Credit scorecard

Credit Scorecard
BY
TUHIN CHATTOPADHYAY, PH.D.
1

Introduction
 Credit scoring means applying a statistical model to assign a risk
score to a credit application. Credit scoring techniques assess the
risk in lending to a particular client.
 They not only identify “good” applications and “bad”
applications (where negative behaviour, e.g., default, is
expected) on an individual basis, but also they forecast the
probability that an applicant with any given score will be “good”
or “bad”.
 These probabilities or scores, along with other business
considerations, such as expected approval rates, profit, churn,
and losses, are then used as a basis for decision making.
2

Types of clients:
 Good and Bad: Based on the client’s number of days after the
due date (days past due, DPD) and the amount past due.
 Indeterminate: On the border between good and bad clients.
 Insufficient: Clients with the very short history, which makes
impossible the correct definition of dependent variable (good /
bad client).
 Excluded: Typically clients with so wrong data as to be misleading
(e.g. frauds). They are also marked as “hard bad”.
 Rejected: Applicants who belong to a category that will not be
assessed by a model (scorecard), e.g. VIPs.
3

Business Objectives
1. Who should get credit?
2. How much credit they should receive?
3. Which operational strategies will enhance the
profitability of the borrowers to the lenders?
4

Research Objectives
1. Applying a statistical model to assign a risk score to a credit
application or an existing credit account
2. Building the statistical model
3. Monitoring the accuracy of one or more statistical models
4. Monitoring the effect that score-based decisions have on key
business performance indicators
5

Research Challenges
 To select the best model (out of Cox Proportional Hazard
Model, logistic regression, decision trees, discriminant analysis,
neural networks, ensemble models etc.) according to some
measure of quality (Gini index, which is most widely used in
Europe, KS, which is most widely used in North America and Lift)
at the time of development.
 To monitor the quality of the model after its deployment into
real business.
6

Research Methodology
Step 1
• Data Partition – Training & Validation
Step 2
• Interactive Grouping – Coarse Coding (“Discretizing”) Predictors
Step 3
• Scorecard – Model Building (Logistic Regression)
Step 4
• Scorecard Evaluation – KS, LC, Gini, Lift
Step 5
• Reject Inference – Fuzzy, Hard Cutoff and Parcelling
Step 6
• Data Partition (2) – Training, Testing & Validation
Step 7
• Research Design – 3 Experiments
Step 8
• Model Building – Cox, Discriminant, CART, LR, NN & Ensembles
Step 9
• Model Comparison – ROC, AUR, AIC, BIC, Gini, Cumulative Lift
Step 10
• Monitoring the Scorecard – Vintage Analysis & Population Analysis
8

Variables for Model
Development
9

Tabulation of Data
 All borrowers should be marked in the target column as
“Good” or “Bad” by a certain rule. For example: all the
borrowers to pay in 30 days, are “Good”, but borrowers
with a delay of more than 90 days are marked as “Bad”.
14

Tabulation of Data
 Historical data should include a set of characteristics and
a target variable. All of scorecard development
methods quantify the relationship between the
characteristics (input columns) and “Good/Bad”
performance (target column).
15

Exclusions
 Certain types of accounts need to be excluded from the
dataset. For example: bank workers or VIP clients records
could be excluded from data set.
16

 Those characteristics, whose usage is not reasonable, should
be marked with caution. For example: on the picture you can
see that the “Good/ Bad” distribution does not depend on the
Home Ownership characteristics.
Don’t Remove but Be Cautious!19

Step 1: Partition the Data
 Training data set: Used for preliminary model fitting.
 Validation data set: Used to prevent a modelling node from
overfitting the training data and to compare models.
 Test data set: used for a final assessment of the model.
 Training: 70/80 & Validation: 30/20
20

Step 2: Interactive Grouping –
Coarse Coding (“Discretizing”)
Predictors/ Binning
 Binning means the process of transforming a numeric
characteristic into a categorical one as well as re-grouping
and consolidating categorical characteristics.
 Initial automatic grouping of input variables into bins to
provide optimal splits.
 Regroup the variables through an interactive interface.
 Screen or select variables.
21

Why Binning is Required?
 Increases scorecard stability: some characteristic values can
rarely occur, and will lead to instability if not grouped together.
 Improves quality: grouping of similar attributes with similar
predictive strengths will increase scorecard accuracy.
 Allows to understand logical trends of “Good/Bad” deviations
for each characteristic.
 Prevents scorecard impairment otherwise possible due to
seldom reversal patterns and extreme values.
 Prevents overfitting(overtraining) possible with numerical
variables.
22

Automatic Binning
 The most widely used automatic binning algorithm is Chi-
merge.
 Chi-merge is a process of dividing into intervals (bins) in the
way that neighbouring bins will differ from each other as
much as possible in the ratio of “Good” and “Bad” records in
them.
 For visual cross-verification of automatic binning results one
can use WOE values
23

Interactive Grouping @
SAS E-Miner
 Initial automatic grouping of input variables into bins to
provide optimal splits.
 Regroup the variables through an interactive interface.
 Screen or select variables.
24

Information Value (IV)
 IV is used to evaluate a characteristic’s overall predictive power
i.e. the characteristic’s ability to separate between good and
bad loans.
 < 0.02 is unpredictive
 0.02 - 0.10 is weakly predictive.
 0.10 and 0.30 is moderately predictive.
 > 0.30 is strongly predictive.
 Let’s Reject if the variable’s IV < 0.10.
 Here L is the number of attributes for the characteristic variable.
26

Weight of Evidence (WOE)
 Weight of evidence (WOE) measures the strength of an
attribute of a characteristic in differentiating good and bad
accounts.
 Weight of evidence is based on the proportion of good
applicants to bad applicants at each group level.
 Negative values indicate that a particular grouping is isolating
a higher proportion of bad applicants than good applicants
i.e. negative WOE values are worse in the sense that
applicants in that group present a greater credit risk.
 For each group i of a characteristic WOE is calculated as
follows:
27

Sharply-varied and illogical WOE
graph after automatic binning
30

Manual Specification of
Cut-Off Value
@ Split Bin Window
31

Smooth and logical WOE
decline after manual correction
35

Decision from Scorecard
Note: A scorecard is scaled with the Odds, Scorecard Points
and Points to Double the Odds properties.
38

Logistic Regression
 The regression coefficients are used to scale the scorecard.
Scaling a scorecard refers to making the scorecard conform
to a particular range of scores.
 Logistic regression yields prediction probabilities for whether or
not a particular outcome (e.g., Bad Credit) will occur.
 Logistic regression models are linear models, in that the logit-
transformed prediction probability is a linear function of the
predictor variable values.
 Thus, a final score card model derived in this manner has the
desirable quality that the final credit score (credit risk) is a
linear function of the predictors, and with some additional
transformations applied to the model parameter, a simple
linear function of scores that can be associated with each
predictor class value after coarse coding.
 So the final credit score is then a simple sum of individual score
values that can be taken from the scorecard.
40

Logistic Regression
 Given a vector of application characteristics x, the probability
of default p is related to vector x by the relationship
• where coefficients wi represent the importance of specific loan
application characteristic coefficients xi in the logistic
regression.
• Three types: Forward, Backward and Stepwise
• Coefficients wi are obtained by using maximum likelihood
estimation (MLE).
41

Regression Coefficients
from the Scorecard Node
42

Score-Points Scaling
 For each attribute, its Weight of Evidence and the
regression coefficient of its characteristic now could be
multiplied to give the score points of the attribute.
 An applicant’s total score would then be proportional to
the logarithm of the predicted bad/good odds of that
applicant.
43

Scaling a Scorecard
Objectives:
1. To determine the odds at a certain score.
2. To determine the points required to double the
odds.
44

Score-Points Scaling Mechanism
 Score points are commonly scaled linearly to take more
friendly (integer) values and conform to industry or company
standards.
 We scale the points such that a total score of 600 points
corresponds to good/bad odds of 50 to 1 and an increase of
the score of 20 points corresponds to a doubling of the
good/bad odds.
 The scorecard points
are scaled so that a
total score of 600
corresponds to
good:bad odds of 30:1
and that an increase of
20 points corresponds
to a doubling of the
good:bad odds.
45

 For the derivation of the scaling rule that transforms the
score points of each attribute, the calculation is as follows:
 Score =
 The scaling rule is implemented in the Properties panel of
the Scorecard node:
Score-Points Scaling Calculation46

Step 4: Scorecard Evaluation 49

Distribution of Functions, KS
 A score of around 2.5 or smaller has a population including
approximately 30% of good clients and 70% of bad clients.
50

In this graph, the X axis shows the credit score values (sums), and the Y axis
denotes the cumulative proportions of observations in each outcome class
(Good Credit vs. Bad Credit) in the hold-out sample. The further apart are the
two lines, the greater is the degree of differentiation between the Good
Credit and Bad Credit cases in the hold-out sample, and thus, the better
(more accurate) is the model.
51

• Kolmogorov-Smirnov statistic is the maximum distance between the empirical
distribution functions for the good applicants and the bad applicants. The
difference is plotted, for all cut-offs, in the Kolmogorov-Smirnov Plot.
• The weakness of reporting only the maximum difference between the curves
is that it provides only a measure of vertical separation at one cutoff value,
but not overall cutoff values. In the plot, the best cutoff is 180. At a cutoff
value of 180, the scorecard best distinguishes between good and bad loans.
52

Lorenz Curve (LC)
 By rejecting 20% of good clients, we reject almost 60% of bad
clients at the same time.
53

Receiver Operating Characteristic
(ROC) Curve
 Illustrates the performance of a binary classifier system as its
discrimination threshold is varied.
 The curve is created by plotting the true positive rate (TPR)
against the false positive rate (FPR) at various threshold
settings.
 The true-positive rate is also known as sensitivity or recall. The
false-positive rate is calculated as (1 - specificity).
54

True
Positive
(Sensitivity,
Recall)
False
Negative
(Type II
Error)
False
Positive
(Type I
Error)
True
Negative
(Specificity)
55

Area Under the Receiver operating
characteristic curve (AUR)
 The closer the curve follows the left-hand
border and then the top border of the
ROC space, the more accurate the test.
 The AUR measures the area below each
of the curves.
 A scorecard that is no better than
random selection has an AUR value equal
to 0.50.
 The maximum value of the AUR is 1.0.
56

Akaike Information Criterion (AIC)
 We start with a set of candidate models, and then find the models' corresponding
AIC values.
 There will almost always be information lost due to using a candidate model to
represent the "true" model (i.e. the process that generates the data). We wish to
select, from among the candidate models, the model that minimizes the
information loss.
 Given a set of candidate models for the data, the preferred model is the one with
the minimum AIC value.
 Suppose that there are R candidate models. Denote the AIC values of those
models by AIC1, AIC2, AIC3, …, AICR. Let AICmin be the minimum of those values.
Then exp((AICmin − AICi)/2) can be interpreted as the relative probability that
the ith model minimizes the (estimated) information loss.
 As an example, suppose that there are three candidate models, whose AIC values
are 100, 102, and 110. Then the second model is exp((100 − 102)/2) = 0.368 times as
probable as the first model to minimize the information loss. Similarly, the third
model is exp((100 − 110)/2) = 0.007 times as probable as the first model to minimize
the information loss.
 The quantity exp((AICmin − AICi)/2) is the relative likelihood of model i.
57

Gini Coefficient
 It takes values between -1 and 1.
 The ideal model, i.e., a scoring function that
perfectly separates good and bad clients, has a
Gini index equal to 1.
 On the other hand, a model that assigns a
random score to the client has a Gini index equal
to 0.
58

Bayesian Information Criterion (BIC)
or Schwarz Criterion (SBC, SBIC)
 When picking from several models, the one with the lowest BIC
is preferred.
 The strength of the evidence against the model with the
higher BIC value can be summarized as follows:
ΔBIC Evidence against higher BIC
0 to 2 Not worth more than a bare mention
2 to 6 Positive
6 to 10 Strong
>10 Very Strong
59

Calculation of Lift Ratio
 Assume that we have a score of 1000 clients, of which 50 are
bad.
 The proportion of bad clients is 5%.
 Sort customers according to score and split into ten groups,
i.e., divide it by deciles of score.
 In each group, in our case around 100 clients, then count bad
clients.
 This will get their share in the group (Bad Rate).
 Absolute Lift in each group is then given by the ratio of the
share of bad clients in the group to the proportion of bad
clients in total.
60

Absolute and Cumulative Lift61

Lift Chart
 Lift is a measure of the effectiveness of a predictive model
calculated as the ratio between the results obtained with and
without the predictive model.
 Lift is the ratio of the percent of targets (that is, bad loans) in
each decile to the percent of targets in the entire data set.
62

Cumulative lift chart
Cumulative lift is the cumulative ratio of the percent of targets (i.e.,
bad loans) up to the decile of interest to the percent of targets in the
entire data set.
 The Cumulative Lift Chart shows you the lift factor of how many
times it is better to use a model in contrast to not using a model.
 The x-coordinate of the chart shows the percentage of the
cumulated number of sorted data records of the current model.
The data records are sorted in descending order by the confidence
that the model assigns to a prediction of the selected value of the
target field.
 The y-coordinate of the Cumulative Lift Chart shows the cumulated
lift factor or the cumulative average percentage of the selected
target field value.
63

Cumulative Lift Chart for a
Single Model
64

Step 5: Reject Inference
 How to deal with the inherent bias when modelling is based on
a training dataset consisting only of those previous applicants
for whom the actual performance (Good Credit vs. Bad Credit)
has been observed;
 There are likely another significant number of previous
applicants, that had been rejected and for whom final "credit
performance" was never observed.
 How to include those previous applicants in the modelling, in
order to make the predictive model more accurate and robust
(and less biased), and applicable also to those individuals.
65

Benefits of Reject Inference 66

Inclusion of Rejects Data
Drag and drop the REJECTS data
source onto the diagram and connect
it with the Reject Inference node. Make
sure that the REJECTS data source is
defined as a SCORE data set.
67

Inference Methods
1. Fuzzy: Allocates weight to observations in the augmented
data set. The weight reflects the observation's tendency to
be “good” or “bad”.
2. Hard Cutoff: Classifies observations as either good or bad
based on a cutoff score.
3. Parceling: Distributes binned, scored rejected applicants into
either a good bin or a bad bin.
68

Rejection Rate
 Specify a value for the Rejection Rate property when using
either the Hard Cutoff or Parceling inference method.
 The Rejection Rate is used as a frequency variable.
 The rate of bad applicants is defined as the number of bad
applicants divided by the total number of applicants.
 The value for the Rejection Rate property must be a real
number between 0.0001 and 1. The default value is 0.3.
69

Fuzzy
 The partial classification information is based on the probability of
being good or bad based on the model built with the
CS_ACCEPTS data set that is applied to the CS_REJECTS data set.
 Fuzzy classification multiplies these probabilities by the user-
specified Reject Rate parameter to form frequency variables.
 This results in two observations for each observation in the Rejects
data. Let p(good) be the probability that an observation
represents a good applicant and p(bad) be the probability that
an observation represents a bad applicant. The first observation
has a frequency variable defined as (Reject Rate)*p(good) and
a target variable of 0. The second observation has a frequency
variable defined as (Reject Rate)*p(bad) and a target value of 1.
 Fuzzy is the default inference method.
70

Parceling
 Distribution is based on the expected bad rates that are
calculated from the scores from the logistic regression model.
 The parameters that must be defined for parcelling vary
according to the Score Range method that one selects in the
Parceling properties group.
 All parcelling classifications require to specify the Rejection
Rate, Score Range Method, Min Score, Max Score, and Score
Buckets properties.
71

Parceling Properties (Score Buckets)
1. Score Range Method: To specify how you want to define the
range of scores to be bucketed.
 Accepts — Distributes the rejected applicants into equal-sized
buckets based on the score range of the CS_ACCEPTS data set.
 Rejects — Distributes the rejected applicants into equal-sized
buckets based on the score range of the CS_REJECTS data set.
 Scorecard — Distributes the rejected applicants into equal-sized
buckets based on the score range that is output by the
augmented data set.
 Manual — Distributes the rejected applicants into equal-sized
buckets based on the range that you input.
2. Score Buckets: To specify the number of buckets that you want to
use to parcel the data set into during attribute classification.
Permissible Score Buckets property values are integers between 1
and 100. The default setting for the Score Buckets property is 25.
72

Step 6: Partition the Data
 Training data set: used for preliminary model fitting.
 Validation data set: used to prevent a modelling node from
overfitting the training data and to compare models.
 Test data set: used for a final assessment of the model.
 60% for training, 20% for validation and 20% for testing
73

Step 7: Experimental Design
 Experiment 1: Data set without any variable transformations or
variable reduction.
 Experiment 2: Data set without any variable transformations,
but eliminated the variables that are weakly correlated with the
target variable.
 Experiment 3: With variable transformations - such as bucketing
for variables that had highly skewed distributions etc.
74

Statistical Design
 In each experiment, eight different data mining tools: neural
networks, decision trees, logistic regression, discriminant analysis,
Cox Proportional Hazard Model and stochastic gradient
boosting, random forest, SVM will be employed.
 Finally, the eight tools will be combined into an ensemble model
to increase the reliability of the classification accuracy by
improving the stability of the three disparate non-linear models.
 The ensemble model averages the posterior probabilities for
class target variable BAD from the six tools.
 Given the posterior probabilities, each case can be classified
into the most probable class.
 So there will be a total of nine comparisons in each of the three
experiments.
75

Step 8: Model Development
1. Cox Proportional Hazard Model:
 Cox model (for short) predicts the probability of failure,
default, or "termination" of an outcome within a specific time
interval.
 An alternative and refinement to logistic regression in
particular when "life-times" for credit performance (until
default, early pay-off, etc.) are available in the training data.
2. Artificial Neural Networks
3. Stochastic Gradient Boosting
4. Discriminant Analysis
5. Logistic Regression
6. Decision Tree
7. Random Forest
8. SVM
76

Classification and Regression Trees
(CART)
78

Why Decision Tree?
 A decision tree may outperform a scorecard in terms of predictive
accuracy because, unlike the scorecard, it detects and exploits
interactions between characteristics.
 In a decision tree model, each answer that an applicant gives
determines what question is asked next. If the age of an applicant
is, for example, greater than 50, the model may suggest granting a
credit without any further questions because the average bad
rate of that segment of applications is sufficiently low. If, on the
other extreme, the age of the applicant is below 25, the model
may suggest asking next about time of employment. Then, credit
might be granted only to those who have exceeded 24 months of
employment, because only in that subsegment of younger adults
is the average bad rate sufficiently low.
 A decision tree model consists of a set of “if ... then ... else” rules
that are still quite straightforward to apply.
 The decision rules also are easy to understand, perhaps even more
so than a decision rule that is based on a total score made up of
many components.
79

Model Comparison with Ensemble
83

The AUCs of benchmark
model and new models
84

Cumulative Lift Chart for Multiple Models
85

Stability and Performance of the
Models 86

Step 10: Monitoring the Scorecard
 Population Stability Reports: To capture and track changes in the
population of applications (the composition of the applicant pool
with respect to the predictors)
 Scorecard Performance: The predictions from the scorecard may
become increasingly inaccurate. Thus, the accuracy of the
predictions from the model must be tracked, to determine when a
model should be updated or discarded (and when a new model
should be built).
 Vintage Analysis (Delinquency Reports): The actual observed rate of
default (Bad Credit) may change over time (e.g., due to economic
conditions).
89

Population Stability Reports
 Population stability reports are used for monitoring trends in credit scoring.
 Over time, economic factors and changes within a financial institution
such as marketing campaigns or credit offers can affect the credit
scoring process.
 The purpose of a population stability report is to detect shifts or trends
within the credit applicant pool and factors related to these.
 With the information from the population stability report, the institution
can update credit scorecards as well as make changes to better suite
the needs of its customer base.
 The report may contain items such as the mean score or a comparison of
actual and expected distribution of scores from the scorecard, a
comparison of actual versus expected distributions of customer
characteristics used in for scoring, approval rates, etc.
90

Vintage Analysis
 A vintage is a group of credit accounts that all originated within
a specific time period, usually a year.
 Vintage analysis is used in credit scoring and refers to the
process of monitoring groups of accounts and comparing
performance across past groups.
 The comparisons take place at similar loan ages, allowing for
the detection of deviation from past performance.
 Typically, a graphical representation is used for this purpose,
such as one showing the relationship between months on the
books and the percentage of delinquent accounts across
multiple vintages.
91

Last but not the Least:
Profit Analysis
 Correct Decision: The bank predicts that a
customer’s credit is in good standing (and
hence would obtain the loan), and the
customer is indeed has good credit.
 Bad Decision: If the model or the manager
makes a false prediction that the customer’s
credit is in good standing, yet the opposite is
true, then the bank will result in a unit loss.
92

Profit Analysis
 Assume that a correct decision of the bank would result in 35% of the
profit at the end of a specific period, say 3–5 years.
 In the second column of the matrix, the bank predicted that the
customer’s credit is not in good standing and declined the loan.
Hence there is no gain or loss in the decision. The data has 70% credit-
worthy (good) customers and 30% not-credit-worthy (bad) customers.
 A manager without any model that gives everybody the loan would
result in the following negative profit per customer: (700*0.35-
300*1.00)/1000 = -55/1000 = -0.055 unit loss.
 This number (-0.055 unit loss) may seem small. But if the average of the
load is $20,000 for this population (n = 1000), then the total loss will be
(-0.055 unit loss)*($20,000 per unit per customer)*(1,000 customers) = -
$1,100,000, which would be a whopping one million and one hundred
thousand dollar loss.
93

Profit Analysis
 Then the total profit would be Profit = True Positive*$20,000*0.35 –
False Positive*$20,000 = 608*$20,000*0.35 – 192*$20,000 = $416,000
 The difference of model vs. no-model is $416,000 – (-$1,100,000) =
$1,516,000, which is about 1.5 million dollars of profit.
94

 The table shows that the Neural Network achieves the best profit at
5% cutoff and the Regression achieves the best profit at the 5% or
10% cutoff. In short, if we use the Neural Network model to select
the top 5% of the customers, then the model would produce a
Total Profit of 5.25 units for each unit of the investment in the
Holdout data (n=300).
 Assume that we have a new population of 1,000 customers with
average loan of $20,000. The Neural Network model would select
the top 5% of the customer and results in a total profit of quite a bit
of money indeed.
 Total Profit = Mean Profit*Cutoff*Population Size =
0.35*0.05*1000*$20,000 = $350,000
96

References
1. Chengwei Yuan (2014), Classification of Bad Accounts in Credit
Card Industry.
2. Chamont Wang, Profit Analysis of the German Credit Data
3. Joshua White and Scott Baugess (2015) Qualified Residential
Mortgage: Background Data Analysis on Credit Risk Retention.
Division of Economic and Risk Analysis (DERA). U.S. Securities and
Exchange Commission
4. Jozef Zurada & Martin Zurada (University of Louisville). How Secure
Are “Good Loans”: Validating Loan-Granting Decisions And
Predicting Default Rates On Consumer Loans. The Review of Business
Information Systems, 2002, Volume 6, Number 3
5. Kocenda, Evzen and Vojtek, Martin, Default Predictors in Retail
Credit Scoring: Evidence from Czech Banking Data (April 18, 2011).
William Davidson Institute Working Paper No. 1015.
98

4. Martin ŘEZÁČ & František ŘEZÁČ (Masaryk University, Brno, Czech
Republic) How to Measure the Quality of Credit Scoring Models.
Finance a úvěr-Czech Journal of Economics and Finance, 61, 2011,
no. 5
5. SAS Institute Inc. 2012. Developing Credit Scorecards Using Credit
Scoring for SAS® Enterprise Miner™ 12.1. Cary, NC: SAS Institute Inc.
6. Statistical Applications of Credit Scoring
http://www.statsoft.com/Textbook/Credit-Scoring
7. William H. Greene (1992) A Statistical Model for Credit Scoring New
York University.
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