Types of Scoring

Credit Scoring

• Estimate if customer will pay / no pay based upon various information– Applicant Characteristics– Credit Bureau Information– Repayment behaviour of other customers

• Develop models (scorecards) estimating the probability of default p(Default)

• Typically assign points to each piece of information, add all points and compare with threshold

Judgemental vs. Statistical

• Judgemental– Based upon experience– 5 c’s Character, Capital, Collateral, Capacity ,

Condition– ID, Ability, Intent

• Statistical– Based upon multivariate correlations between input

and risk of default

• Both assume that the future will resemble the past

Types of Credit Scoring

• Judgemental (Qualitative credit scoring)

• Application Scoring

• Behavioural Scoring

• Profit Scoring

• Bankruptcy Prediction

• Fraud Prediction

Application Scoring

• Estimate probability of default at the time the customer applies for the loan

• Use predetermined definition of default– E.g. 90 days past due

• Application variables versus credit reference agency variables

• Snap shot to snap shot

• Static

Example Application Scorecard

Behavioural Scoring

• Existing customers– Already have the credit– Already have products (Hybrid)

• Update risk assessment to take into account the customers recent behaviour

• Uses include– Capital– Credit limits for revolving credit

• Video clip to snap shot• Dynamic

Behavioural Scoring (Cont)

• Estimate future defaults of a given portfolio of customers

• Debt provisioning and Profit Scoring• Many, Many Variables

– Input selection

• Behavioural Scoring can be used for– Authorising accounts for ‘special’ treatment– Setting credit limits– Renewals / Revivals– Collections Strategies

Bankruptcy Prediction

• Binary approach– Predict bankruptcy versus non bankruptcy

given ratios describing financial status of companies

• Multiclass approach– Assign ratings (e.g. AAA, AA, A, BBB, …) to

reflect creditworthiness– Each rating corresponds to a default

probability (PD)

Developing a Rating Based System

• Application and behavioural scoring models provide ranking of customers according to risk

• This was ‘ok’ in the past (e.g. for loan approvals from banks) but Basel II required ‘well calibrated default probabilities’

• Map the scores (or probabilities) of customers to a number of distinct borrower grades / pools

• Decide upon the number of classes and their definition• Impact upon regulatory capital!• Classes should be sufficiently discriminatory and stable

(Migration matrix)

Developing a Rating System

• For retail“For each pool identified, the bank must be able to provide quantitative measures of loss characteristics (PD, LGD and EAD) for that pool. The level of differentiation for IRB purposes must ensure that the number of exposures for a given pool is sufficient to allow for meaningful quantification and validation of the loss characteristics at the pool level. There must be a meaningful distribution of borrowers and exposures across pools. A single pool must not include an undue concentration of the banks total retail exposure” paragraph 409 of the Basel Capital Accord

So What

• Basel II rewards with smaller working capital requirements (Big carrot)

• Basel II sets high standards for scorecard development and monitoring (Big stick)

• Inevitably this means more accurate models and data within credit industry– Opportunity for debt agencies to benefit from these

improvements– Challenge for debt agencies to gain benefits first (and

sustain them)

Pre-processing Data For Credit Scoring

Pre-processing Data For Credit Scoring

• Types of variables• Sampling• Missing Values• Outlier Detection• Feature construction and transformation• Discretion and Grouping of Attributes• Coding Nominal and Ordinal Variables• Segmentation• Definition of Target Variable

Types of Variables

• Continuous– E.g. Income, amount of savings, …

• Discrete– Nominal

• E.g. Purpose of loan, marital status

– Ordinal• E.g. Age encoded as young, middle age and old

– Binary• E.g. Gender

Sampling

• Sample of past customers needs to be a similar as possible to current customers

• Stratified sampling• Timing of sampling

– How far back do I go– Trade off. Many data vs. recent data

• Number of ‘Bads’ verses Number of ‘Goods’– Undersampling verses Oversampling?

• Make sure performance window is long enough to stabilise bad rate!

• Reject Inference

Reject Inference

Reject Inference

• Statistical Methods– Hard Cut Off Augmentation– Parcelling– Nearest Neighbour methods

• Gain Extra Information– CRA

• Apply to everybody!

• Withdrawal inference?

Missing Values

• Keep or Delete or Replace• Keep

– The fact that a variable is missing can be important information!

– Encode variable in a special way• Delete

– When too many variables are missing removing the variable or the observation may be an option

– Horizontally verses Vertically missing values• Replace

– Estimate missing value using imputation procedures– Mean versus Median

Outliers

• Typically due to recording / data entry errors (noise)• Types of Outliers

– Valid observation (E.g. salary of Directors)– Invalid observation (E.g. Age = -2003)– Univariate outliers verses Multivariate outliers

• Detection verses Treatment• Detection

– ‘Orientation Reports’– Histogram, Box Plot, Max, Min

• Treatment– Treat as Missing– Truncation

Discretisation and Grouping of Attribute Values

• Motivation– Group values of discrete variables for robust analysis– Interpretation (e.g. point based scorecard)– Create concept hierarchies (Group low level concepts

e.g. raw age data to higher level concepts such as 'young', 'middle aged', 'old’)

• Also called ‘Coarse Classing’ or ‘Classing’• Methods

– Equal interval binning– Equal frequency binning (histogram equalisation)– Chi-squared analysis– Entropy based discretisation (Decision Tree)

The Binning Method

• E.g. Consider the attribute ‘Income’– 1000, 1200, 1300, 2000, 1800, 1400

• Equal Interval Binning– Bin Width = 500– Bin 1 (1000 – 1500) : 1000, 1200, 1300, 1400– Bin2 (1500 – 2000) 1800, 2000

• Equal Frequency Binning (Histogram equalisation)– 2 Bins– Bin 1 : 1000, 1200, 1300– Bin 2 : 1400, 1800, 200

Recoding Nominal / Ordinal Variables

• Discrete variables– Dummy encoding

• Weights of Evidence (WoE) coding

Dummy Coding

• Set 1 dummy to 0 because of perfect correlation

• Purpose, Job, Marital Status, Residential Status, …

• Many Dummies!• Explosion of data set!

Weights of Evidence (WoE)

• Measure strength of each (grouped) attribute in separating goods and bads

• Higher the WoE means the less risk the attribute has

Weight of Evidence attribute = ln(p_good attribute /p_bad attribute) Where p_good attribute = number of good attribute / number of good total

Where p_bad attribute = number of bad attribute / number of bad total

If p_good attribute > p_bad attribute then WoE > 0If p_good attribute < p_bad attribute then WoE < 0

Weight of Evidence

Interval Interval Interval Bad

Age Obs Obs Goods Good Bads Bads Rate WoE

Missing 50 2.50% 42 2.33% 8 4.12% 0.16 -57.28

18 to 22 200 10.00% 152 8.42% 48 24.74% 0.24 -107.83

23 to 26 300 15.00% 246 13.62% 54 27.84% 0.18 -71.47

27 to 29 450 22.50% 405 22.43% 45 23.20% 0.10 -3.38

30 to 35 500 25.00% 475 26.30% 25 12.89% 0.05 71.34

35 to 44 350 17.50% 339 18.77% 11 5.67% 0.03 119.71

44 plus 150 7.50% 147 8.14% 3 1.55% 0.02 166.08

2,000 1,806 194 0.10

Information Value 0.650

Information Value (IV)

• The Information Value is a measure of the predictive value of a characteristic. It is used to– Judge the appropriateness of the classing– Select predictive characteristics

• The IV is similar to entropy:IV = ∑((p_good attribute – p_bad attribute ) * WoE attribute)

• In reality becomes an arbitrary cut off to filter out variables

• A univariate analysis

Segmentation

• When more than one scorecard is required

• Build a scorecard for each segment separately

• Based upon expert knowledge or based upon statistics

• Beware not to over segment!!!!

Definitions of Bad

• 30 / 60 / 90 days past due• Charge / Write Off• Bankrupt• Claim over £x• Profit based• Negative NPV• Less that x% owed collected• Fraud over £500

Building Regression Scorecards

Linear Regression for Classification

• Y = • Use Ordinary Least Squares (OLS) regression to

estimate• Y = 1 if good payer; Y = 0 if bad payer• Statistical problems

– Residuals are not normally distributed– Residuals have unequal variances

• P can be > 1 and < 0 !!• Regression discriminant analysis

Logistic Regression