡

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)

ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

30

Generalised PH: Illustration

ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

31

HAZARD RATE SURVIVAL TIME Fixed Baseline: Baseline Variable Baseline: Baseline + Macroeconomic Index Final Hazard: Baseline + Macroeconomic Index + Behavioural

Threshold Regression Model

32

TRM: Overview

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) 𝛸

𝜍𝛸−1 𝛽 −𝐸𝐸𝑡 1−𝜍

• vs. 𝛸

𝜍𝛸−1 𝛽 +𝛸−1 ҧ 𝑞 1−𝜍

(Basel II)

ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

33

HAZARD RATE SURVIVAL TIME

Modelling Survival Time

actual_default mig_default

TRM: Savings Process

ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

34

CONSUMER SAVINGS (OR FIRM’S ASSETS) SURVIVAL TIME Account 1 Account 2 Account 3 Account 4 Account 5 Threshold

“Time to Default”

Model: 𝑇

𝑘 𝑢 = 𝜈𝑘 + 𝜏

𝜍𝐹 𝑢 + 1 − 𝜍𝜁𝑘 𝑢

• Prob. of Default: PD = 𝑄 𝑇

𝑘 𝑈 < 𝐿

Model drift using customer data: 𝜈𝑘 = 𝛽 + σ𝑚 𝛾𝑚𝑌𝑚

“Initial Distance to Default”

Wider Topics in Consumer Credit Risk

• Profit Scoring
• Economic Value
• Data Science

35

AGENDA

ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

36

SOME HISTORY AND INITIAL SOLUTIONS WITH THEIR LIMITATIONS ALTERNATIVE SOLUTIONS PRELIMINARY RESULTS

Some History…

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!

ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

37

Credit Profit Scoring: Rationale

ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

38

Credit Loss Probability

• f 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

Profit Scoring: Rationale

• 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.

ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

39

Profit Scoring: Preliminary Results

• 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

• utperforms 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.

ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

40

Concluding Remarks

41

Areas of Further Research

ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

42

• 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,

• pinions, 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.