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Scoring SystemsChapter 16
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EXAMPLE: CREDIT CARD
APPLICATION
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Chapter 16Scoring Systems
EXAMPLE: CREDIT CARD
APPLICATION
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Description Mathematical methods (scoring systems) Customer selection Allocate resources among customers
Purposes
Replace individual judgment with a cheaper andmore reliable method
Augment individual judgment by variable
reduction
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Introduction
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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 aloan vs customers who defaulted on aloan)
Chapter 16Scoring Systems
Method
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Find variables associated with good/badresults
Determine a simple numerical score thatidentifies the risk (probability) of
good/bad results Determine a risk cut-off level thatmaximizes firm effectiveness
Customers over cut-off accepted, below
cut-off rejected
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Method
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Customer solicitation Lead generation for cold calls, list generation
for mailingsreduces costs by eliminatingunlikely 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 16Scoring Systems
RelevanceUses of Scoring
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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 provisionChapter 16Scoring Systems
Relevance - Breadth of Corporate Use
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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/homewho to accept/reject, level of premium credit
score as a predictor of auto accidents Education Accept/rejecttoo good to go here financial aid as
enticement to attend
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Relevance - Breadth of Corporate Use
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History of Scoring Systems
Developed in 1941 for use by HouseholdFinance Co. (HFC)
Acceptance by banks in the 1970s Profitability
Equal Credit Opportunity Act (ECOA) andRegulation 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 the1980s/90s due to increased computationalability
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Many models derived "in-house U.S. firms
Fair, Isaac and Co.California MDSGeorgia 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
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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
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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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Methods
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Numerical Risk Score
Example: direct mail costs $0.45 perpiece if it lands in the trash and anaverage profit of $20 per positiveresponse, 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.
BadofCostGoodofProfit
BadofCost
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Data Collection:
Dependent Variable: Separate historicalresults into "good" and "bad" groups
(0,1) dependent variable
Independent Variables: Information from
appropriate sources (e.g., creditapplication, purchasing behavior) thatmay be associatedwith outcome
Expensive, time consuming in somecasesChapter 16Scoring Systems 14
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Usual procedure: divide all independent variables into (0,1)
variables
For example: If income < 25,000, then variable IN1 = 1, elseIN1 = 0
If 25,000 < income < 50,000, then variable IN2 = 1, else IN2= 0, etc.
Income Inc
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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 thetwo groups Recursive partitioning - repeatedly splitting into
two groups as alike as possible in terms ofindependent variables, and as different as possiblein terms of the dependent variable
Nested regression or discriminant analysis - moreclosely examines those "on the bubble"
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Models
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Example: Profit $1, Loss $9, so P = .90 Rule: accept all accounts with score >.90
Regression: Dependent variable: 1 if good, 0if badY = 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 (
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Probability of good accountAnn Bob Craig Dave Eileen Frank1.30 .70 .85 .80 .80 -.20
Chapter 16Scoring Systems
Credit Card Account Modeling
Multiple Regression Model
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Paid = 1 * * * * * * *
Fitted Regression Line
Defaulted = 0 * ** * * * *Chapter 16Scoring Systems
Multiple Regression Fit of a PerfectData Set
LoanResult
20 25 30 35 40 45 50Age
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Paid = 1 * * * * * * *
Fitted Regression Line
Defaulted =0 * ** * * * *Chapter 16Scoring Systems
Multiple Regression Fit of a PerfectData Set
LoanResult
20 25 30 35 40 45 50Age
20
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Logistic Regression
Logisitic regressionfits the function:
Which becomes:
Determine the cutoffscore based on themonetaryrelationship between
good and badaccounts
)1(ln
odds
oddsscore
)1(
score
score
e
eodds
718.2e
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Scorecard Example
Calculate the cutoff score Assume that the probability of a good accountwould have to be 90% for approval
The cutoff score would be:
20.2)90.1(
90.lnscorecutoff
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Scorecard Example
Logistic regression gives the followingequation:
Multiply all values X 100 for simplicity
yrs)0.25(5to1010yrs)0.53(er)0.26(labor-er)0.25(manag
ed)0.33(retir5)0.20(26to3-5)0.15(36to556).5(age
ing)0.05(check-C)&(S0.85)0.05(other-home)own(3.18.0score
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Scorecard Example
Base a scorecard on the fitted equation: Everyone starts with 80 points
Residence Own Home+130
Other-5
BankAccounts Savings and Checking with bank+85Checking 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, whoworked for 8 years for his previousemployer would score:
Since 313>220, the loan would beapproved
313253350513080
(5to10yrs)retired56agecheckingownbase
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Other Scoring Models
Decision-Tree Score Cards Follow a path based on demographic
characteristics until a branch ends inacceptance or rejection
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Applicant
Own Home Rent Other than
rent or own
Probability of
good account
0.95 0.89 0.73
DeclineAcct w/ bank No Account
with bank
0.99 0.92
Accept
Recursive Partitioning
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Analyzes customer behaviorinstead of
demographic characteristics ExampleBad 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 16Scoring Systems
Behavioral Scoring
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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 topay
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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Behavioral Scoring
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Problems with Scoring Systems
Good vs. Bad doesnt take into accountunderlying differences in customerprofitability
Screening bias
If certain demographics are not present in thecurrent customer base, theres no way tojudge them with a scoring system
Scoring systems are only valid as long asthe 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 non-
minority customers
Impersonal decision making
Federal Reserve governor denied a Toys RUs credit card
Face Validity: Does the data makesense?
Misuse/nonuse of score cards
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Using SPSS for Logistic Regressionon the MBA S&L caseInitial 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 16Scoring Systems 32
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