Scoring Systems
Chapter 16
EXAMPLE: CREDIT CARD
APPLICATION
Chapter 16 – Scoring Systems
1
EXAMPLE: CREDIT CARD
APPLICATION
Chapter 16 – Scoring Systems
2
Introduction
• 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
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Method
• 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)
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Method
• 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
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Relevance – Uses of Scoring
• 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
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Relevance - Breadth of Corporate Use
• 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
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Relevance - Breadth of Corporate Use
• 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
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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
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The Market
• 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%
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Methods
• 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
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Methods
• 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"
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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
Cost of Bad
.45

 2.2%
Profit of Good  Cost of Bad (20.00  .45)
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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
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Data Collection:
•
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
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Models
• 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"
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Credit Card Account Modeling
Multiple Regression Model
• 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)
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Credit Card Account Modeling
Multiple Regression Model
• Probability of good account
Ann
Bob
Craig
Dave Eileen Frank
1.30
.70
.85
.80
Chapter 16 – Scoring Systems
.80
-.20
18
Multiple Regression Fit of a Perfect
Data Set
* *
Paid = 1
Loan
Result
Defaulted = 0
* **
**
Fitted Regression Line
20
* **
25
Chapter 16 – Scoring Systems
*
30
** *
35 40
Age
45
50
19
Multiple Regression Fit of a Perfect
Data Set
* *
Paid = 1
Loan
Result
Defaulted =0
* **
**
Fitted Regression Line
* **
20
25
Chapter 16 – Scoring Systems
*
30
** *
35 40
Age
45
50
20
Logistic Regression
• Logisitic regression
fits the function:
 odds 
score  ln 

(
1

odds
)


• Which becomes:
e score
odds  score
(e
 1)
– Determine the cutoff
score based on the
monetary
relationship between
good and bad
accounts
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e  2.718
21
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:
 .90 
cutoff score  ln 
 2.20

 (1  .90) 
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Scorecard Example
• Logistic regression gives the following
equation:
score  0.8  1.3(own home) - 0.05(other )  0.85 (S & C) - 0.05(check ing)
 .5(age  56)  0.15(36to5 5) - 0.20(26to3 5)  0.33(retir ed)
 0.25(manag er) - 0.26(labor er)  0.53( 10yrs)  0.25(5to10 yrs)
• Multiply all values X 100 for simplicity
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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
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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:
base  own  checking  age  56  retired  (5to10yrs)
80  130  5  50  33  25  313
• Since 313>220, the loan would be
approved
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Other Scoring Models
• Decision-Tree Score Cards
– Follow a path based on demographic
characteristics until a branch ends in
acceptance or rejection
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Recursive Partitioning
• Probability of
good account
Applicant
0.95
Own Home
0.99
0.92
Acct w/ bank
No Account
with bank
0.89
Rent
0.73
Other than
rent or own
Decline
Accept
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Behavioral Scoring
• 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
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Behavioral Scoring
• 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
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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
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Implementation Problems
• Fairness
– Scoring systems may lock out minorities
– Manual overrides (exceptions) may favor nonminority 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
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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 cutoff appropriate for the case data.
Chapter 16 – Scoring Systems
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