scoring systems chapter 16. example: credit card application chapter 16 – scoring systems1

Scoring SystemsChapter 16

EXAMPLE: CREDIT CARD APPLICATION

Chapter 16 – Scoring Systems 1

Chapter 16 – Scoring Systems

EXAMPLE: CREDIT CARD APPLICATION

2

•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


Introduction

3

• 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)


Method

4

• 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


Method

5

• 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


Relevance – Uses of Scoring

6

• 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


Relevance - Breadth of Corporate Use

7

• 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


Relevance - Breadth of Corporate Use

8

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


• 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


• 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


Methods

11

• 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"


Methods

12

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 ofCost Good ofProfit

Bad ofCost


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


• 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


Data Collection:

15

• 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"


Models

16

• Example: Profit $1, Loss $9, so P = .90− Rule: accept all accounts with score >.90

• Regression: Dependent variable: 1 if good, 0 if 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 (<25)+ .15 Retired + .05 Mgr - .05 Laborer+ .10 (10+ yrs job) + .05 (5-10 yrs)


Credit Card Account Modeling Multiple Regression Model

17

• Probability of good account

Ann Bob Craig Dave Eileen Frank

1.30 .70 .85 .80 .80 -.20


Credit Card Account Modeling Multiple Regression Model

18

Paid = 1 * * * * * * *

Fitted Regression Line

Defaulted = 0 * ** * * * *


Multiple Regression Fit of a Perfect Data Set

LoanResult

20 25 30 35 40 45 50Age

19

Paid = 1 * * * * * * *

Fitted Regression Line

Defaulted =0 * ** * * * *


Multiple Regression Fit of a Perfect Data Set

LoanResult

20 25 30 35 40 45 50Age

20

Logistic Regression• Logisitic regression

fits the function:

• Which becomes:– Determine the cutoff

score based on the monetary relationship between good and bad accounts

)1(

lnodds

oddsscore

)1(

score

score

e

eodds

718.2e


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.lnscore cutoff


Scorecard Example• Logistic regression gives the following

equation:

• Multiply all values X 100 for simplicityyrs)0.25(5to1010yrs)0.53(er)0.26(labor-er)0.25(manag

ed)0.33(retir5)0.20(26to3-5)0.15(36to5 56).5(age

ing)0.05(check-C)&(S 0.85 )0.05(other- home)own (3.18.0 score


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


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

313253350513080

(5to10yrs)retired56agecheckingownbase


Other Scoring Models• Decision-Tree Score Cards

– Follow a path based on demographic characteristics until a branch ends in acceptance or rejection


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


• 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


Behavioral Scoring

28

• 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


Behavioral Scoring

29

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


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


Using SPSS for Logistic Regression on 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.


scoring systems chapter 16. example: credit card application chapter 16 – scoring systems1

Documents

scoring systems chapter

use of scoring

scoring systems1 slide

scoring systems9 slide

scoring systems13 slide

scoring systems14 slide

scoring systems10 slide

scoring systems methods