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 Customers
2. 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 decline
2. 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)
SCORE
NUMBER OF CUSTOMERS
BAD RATE (%)
GROUP
MEAN
MAX.
MIN.
BASE (1)
CUMULATIVE
BAD (2)
GOOD (3)
20
825
837
821
86,298
86,298
46
86,252
19
816
819
814
126,616
212,914
99
126,517
18
811
812
811
60,653
273,567
39
60,614
17
808
809
807
112,170
385,737
90
112,080
16
804
805
802
112,526
498,263
106
112,420
15
800
801
798
128,083
626,346
157
127,926
14
796
797
795
100,795
727,141
145
100,650
13
792
794
791
97,430
824,571
207
97,223
12
788
790
786
116,575
941,146
360
116,215
11
781
784
777
118,460
1,059,606
602
117,858
10
773
776
769
105,071
1,164,677
936
104,135
9
763
768
759
113,592
1,278,269
1,216
112,376
8
754
758
751
104,613
1,382,882
1,129
103,484
7
746
749
743
100,856
1,483,738
1,307
99,549
6
737
741
733
112,088
1,595,826
1,798
110,290
5
727
731
722
102,617
1,698,443
2,149
100,468
4
713
720
703
114,468
1,812,911
3,414
111,054
3
690
702
675
104,289
1,917,200
4,546
99,743
2
643
674
600
109,672
11,235
98,437
1
520
599
330
106,976
2,026,872
2,133,848
21,131
85,845
50,712
2,083,136
Total
MARGINAL*
0.05
0.08
0.06
0.08
0.09
0.12
0.14
0.21
0.31
0.51
0.89
1.07
1.08
1.3
1.6
2.09
2.98
4.36
10.24
19.75
CUMULATIVE**
CUMULATIVE %
#
GOOD
(4)
BAD
(5)
##
0.05
4.14
0.09
0.07
10.21
0.29
0.07
13.12
0.36
0.07
18.50
0.54
0.08
23.90
0.75
0.09
30.04
1.06
0.09
34.87
1.34
0.11
39.54
1.75
0.13
45.12
2.46
0.17
50.78
3.65
0.24
55.78
5.50
0.31
61.17
7.89
0.37
66.14
10.12
0.43
70.92
12.70
0.52
76.21
16.24
0.61
81.03
20.48
0.76
86.37
27.21
0.96
91.15
36.18
1.46
2.38
95.88
58.33
100
100
K_S
(%)
(4) - (5)
4.05
9.92
12.76
17.96
23.15
28.98
33.53
37.79
42.66
47.13
50.28
53.28
56.02
58.22
59.97
60.55
59.16
54.97
37.55
0
Power of Separation (5/7)
KS Statistics (2)
KS Statistics
100
90
80
70
Cumulative GOOD
50
Cumulative BAD
KS=60.55%
40
30
20
10
20
18
16
14
12
10
8
6
4
0
2
KS %
60
Power of Separation (6/7)
ROC Statistics
ROC Statistics
1
Gini = 2 * (Area
Under Curve – 0.5)
0.9
0.8
0.7
Area Under Curve=88.4%
Hit Rates
0.6
0.5
hitrate
0.4
0.3
0.2
0.1
0
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
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.