Tier Pricing

By T.Y. Lee

Table of Contents

• Background• Framework• Process • Power of Separation• Adverse Selection • Conclusion

Background (1/2)

• Dual Card Crisis in 2005• Financial Authority order banks to do Tier

Pricing (or Risk Based Pricing) to manage risk

Background (2/2)

• Common response in Taiwan: – separate risk into tiers according to rough

definition of revolvers vs. transactors• Pros: can be easily done and implemented• Cons: loss of opportunities because of low

power of separation – there are other factors determining risk

Framework (1/2)

• What I Did:– In addition to looking at risk, I also looked at

potential revenue (or profit)– Set up a two-dimension framework and developed a

scorecard for each dimension– Risk Scorecard on vertical axis– Revenue (or Profit) Scorecard on horizontal axis– There are 2 phases:

1. Existing Customers2. New Applicants

Framework (2/2)

Process (1/2)

• For existing customers:

– We have their information in-house– Both scorecards are updated monthly with

latest customer information on consumption and payment

– Set different strategies for customers in different cells

– Movements between cells must be monitored

Process (2/2)

• For New Applicants:

– We do not have their information in-house, need to check Joint Credit Information Center (JCIC) for information

– Usually on first come first serve basis– There are 2 stages:

1. To decide whether to approve or decline2. If approved, one should determine the interest

rate and the credit limit

Power of Separation (1/7)

• Key to the success of this framework is the “Power of Separation” of scorecards, especially Risk scorecards –

– assuming other things equal

Power of Separation (2/7)

Power of Separation (3/7)

• How to Measure Power of Separation:– KS (Kolmogorov–Smirnov)

• Advantage: easily understood and practical• Disadvantage: not good with small BAD sample

and not statistically intuitive– ROC (Receiver Operating Characteristics)

• Advantage: statistically intuitive and deals with small BAD sample well

• Disadvantage: difficult to determine rank order– Gini –

• similar to ROC

Power of Separation (4/7)• KS Statistics (1)

MEAN MAX. MIN. BASE (1) CUMULATIVE BAD (2) GOOD (3) MARGINAL* CUMULA-TIVE**

GOOD#

(4)BAD ##

(5)

20 825 837 821 86,298 86,298 46 86,252 0.05 0.05 4.14 0.09 4.0519 816 819 814 126,616 212,914 99 126,517 0.08 0.07 10.21 0.29 9.9218 811 812 811 60,653 273,567 39 60,614 0.06 0.07 13.12 0.36 12.7617 808 809 807 112,170 385,737 90 112,080 0.08 0.07 18.50 0.54 17.9616 804 805 802 112,526 498,263 106 112,420 0.09 0.08 23.90 0.75 23.1515 800 801 798 128,083 626,346 157 127,926 0.12 0.09 30.04 1.06 28.9814 796 797 795 100,795 727,141 145 100,650 0.14 0.09 34.87 1.34 33.5313 792 794 791 97,430 824,571 207 97,223 0.21 0.11 39.54 1.75 37.7912 788 790 786 116,575 941,146 360 116,215 0.31 0.13 45.12 2.46 42.6611 781 784 777 118,460 1,059,606 602 117,858 0.51 0.17 50.78 3.65 47.1310 773 776 769 105,071 1,164,677 936 104,135 0.89 0.24 55.78 5.50 50.289 763 768 759 113,592 1,278,269 1,216 112,376 1.07 0.31 61.17 7.89 53.288 754 758 751 104,613 1,382,882 1,129 103,484 1.08 0.37 66.14 10.12 56.027 746 749 743 100,856 1,483,738 1,307 99,549 1.3 0.43 70.92 12.70 58.226 737 741 733 112,088 1,595,826 1,798 110,290 1.6 0.52 76.21 16.24 59.975 727 731 722 102,617 1,698,443 2,149 100,468 2.09 0.61 81.03 20.48 60.554 713 720 703 114,468 1,812,911 3,414 111,054 2.98 0.76 86.37 27.21 59.163 690 702 675 104,289 1,917,200 4,546 99,743 4.36 0.96 91.15 36.18 54.972 643 674 600 109,672 2,026,872 11,235 98,437 10.24 1.46 95.88 58.33 37.551 520 599 330 106,976 2,133,848 21,131 85,845 19.75 2.38 100 100 0

Total 50,712 2,083,136

# Cumulative good rate = Cumulative good in column (3) / 2,083,136## Cumulative bad rate = Cumulative bad in column (2) / 50,712

GROUPK_S(%)

(4) - (5)

* Marginal bad rate = Bad in column (2) / Base in column (1)

SCORE NUMBER OF CUSTOMERS BAD RATE (%) CUMULATIVE %

** Cumulative bad rate = Cumulative bad / Cumulative number of customers

Power of Separation (5/7)

KS Statistics (2)

KS Statistics

0

10

20

30

40

50

60

70

80

90

100

2 4 6 8 10 12 14 16 18 20

KS

% Cumulative GOODCumulative BAD

KS=60.55%

Power of Separation (6/7)ROC Statistics

ROC Statistics

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.05 0.11 0.17 0.23 0.29 0.35 0.41 0.47 0.54 0.62 0.73 0.87 0.96

Type II Error

Hit

Rat

es

hitrate

Area Under Curve=88.4%

Gini = 2 * (Area Under Curve – 0.5)

Power of Separation (7/7)Citi Benchmarks

Adverse Selection (1/5)

• An Example:– Banks A & B are targeting potential customers

1 & 2– Both banks use scorecards, but the one used

in Bank A is more accurate than the one used in Bank B

– Customer 1 is actually riskier than customer 2– Customer 1 eventually defaults in the future

but customer 2 remains in good standing

Adverse Selection (2/5)

– Bank A correctly identifies that customer 1 is riskier because its model is more accurate

– Unfortunately Bank B did not because its model is inferior

Adverse Selection (3/5)

– Scenario 1:• Bank B approves customer 1’s application but

reject customer 2’s• Bank A approves customer 2’s application but

reject customer 1’s• Bank A makes profits on customer 2 and avoids

default loss on customer 1• While Bank B suffers default loss on customer 1

and misses opportunity of doing business with customer 2

• Scenario 1 is called adverse selection

Adverse Selection (4/5)

– Scenario 2:• Both banks approve both customers’ application • Due to Risk Based Pricing Bank A charges

customer 2 a lower interest rate and higher rate for customer 1

• Bank B charges customer 2 a higher rate than Bank A and customer 1 a lower rate than Bank A

• Customer 2 does business with Bank A only because of lower interest rate; while customer 1 does business with Bank B only because of lower interest rate as well

Adverse Selection (5/5)

– Scenario 2 (cont’d):• Customer 1 eventually defaults• Bank B suffers loss from customer 1 while Bank A

make profits from customer 2• Scenario 2 is also called adverse selection

Conclusion

• One should look at both risk and reward at the same time to have the whole picture

• Scorecards are powerful tools, if one knows how to use it

Q & A

Appendix

• Revolvers• Transactors

Revolvers

• Different banks may have different definitions, such as:– Ever have balance greater than 0 after

payment in the past 3 month– Ever have balance greater than 0 after

payment in the past 6 month– Ever have balance greater than 1,000 after

payment in the past 3 month– Etc.

Transactors

• Different banks may have different definitions, such as:– Never have balance greater than 0 after

payment in the past 3 month– Never have balance greater than 0 after

payment in the past 6 month– Never have balance greater than 1,000 after

payment in the past 3 month– Etc.