1.
Scoring Systems
Chapter 16

2.
EXAMPLE: CREDIT CARD
APPLICATION
Chapter 16 – Scoring Systems 1

3.
Chapter 16 – Scoring Systems
EXAMPLE: CREDIT CARD
APPLICATION
2

4.
• Description
− Mathematical methods (scoring systems)
• Customer selection
• Allocate resources among customers
• Purposes
− Replace individual judgment with a cheaper and
more reliable method
− Augment individual judgment by variable
reduction
Chapter 16 – Scoring Systems
Introduction
3

5.
• Typically the decision is either “accept”
or “reject”, in other words a 0 or a 1
• Separate existing customers into two
groups:
− "good" and "bad”
• (Example: Customers who paid back a
loan vs customers who defaulted on a
loan)
Chapter 16 – Scoring Systems
Method
4

6.
• Find variables associated with good/bad
results
• Determine a simple numerical score that
identifies the risk (probability) of
good/bad results
• Determine a risk cut-off level that
maximizes firm effectiveness
• Customers over cut-off accepted, below
cut-off rejected
Chapter 16 – Scoring Systems
Method
5

7.
• Customer solicitation
− Lead generation for cold calls, list generation
for mailings – reduces costs by eliminating
unlikely customers from list
• Customer evaluation
− Credit granting, school admissions
• Resource allocation to customers
− Live telephone call, automated call, letter,…
• Data reduction (Apgar, Apache medical
scores)
− Simplifying information
Chapter 16 – Scoring Systems
Relevance – Uses of Scoring
6

8.
• Types of companies that use scoring
− Retail Banks
• Finance Houses
− Loan approval for credit cards, auto loans, home loans,
small business loans
− Solicitation for products (pre-approved credit cards)
− Credit limit settings and extensions
− Credit usage
− Customer retention
− Collection of bad debts
• Merchant Banks
− Corporate bankruptcy prediction from financial ratios
• Utility Companies
− Credit line establishment
− Length of service provision
Chapter 16 – Scoring Systems
Relevance - Breadth of Corporate Use
7

9.
• IRS
− Income tax audits
• Parole Boards
− Paroling prisoners
• Mass Mail/Telemarketing
• Retailers
− Target market identification (e.g., high incomes)
− Selecting solicitation targets (response rate prediction)
• Insurance
− Auto/home – who to accept/reject, level of premium credit
score as a predictor of auto accidents
• Education
− Accept/reject – “too good to go here” financial aid as
enticement to attend
Chapter 16 – Scoring Systems
Relevance - Breadth of Corporate Use
8

10.
History of Scoring Systems
• Developed in 1941 for use by Household
Finance Co. (HFC)
• Acceptance by banks in the 1970’s
– Profitability
– Equal Credit Opportunity Act (ECOA) and
Regulation B prohibited discrimination in lending
• Discrimination could be proven statistically
• Scoring was designed as a “statistically sound,
empirically based” system of granting credit
• Explosion in the use of scoring in the
1980’s/90’s due to increased computational
ability
Chapter 16 – Scoring Systems 9

11.
• Many models derived "in-house“
• U.S. firms
− Fair, Isaac and Co. – California
− MDS – Georgia
− Mathtec - New Jersey
• European firms
− Scorelink
− Scorex Ltd.
− CCN Systems
• Results
− Bank credit cards: average reduction in ratio of bad
debts/total portfolio of 34%, need fewer lenders
− Direct mail: cuts mailing costs 50% while cutting
response rate only 13%
The Market
Chapter 16 – Scoring Systems 10

12.
• Example:
− Profit from good account, $1; loss from a bad
account, $9
− Approve 100 accounts each with odds of 95%
good
− Profit = 95x$1 - 5x$9 = $50
− Approve 100 accounts each with odds of 80%
good
− Profit = 80x$1 - 20x$9 = -$100
− Approve accounts until
• Expected Profit = Expected Loss from marginal
account
Chapter 16 – Scoring Systems
Methods
11

13.
• Example
− P= Odds of good account
− Expected Profit = Profit x P
− Expected Loss = Loss x (1-P)
− Profit x P = Loss x (1-P)
− Profit x P = Loss - (Loss x P)
− P = Loss / (Profit + Loss)
− P=9/(9+1)=90%
• Conclusion: need accurate assessment of
"odds"
Chapter 16 – Scoring Systems
Methods
12

14.
Numerical Risk Score
• Example: direct mail costs $0.45 per
piece if it lands in the trash and an
average profit of $20 per positive
response, it would be profitable to send
mailings to those with a probability of 2.2%
or higher of responding
%
2
.
2
)
45
.
00
.
20
(
45
.
Bad
of
Cost
Good
of
Profit
Bad
of
Cost




Chapter 16 – Scoring Systems 13

15.
Data Collection:
• Dependent Variable: Separate historical
results into "good" and "bad" groups
– (0,1) dependent variable
• Independent Variables: Information from
appropriate sources (e.g., credit
application, purchasing behavior) that
may be associated with outcome
• Expensive, time consuming in some
cases
Chapter 16 – Scoring Systems 14

16.
• Usual procedure: divide all independent variables into (0,1)
variables
• For example: If income < 25,000, then variable IN1 = 1, else
IN1 = 0
• If 25,000 < income < 50,000, then variable IN2 = 1, else IN2
= 0, etc.
Income Inc<25 25<Inc<50 Inc>50
26,555 0 1 0
33,456 0 1 0
113,000 0 0 1
90,000 0 0 1
15,000 1 0 0
12,000 1 0 0
Chapter 16 – Scoring Systems
Data Collection:
15

17.
• Modeling techniques that give "odds" of a
good/bad outcome
− Multiple regression
− Logistic regression - designed for (0,1) dependent
variable
− Discriminant analysis - develops variable weights
for the maximum separation of the means of the
two groups
− Recursive partitioning - repeatedly splitting into
two groups as alike as possible in terms of
independent variables, and as different as possible
in terms of the dependent variable
− Nested regression or discriminant analysis - more
closely examines those "on the bubble"
Chapter 16 – Scoring Systems
Models
16

18.
• Example: Profit $1, Loss $9, so P = .90
− Rule: accept all accounts with score >.90
• Regression: Dependent variable: 1 if good, 0
if bad
Y = B0 +B1X1 +B2X2...
.40 + .20 Own Home - .75 Other
+ .40 S+C w/bank +.25 S+C + .15 checking
+ .15 (56+yrs old) + .10 (36-55) + .05 (<25)
+ .15 Retired + .05 Mgr - .05 Laborer
+ .10 (10+ yrs job) + .05 (5-10 yrs)
Chapter 16 – Scoring Systems
Credit Card Account Modeling
Multiple Regression Model
17

19.
• Probability of good account
Ann Bob Craig Dave Eileen Frank
1.30 .70 .85 .80 .80 -.20
Chapter 16 – Scoring Systems
Credit Card Account Modeling
Multiple Regression Model
18

20.
Paid = 1 * * * * * * *
Fitted Regression Line
Defaulted = 0 * ** * * * *
Chapter 16 – Scoring Systems
Multiple Regression Fit of a Perfect
Data Set
Loan
Result
20 25 30 35 40 45 50
Age
19

21.
Paid = 1 * * * * * * *
Fitted Regression Line
Defaulted =0 * ** * * * *
Chapter 16 – Scoring Systems
Multiple Regression Fit of a Perfect
Data Set
Loan
Result
20 25 30 35 40 45 50
Age
20

22.
Logistic Regression
• Logisitic regression
fits the function:
• Which becomes:
– Determine the cutoff
score based on the
monetary
relationship between
good and bad
accounts








)
1
(
ln
odds
odds
score
)
1
( 
 score
score
e
e
odds
718
.
2

e
Chapter 16 – Scoring Systems 21

23.
Scorecard Example
• Calculate the cutoff score
– Assume that the probability of a good account
would have to be 90% for approval
– The cutoff score would be:
20
.
2
)
90
.
1
(
90
.
ln
score
cutoff 








Chapter 16 – Scoring Systems 22

24.
Scorecard Example
• Logistic regression gives the following
equation:
• Multiply all values X 100 for simplicity
yrs)
0.25(5to10
10yrs)
0.53(
er)
0.26(labor
-
er)
0.25(manag
ed)
0.33(retir
5)
0.20(26to3
-
5)
0.15(36to5
56)
.5(age
ing)
0.05(check
-
C)
&
(S
0.85
)
0.05(other
-
home)
own
(
3
.
1
8
.
0
score











Chapter 16 – Scoring Systems 23

25.
Scorecard Example
• Base a scorecard on the fitted equation:
– Everyone starts with 80 points
Residence Own Home
+130
Other
-5
Bank
Accounts
Savings and Checking with bank
+85
Checking only
-5
Age 56+
+50
36-55
+15
26-35
-20
Work Retired
+33
Manager
+25
Laborer
-26
Time on Job 10 yrs or more
+53
5-10 yrs on job
+25
Chapter 16 – Scoring Systems 24

26.
Scorecard Example
• A 65 year old retired homeowner with only
a checking account with the bank, who
worked for 8 years for his previous
employer would score:
• Since 313>220, the loan would be
approved
313
25
33
50
5
130
80
(5to10yrs)
retired
56
age
checking
own
base












Chapter 16 – Scoring Systems 26

27.
Other Scoring Models
• Decision-Tree Score Cards
– Follow a path based on demographic
characteristics until a branch ends in
acceptance or rejection
Chapter 16 – Scoring Systems 27

28.
Applicant
Own Home Rent Other than
rent or own
• Probability of
good account
0.95 0.89 0.73
Decline
Acct w/ bank No Account
with bank
0.99 0.92
Accept
Recursive Partitioning
Chapter 16 – Scoring Systems 27

29.
• Analyzes customer behavior instead of
demographic characteristics
• Example – Bad Debt Collection
− Costs (GE Capital 1990):
• $12 billion portfolio
• $1 billion delinquent balances
• $150 million collection efforts
• $400 million write-offs
− Resources:
• Letters (many types)
• Interactive taped phone messages
• (2 levels of severity)
• Live phone calls from a collector
• Legal procedures
Chapter 16 – Scoring Systems
Behavioral Scoring
28

30.
• Daily Volume:
− 50,000 taped calls
− 30,000 live calls
• Need for strategy:
− Too expensive - actual costs and goodwill to
personally call each delinquent
− Customers require different amounts of prodding to
pay
• Results:
− Scoring indicated that more customers should be
handled by "doing nothing“
− Scoring reduced losses by $37 million/year, using
fewer resources and with more customer goodwill
Chapter 16 – Scoring Systems
Behavioral Scoring
29

31.
Problems with Scoring Systems
• “Good” vs. “Bad” doesn’t take into account
underlying differences in customer
profitability
• Screening bias
– If certain demographics are not present in the
current customer base, there’s no way to
judge them with a scoring system
• Scoring systems are only valid as long as
the customer base remains the same
– Update every three to five years
Chapter 16 – Scoring Systems 30

32.
Implementation Problems
• Fairness
– Scoring systems may lock out minorities
– Manual overrides (exceptions) may favor non-
minority customers
• Impersonal decision making
– Federal Reserve governor denied a Toys R
Us credit card
• Face Validity: Does the data make
sense?
• Misuse/nonuse of score cards
Chapter 16 – Scoring Systems 31

33.
Using SPSS for Logistic Regression
on the “MBA S&L” case
Initial screen:
Open file from CD-ROM, chapter16_mbas&l_case_SPSS_format
On menu: Analyze, Regression, Binary Logistic
In the logistic regression menu:
“good” is the dependent variable
Choose independent variables as you see fit
Under “options” the “classification cut-off” is set at 0.5. Insert a cut-
off appropriate for the case data.
Chapter 16 – Scoring Systems 32