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 SURVEY OF THE CONSUMER ACTUARIAL TECHNIQUES IN WIDER TOPICS IN CREDIT RISK LANDSCAPE CONSUMER CREDIT RISK CONSUMER CREDIT RISK 2 ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

Survey of the Credit Scoring • Impairment Analysis • Landscape Capital Requirements • 3

Credit Risk in a Nutshell Exposure Probability Loss Given Credit Loss Given of Default Default [ECL] Default [PD] [LGD] [EAD] The likelihood of The loss to be The loan balance The proportion of moving into default incurred over at the point of the principal-at- over some horizon some horizon default risk that is lost (analogous to 𝑜 𝑟 𝑦 ) 4 ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

Portfolio Loss Distribution "Unexpected Loss" DENSITY IFRS9 E[L] Basel E[L] VaR( α ) PORTFOLIO LOSS 5

Credit Scoring 6

Credit Scoring Purpose: Credit Scoring Model Assessing the risk of default • Risk Group 5 Inputs: Demographic data, e.g., age, income • Behavioural data, e.g., delinquency, utilisation • OBSERVED PD Economic data, e.g., interest rate, GDP • Risk Group 4 Uses: Risk Group 3 Application scoring • Impairment analysis • Risk Group 1 Capital analysis • Risk Group 2 Credit collections • MODEL PD 7 ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

Credit Scoring Modified Logistic Regression Main techniques: Logistic regression • DEFAULT RATE Decision trees • Measures of success: Goodness of fit (e.g., Hosmer-Lemeshow test) • CALENDAR TIME Discriminatory power (e.g., Gini statistic) • default rate log-logistic Standard Logistic Regression Complications: Dealing with varying time horizons • Dealing with time-varying covariates • DEFAULT RATE Some literature: Calibration problem: Crook, Hamilton and Thomas (1992) • Modelling with macroeconomic variables: Malwandla (2016) • CALENDAR TIME default rate logistic 8 ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

Credit Scoring Population Credit Utilisation Credit Utilisation < 20% >= 20% Delinquent on Delinquent on Age < 25 Age >=25 Other Loans = Other Loans = 'Yes' 'No' RG2: PD=2.0% RG1: PD=1.5% In Default on In Default on Number of Number of Other Loans = Other Loans = Months Since Months Since 'Yes' 'No' Delinquent <= 6 Delinquent > 6 RG6: PD=12% RG5: PD=8.0% RG4: PD=5% RG3: PD=3.0% 9 ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

Impairment Provisions 10

Impairment Provisions Analytical complications: Purpose: Three stages of IFRS 9 impairments: • Estimating the credit impairment provision for • Stage 1 [“insignificant” deterioration]: 1 -year EL Modelling with variable horizon IFRS 9 published accounts • Stage 2 [“significant” deterioration]: lifetime EL Modelling with macroeconomic variables • Concerned with estimating the mean of the • Stage 3 [default]: lifetime EL credit loss distribution ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019 11

Capital Requirements 12

Capital Requirements Point-in-Time PD Purpose: Setting the capital requirement • Concerned with estimating the tail of the credit loss distribution • DEFAULT RATE Basel III: Expected Loss: 𝐹 𝑀 = 𝑄𝐸 × 𝐹𝐵𝐸 × 𝑀𝐻𝐸 • Unexpected Loss: U𝑀 𝛽 ≈ 𝐺 −1 𝛽 × 𝐹𝐵𝐸 × 𝑀𝐻𝐸 − 𝐹 𝑀 • Basel-Vasicek framework: TIME 𝑄𝐸 follows a Vasicek distribution • lower (95% CI) upper (95% CI) portfolio default rate 𝐹𝐵𝐸 and 𝑀𝐻𝐸 are assumed to be constant • Risk is measured on a through-the-cycle basis • Through-the-Cycle PD Point-in-time vs through-the-cycle: Point-in-time – more ‘purist’ and forward -looking • Through-the-cycle: more stable, better planning, macroprudential • DEFAULT RATE Some literature: Modelling risk on PiT vs. TTC basis: Malwandla (2016) • TIME lower (95% CI) upper (95% CI) portfolio default rate 13 ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

Re-deriving the Basel-Vasicek Framework Given: …a portfolio of 𝑜 loans… … 𝐸 𝑗 is Bernoulli random variable indicating default on loan 𝑗 … … 𝑞 𝑗 𝐹 is the probability of default on loan 𝑗 … … and 𝐹 is the only systemic risk variable. 1 We are interested in the distribution of 𝑄 = 𝑜 𝑜 σ 𝑗=1 𝐸 𝑗 14 ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

We need an assumption… All loans are homogenous in risk: 𝑞 𝑗 𝐹 = 𝑞 𝐹 . This produces a scaled compound binomial distribution for 𝑄 : ∞ 𝐶 𝑜,𝑞 𝑓 𝑜𝑦 𝑕 𝐹 𝑓 𝑒𝑓 . 𝐺 𝑞 𝑦 = ׬ −∞ 15 ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

And another… The portfolio is infinitely large: 𝑜 → ∞ . By the Law of Large Numbers, this produces: 𝑜 𝑄 = 1 𝑜 ෍ 𝐸 𝑗 → 𝑞 𝐹 . 𝑗=1 16 ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

ҧ And one more… The systemic risk is normally distributed: 𝐹~𝑂 0, 𝜏 2 . This produces the Vasicek distribution: Ф −1 𝑦 −Ф −1 𝑞 , 𝐺 𝑞 𝑦 = Ф 𝜏 where 𝜏 is the volatility of the system ≡ systemic risk 17 ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

Capital Requirement as a Quantile of the Distribution The capital requirement is given by: Q 𝛽 ≈ 𝐺 −1 𝛽 × 𝐹𝐵𝐸 × 𝑀𝐻𝐸 for: 𝜍 1 𝐺 −1 𝛽 = 𝛸 1 − 𝜍 𝛸 −1 𝛽 + 1 − 𝜍 Ф −1 𝑄𝐸 where: 𝜏 1+𝜏 is termed the asset correlation coefficient • 𝜍 = 𝛽 is the chosen capital level (typically 99.9%) • 𝑄𝐸 , 𝐹𝐵𝐸 and 𝑀𝐻𝐸 are portfolio averages • 18 ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

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: 15% 𝑔𝑝𝑠 𝑛𝑝𝑠𝑢𝑕𝑏𝑕𝑓 4% 𝑔𝑝𝑠 𝑠𝑓𝑤𝑝𝑚𝑤𝑗𝑜𝑕 𝜍 = ൞ 𝑔 𝑄𝐸 𝑝𝑢ℎ𝑓𝑠 𝑠𝑓𝑢𝑏𝑗𝑚 𝑓𝑦𝑞𝑝𝑡𝑣𝑠𝑓𝑡 19 ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

The portfolio is infinitely large. The Seven The portfolio is homogenous. Deadly The exposure at default is constant and known. Assumptions 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

DENSITY DENSITY 0,1% 0,1% 21 0,4% 0,4% 0,7% 0,7% 1,0% 1,0% The Large Homogenous Portfolio (LHP) Assumption ACTUARI AL SOCI E TY 2019 CONV E NTI ON 1,3% 1,3% 1,6% 1,6% 1,9% 1,9% 2,2% 2,2% 2,5% 2,5% 2,8% 2,8% LHP Assumption (n = 1,000) Empirical (n = 1000) LHP Assumption (n = 100) 3,1% 3,1% Empirical (n = 100) 3,4% 3,4% 3,7% 3,7% 4,0% 4,0% 4,3% 4,3% DEFAULT RATE DEFAULT RATE 4,6% 4,6% 4,9% 4,9% 5,2% 5,2% 5,5% 5,5% 5,8% 5,8% 6,1% 6,1% LHP (n = 100) LHP (n = 1000) 6,4% 6,4% 6,7% 6,7% 7,0% 7,0% 7,3% 7,3% 7,6% 7,6% 7,9% 7,9% | 8,2% 8,2% 22 - 23 OCTOBER 2019 8,5% 8,5% 8,8% 8,8% 9,1% 9,1% 9,4% 9,4% 9,7% 9,7% 10,0% 10,0% DENSITY DENSITY 0,1% 0,1% 0,4% 0,4% 0,7% 0,7% 1,0% 1,0% 1,3% 1,3% 1,6% 1,6% 1,9% 1,9% 2,2% 2,2% 2,5% 2,5% 2,8% 2,8% LHP Assumption (n = 25,000) Empirical (n = 25000) 3,1% 3,1% LHP Assumption (n = 500) Empirical (n = 500) 3,4% 3,4% 3,7% 3,7% 4,0% 4,0% 4,3% 4,3% DEFAULT RATE DEFAULT RATE 4,6% 4,6% 4,9% 4,9% 5,2% 5,2% 5,5% 5,5% 5,8% 5,8% 6,1% 6,1% LHP (n = 500) LHP (n = 25000) 6,4% 6,4% 6,7% 6,7% 7,0% 7,0% 7,3% 7,3% 7,6% 7,6% 7,9% 7,9% 8,2% 8,2% 8,5% 8,5% 8,8% 8,8% 9,1% 9,1% 9,4% 9,4% 9,7% 9,7% 10,0% 10,0%

Actuarial Techniques in Exogenous Maturity Vintage • Survival Analysis • Consumer Credit Risk 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 + 𝑁 𝑢−𝑡 + 𝐹 𝑢 + 𝑊 • 𝑡 Exogenous component 𝐹 𝑢 modelled via time series • Analytical challenges: Problem: identifiability, Yang (2006), Fu (2008) • Solution: substituting vintage with behavioural score, Malwandla • (e.2020) 24 ACTUARI AL SOCI ETY 2019 CONV ENTI ON | 22 - 23 OCTOBER 2019

EMV: Components Origination (Behavioural) Component Maturity Component DEFAULT RISK DEFAULT RISK BEHAVIOURAL RISK SCORE ACCOUNT MATURITY Exogenous Component Model Accuracy DEFAULT RATE DEFAULT RISK PERIOD (CALENDAR TIME) OBSERVATION DATE (CALENDAR TIME) Exogenous Effect Macroeconomic Fit Actual PD Predicted PD 25 ACTUARI AL SOCI E TY 2019 CONV E NTI ON | 22 - 23 OCTOBER 2019