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Copyright © 2018 CapitaLogic Limited
This presentation file is prepared in accordance with
Chapter 7 of the text book
“Managing Credit Risk Under The Basel III Framework, 3rd ed”
Website : https://sites.google.com/site/crmbasel
E-mail : crmbasel@gmail.com
Chapter 7
Credit Ratings
and FICO Scores
Copyright © 2018 CapitaLogic Limited 2
Declaration
 Copyright © 2018 CapitaLogic Limited.
 All rights reserved. No part of this presentation file may be
reproduced, in any form or by any means, without written
permission from CapitaLogic Limited.
 Authored by Dr. LAM Yat-fai (林日辉),
Director, CapitaLogic Limited,
Adjunct Professor of Finance, City University of Hong Kong,
Doctor of Business Administration,
CFA, CAIA, CAMS, FRM, PRM.
Copyright © 2018 CapitaLogic Limited 3
Outline
 Credit assessments
 Credit ratings
 FICO scores
 Appendices
Copyright © 2018 CapitaLogic Limited 4
Probability of default
 Expected loss
 EL ≈ EAD × LGD × PD × RM
 EAD, LGD and RM
 Properties of a credit product
 Designed by the lender
 PD
 Property of a borrower
Copyright © 2018 CapitaLogic Limited 5
What is credit assessment?
 Is a borrower good or bad?
 Good – likely to survive during the lending
period
 Bad – likely to default during the lending period
 What is the PD of a borrower?
 Lending period unified to 1 year
 Subject to annual credit risk review and control
Copyright © 2018 CapitaLogic Limited 6
Credit assessment techniques
Credit assessment
External
(by independent
expert)
Corporate
credit rating
Internal
(by lender)
RetailCorporate
Retail
FICO score
Merton’s corporate
default model
Altman’s Z-score
Credit scoring
Credit scoring
Copyright © 2018 CapitaLogic Limited 7
Outline
 Credit assessments
 Credit ratings
 FICO scores
 Appendices
Copyright © 2018 CapitaLogic Limited 8
Major credit rating agencies
 Global credit rating agencies
 Moody's Investors Service
http://www.moodys.com
 Standard & Poor's
http://www.standardandpoors.com
 Fitch Ratings
http://www.fitchratings.com
 Specialist credit rating agencies
 A.M. Best
http://www.ambest.com
 Dagong Global Credit Rating
http://en.dagongcrg.com
Copyright © 2018 CapitaLogic Limited 9
Solicited rating vs unsolicited rating
 Solicited rating
 A corporation pays a service charge and provides its
confidential information to a credit rating agency for the
purpose of credit assessment in order to obtain a credit
rating
 Potential conflicts of interest
 Business model of the 3 major global CRAs
 Unsolicited rating
 A credit rating agency takes an initiative to rate a
corporation based on publicly available information
 Lenders pay a fee to subscribe credit ratings
Copyright © 2018 CapitaLogic Limited 10
Credit rating scales
Grade S&P’s, Fitch Moody’s
Investment AAA Aaa
AA Aa
A A
BBB Baa
High yield BB Ba
B B
CCC Caa
CC Ca
C C
Copyright © 2018 CapitaLogic Limited 11
Rating definitions (1)
Rating Definition
AAA A corporation rated AAA has an extremely strong
capacity to meet its debt obligations.
AA A corporation rated AA has a very strong capacity to
meet its debt obligations. It differs from a highest
rated borrower only to a small degree.
A A corporation rated A has a strong capacity to meet its
debt obligations but is somewhat more susceptible to
the adverse effects of changes in circumstances and
economic conditions than a borrower in higher rated
categories.
Copyright © 2018 CapitaLogic Limited 12
Rating definitions (2)
Rating Definition
BBB A corporation rated BBB has an adequate capacity to meet its
debt obligations. However, adverse economic conditions or
changing circumstances are more likely to lead to a weakened
capacity of the borrower to meet its debt obligations.
BB A corporation rated BB is judged to have speculative elements
and subject to substantial credit risk.
B A corporation rated B is more vulnerable than a borrower rated
BB, but the borrower currently has the capacity to meet its
debt obligations. Adverse business, financial, or economic
conditions will likely impair the borrower's capacity or
willingness to meet its debt obligations.
Copyright © 2018 CapitaLogic Limited 13
Rating definitions (3)
Rating Definition
CCC A corporation rated CCC starts to experience financial
distress and is dependent upon favorable business,
financial and economic conditions to meet its debt
obligations.
CC A corporation rated CC is currently in financial
distress.
C A corporation rated C is typically in deep financial
distress with very little prospect to meet its debt
obligations.
Copyright © 2018 CapitaLogic Limited 14
Average annual default rates
Credit
quality
Credit
rating
Moody’s (%) S&P’s (%) Fitch (%)
1983 - 2016 1983 - 2016 1990 - 2016
Excellent AAA 0.00 0.00 0.13
Good
AA 0.02 0.02 0.05
A 0.06 0.06 0.06
BBB 0.19 0.18 0.15
Moderate
BB 0.94 0.72 0.73
B 3.56 3.76 2.12
Bad CCC to C 10.54 26.78 21.24
Example 7.2
Example 7.1
Copyright © 2018 CapitaLogic Limited 15
Only 2 AAA corporations
in the world
 Johnson & Johnson
 Microsoft Corporation
These two corporations are richer
than most countries in the world
Copyright © 2018 CapitaLogic Limited 16
Basel III ECAI rating scale
Rating 3-year DR (%)
AAA and AA 0.10
A 0.25
BBB 1.00
BB 7.50
B 20.00
Copyright © 2018 CapitaLogic Limited 17
Basel III ECAI Plus rating scale
Credit quality Credit rating 3-year DR (%) PD (%)
Excellent AAA 0.03 0.0100
Good
AA 0.10 0.0333
A 0.25 0.0834
BBB 1.00 0.3345
Moderate
BB 7.50 2.5652
B 20.00 7.1682
Bad
CCC 40.00 15.6567
CC 65.00 29.5270
C 95.00 63.1597
Example 7.3
Copyright © 2018 CapitaLogic Limited 18
Other credit ratings
Issuer rating
 Financial institutions
 Bank
 Securities firm
 Insurance company
 Governments
 Country
 Super nation
 Municipality
Issue rating
 Corporate bond
 Government bond
 CDO
Copyright © 2018 CapitaLogic Limited 19
Annual country default rates
Credit
quality
Credit
rating
Moody’s (%) S&P’s (%) Fitch (%)
1983 - 2016 1975 - 2016 1995 - 2016
Excellent AAA
0Good
AA
A
BBB
Moderate
BB 0.55 0.5 0.29
B 2.76 2.6 1.30
Bad CCC to C 12.18 37.2 24.14
Copyright © 2018 CapitaLogic Limited 20
10-year country default rates
Credit
quality
Credit
rating
Moody’s (%) S&P’s (%) Fitch (%) Prudent PD
(%)1983 - 2016 1975 - 2016 1995 - 2016
Excellent AAA 0
Good
AA 1.053 0.0 0.00 0.11
A 4.004 5.8 4.00 0.60
BBB 1.628 3.6 3.85 0.39
Moderate
BB 10.928 8.6 4.88 1.15
B 21.367 26.6 8.33 3.05
Bad CCC to C 50.579 79.3 25.00 14.57
 
1
10Prudent PD = 1 - 1 - Maximum of 10-year default rates from Moody's, S&P's, Fitch
Copyright © 2018 CapitaLogic Limited 21
How reliable is credit rating?
 There is NO reliable credit rating
 A credit rating is used as long as it is NOT
very unreliable
 The financial tsunami 2008 has demonstrated
that it cannot solely rely on credit rating to
conduct credit assessment
Copyright © 2018 CapitaLogic Limited 22
Outline
 Credit assessments
 Credit ratings
 FICO scores
 Appendices
Copyright © 2018 CapitaLogic Limited 23
Major retail credit bureaus
 Individual persons
 TransUnion
 Equifax
 Experian
 Small businesses
 Dun & Bradstreet
Copyright © 2018 CapitaLogic Limited 24
Where comes personal credit data?
 Banks’ contribution
 Public records
 Negative data
 Overdue records, bankruptcy records and court
orders
 Positive data
 No. of mortgages and no. of credit cards
Copyright © 2018 CapitaLogic Limited 25
Composition of FICO score
 Payment history (35%)
 The historical records of default, bankruptcy, lawsuit, court order and delayed payment will reduce
the FICO score
 The more recent, frequent and severe the negative payment history is, the lower the FICO score will
be
 Credit utilization (30%)
 A large ratio of outstanding debt amount to total credit limit will reduce the FICO score
 Credit history (15%)
 Credit history is represented by the age of the oldest loan account and the average age of all loan
accounts
 A longer credit history will increase the FICO score
 Credit experience (10%)
 Credit experience means the history of using different types of credit products
 A more diversified credit experience will increase the FICO score
 Recent enquiry (10%)
 The recent enquiries from a large number of loan applications will decrease the FICO score
Copyright © 2018 CapitaLogic Limited 26
FICO scores
Group From To
Annual default
rate (%)
Super prime 740 850 0.4
Prime 680 739 2.8
Alt-A 620 679 7.5
Subprime 550 619 17.0
Deep subprime 350 549 33.8
Copyright © 2018 CapitaLogic Limited 27
Outline
 Credit assessment
 Credit rating
 FICO score
 Appendices
Copyright © 2018 CapitaLogic Limited 28
Copyright © 2018 CapitaLogic Limited 29
Rating migration
 One year migration rate from rating X to
rating Y
No. of corproations rated X 1 year ago and Y 1 year later
No. of corproations rated X 1 year ago
Copyright © 2018 CapitaLogic Limited 30
Rating migration matrix
From
/To (%)
AAA AA A BBB BB B CCC
to C
Default No
rating
AAA 87.05 9.03 0.53 0.05 0.08 0.03 0.05 0.00 3.17
AA 0.52 86.82 8.00 0.51 0.05 0.07 0.02 0.02 3.99
A 0.03 1.77 87.79 5.33 0.32 0.13 0.02 0.06 4.55
BBB 0.01 0.10 3.51 85.56 3.79 0.51 0.12 0.18 6.23
BB 0.01 0.03 0.12 4.97 76.98 6.92 0.61 0.72 9.63
B 0.00 0.03 0.09 0.19 5.15 74.26 4.46 3.76 12.06
CCC
to C
0.00 0.00 0.13 0.19 0.63 12.91 43.97 26.78 15.39
Copyright © 2018 CapitaLogic Limited 31
Aggregated rating migration matrix
From
/To (%)
AAA AA A BBB BB B CCC
to C
Default No
rating
AAA 87.05 96.08 96.61 96.66 96.74 96.77 96.82 96.82 100
AA 0.52 87.34 95.34 95.85 95.90 95.97 95.99 96.01 100
A 0.03 1.80 89.59 94.92 95.24 95.37 95.39 95.45 100
BBB 0.01 0.11 3.62 89.18 92.97 93.48 93.60 93.78 100
BB 0.01 0.04 0.16 5.13 82.11 89.03 89.64 90.36 100
B 0.00 0.03 0.12 0.31 5.46 79.72 84.18 87.94 100
CCC to
C
0.00 0.00 0.13 0.32 0.95 13.86 57.83 84.61 100
Example 7.4
Copyright © 2018 CapitaLogic Limited 32
Interpolation
 Linear interpolation
 2 points define a straight
line
 Cubic interpolation
 4 balanced points define
a balanced curve
0 1
2 3
0 1 2 3
y = a + a x
y = a + a x + a x + a x
Copyright © 2018 CapitaLogic Limited 33
ECAI Plus rating scale
with rating modifiers
Group Rating 3-year DR (%) PD (%)
Excellent AAA 0.0300 0.0100
Good AA+ 0.0678 0.0226
AA 0.1000 0.0333
AA- 0.1341 0.0447
A+ 0.1803 0.0601
A 0.2500 0.0834
A- 0.3692 0.1232
Moderate BBB+ 0.5844 0.1952
BBB 1.0000 0.3345
BBB- 2.0598 0.6914
BB+ 4.1162 1.3913
BB 7.5000 2.5652
BB- 11.0869 3.8413
Poor CCC 40.00 15.6567
CC 65.00 29.5270
C 95.00 63.1597
Example 7.5
Copyright © 2018 CapitaLogic Limited 34
PD vs FICO in the prime range
Middle Probit PD (%)
735 -2.1290 1.6628
730 -2.0854 1.8517
725 -2.0418 2.0585
720 -1.9982 2.2847
715 -1.9546 2.5314
710 -1.9110 2.8000
705 -1.8704 3.0711
700 -1.8301 3.3616
695 -1.7901 3.6722
690 -1.7502 4.0038
685 -1.7107 4.3571
680 -1.6713 4.7329
Example 7.6

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07.2 credit ratings and fico scores

  • 1. Copyright © 2018 CapitaLogic Limited This presentation file is prepared in accordance with Chapter 7 of the text book “Managing Credit Risk Under The Basel III Framework, 3rd ed” Website : https://sites.google.com/site/crmbasel E-mail : crmbasel@gmail.com Chapter 7 Credit Ratings and FICO Scores
  • 2. Copyright © 2018 CapitaLogic Limited 2 Declaration  Copyright © 2018 CapitaLogic Limited.  All rights reserved. No part of this presentation file may be reproduced, in any form or by any means, without written permission from CapitaLogic Limited.  Authored by Dr. LAM Yat-fai (林日辉), Director, CapitaLogic Limited, Adjunct Professor of Finance, City University of Hong Kong, Doctor of Business Administration, CFA, CAIA, CAMS, FRM, PRM.
  • 3. Copyright © 2018 CapitaLogic Limited 3 Outline  Credit assessments  Credit ratings  FICO scores  Appendices
  • 4. Copyright © 2018 CapitaLogic Limited 4 Probability of default  Expected loss  EL ≈ EAD × LGD × PD × RM  EAD, LGD and RM  Properties of a credit product  Designed by the lender  PD  Property of a borrower
  • 5. Copyright © 2018 CapitaLogic Limited 5 What is credit assessment?  Is a borrower good or bad?  Good – likely to survive during the lending period  Bad – likely to default during the lending period  What is the PD of a borrower?  Lending period unified to 1 year  Subject to annual credit risk review and control
  • 6. Copyright © 2018 CapitaLogic Limited 6 Credit assessment techniques Credit assessment External (by independent expert) Corporate credit rating Internal (by lender) RetailCorporate Retail FICO score Merton’s corporate default model Altman’s Z-score Credit scoring Credit scoring
  • 7. Copyright © 2018 CapitaLogic Limited 7 Outline  Credit assessments  Credit ratings  FICO scores  Appendices
  • 8. Copyright © 2018 CapitaLogic Limited 8 Major credit rating agencies  Global credit rating agencies  Moody's Investors Service http://www.moodys.com  Standard & Poor's http://www.standardandpoors.com  Fitch Ratings http://www.fitchratings.com  Specialist credit rating agencies  A.M. Best http://www.ambest.com  Dagong Global Credit Rating http://en.dagongcrg.com
  • 9. Copyright © 2018 CapitaLogic Limited 9 Solicited rating vs unsolicited rating  Solicited rating  A corporation pays a service charge and provides its confidential information to a credit rating agency for the purpose of credit assessment in order to obtain a credit rating  Potential conflicts of interest  Business model of the 3 major global CRAs  Unsolicited rating  A credit rating agency takes an initiative to rate a corporation based on publicly available information  Lenders pay a fee to subscribe credit ratings
  • 10. Copyright © 2018 CapitaLogic Limited 10 Credit rating scales Grade S&P’s, Fitch Moody’s Investment AAA Aaa AA Aa A A BBB Baa High yield BB Ba B B CCC Caa CC Ca C C
  • 11. Copyright © 2018 CapitaLogic Limited 11 Rating definitions (1) Rating Definition AAA A corporation rated AAA has an extremely strong capacity to meet its debt obligations. AA A corporation rated AA has a very strong capacity to meet its debt obligations. It differs from a highest rated borrower only to a small degree. A A corporation rated A has a strong capacity to meet its debt obligations but is somewhat more susceptible to the adverse effects of changes in circumstances and economic conditions than a borrower in higher rated categories.
  • 12. Copyright © 2018 CapitaLogic Limited 12 Rating definitions (2) Rating Definition BBB A corporation rated BBB has an adequate capacity to meet its debt obligations. However, adverse economic conditions or changing circumstances are more likely to lead to a weakened capacity of the borrower to meet its debt obligations. BB A corporation rated BB is judged to have speculative elements and subject to substantial credit risk. B A corporation rated B is more vulnerable than a borrower rated BB, but the borrower currently has the capacity to meet its debt obligations. Adverse business, financial, or economic conditions will likely impair the borrower's capacity or willingness to meet its debt obligations.
  • 13. Copyright © 2018 CapitaLogic Limited 13 Rating definitions (3) Rating Definition CCC A corporation rated CCC starts to experience financial distress and is dependent upon favorable business, financial and economic conditions to meet its debt obligations. CC A corporation rated CC is currently in financial distress. C A corporation rated C is typically in deep financial distress with very little prospect to meet its debt obligations.
  • 14. Copyright © 2018 CapitaLogic Limited 14 Average annual default rates Credit quality Credit rating Moody’s (%) S&P’s (%) Fitch (%) 1983 - 2016 1983 - 2016 1990 - 2016 Excellent AAA 0.00 0.00 0.13 Good AA 0.02 0.02 0.05 A 0.06 0.06 0.06 BBB 0.19 0.18 0.15 Moderate BB 0.94 0.72 0.73 B 3.56 3.76 2.12 Bad CCC to C 10.54 26.78 21.24 Example 7.2 Example 7.1
  • 15. Copyright © 2018 CapitaLogic Limited 15 Only 2 AAA corporations in the world  Johnson & Johnson  Microsoft Corporation These two corporations are richer than most countries in the world
  • 16. Copyright © 2018 CapitaLogic Limited 16 Basel III ECAI rating scale Rating 3-year DR (%) AAA and AA 0.10 A 0.25 BBB 1.00 BB 7.50 B 20.00
  • 17. Copyright © 2018 CapitaLogic Limited 17 Basel III ECAI Plus rating scale Credit quality Credit rating 3-year DR (%) PD (%) Excellent AAA 0.03 0.0100 Good AA 0.10 0.0333 A 0.25 0.0834 BBB 1.00 0.3345 Moderate BB 7.50 2.5652 B 20.00 7.1682 Bad CCC 40.00 15.6567 CC 65.00 29.5270 C 95.00 63.1597 Example 7.3
  • 18. Copyright © 2018 CapitaLogic Limited 18 Other credit ratings Issuer rating  Financial institutions  Bank  Securities firm  Insurance company  Governments  Country  Super nation  Municipality Issue rating  Corporate bond  Government bond  CDO
  • 19. Copyright © 2018 CapitaLogic Limited 19 Annual country default rates Credit quality Credit rating Moody’s (%) S&P’s (%) Fitch (%) 1983 - 2016 1975 - 2016 1995 - 2016 Excellent AAA 0Good AA A BBB Moderate BB 0.55 0.5 0.29 B 2.76 2.6 1.30 Bad CCC to C 12.18 37.2 24.14
  • 20. Copyright © 2018 CapitaLogic Limited 20 10-year country default rates Credit quality Credit rating Moody’s (%) S&P’s (%) Fitch (%) Prudent PD (%)1983 - 2016 1975 - 2016 1995 - 2016 Excellent AAA 0 Good AA 1.053 0.0 0.00 0.11 A 4.004 5.8 4.00 0.60 BBB 1.628 3.6 3.85 0.39 Moderate BB 10.928 8.6 4.88 1.15 B 21.367 26.6 8.33 3.05 Bad CCC to C 50.579 79.3 25.00 14.57   1 10Prudent PD = 1 - 1 - Maximum of 10-year default rates from Moody's, S&P's, Fitch
  • 21. Copyright © 2018 CapitaLogic Limited 21 How reliable is credit rating?  There is NO reliable credit rating  A credit rating is used as long as it is NOT very unreliable  The financial tsunami 2008 has demonstrated that it cannot solely rely on credit rating to conduct credit assessment
  • 22. Copyright © 2018 CapitaLogic Limited 22 Outline  Credit assessments  Credit ratings  FICO scores  Appendices
  • 23. Copyright © 2018 CapitaLogic Limited 23 Major retail credit bureaus  Individual persons  TransUnion  Equifax  Experian  Small businesses  Dun & Bradstreet
  • 24. Copyright © 2018 CapitaLogic Limited 24 Where comes personal credit data?  Banks’ contribution  Public records  Negative data  Overdue records, bankruptcy records and court orders  Positive data  No. of mortgages and no. of credit cards
  • 25. Copyright © 2018 CapitaLogic Limited 25 Composition of FICO score  Payment history (35%)  The historical records of default, bankruptcy, lawsuit, court order and delayed payment will reduce the FICO score  The more recent, frequent and severe the negative payment history is, the lower the FICO score will be  Credit utilization (30%)  A large ratio of outstanding debt amount to total credit limit will reduce the FICO score  Credit history (15%)  Credit history is represented by the age of the oldest loan account and the average age of all loan accounts  A longer credit history will increase the FICO score  Credit experience (10%)  Credit experience means the history of using different types of credit products  A more diversified credit experience will increase the FICO score  Recent enquiry (10%)  The recent enquiries from a large number of loan applications will decrease the FICO score
  • 26. Copyright © 2018 CapitaLogic Limited 26 FICO scores Group From To Annual default rate (%) Super prime 740 850 0.4 Prime 680 739 2.8 Alt-A 620 679 7.5 Subprime 550 619 17.0 Deep subprime 350 549 33.8
  • 27. Copyright © 2018 CapitaLogic Limited 27 Outline  Credit assessment  Credit rating  FICO score  Appendices
  • 28. Copyright © 2018 CapitaLogic Limited 28
  • 29. Copyright © 2018 CapitaLogic Limited 29 Rating migration  One year migration rate from rating X to rating Y No. of corproations rated X 1 year ago and Y 1 year later No. of corproations rated X 1 year ago
  • 30. Copyright © 2018 CapitaLogic Limited 30 Rating migration matrix From /To (%) AAA AA A BBB BB B CCC to C Default No rating AAA 87.05 9.03 0.53 0.05 0.08 0.03 0.05 0.00 3.17 AA 0.52 86.82 8.00 0.51 0.05 0.07 0.02 0.02 3.99 A 0.03 1.77 87.79 5.33 0.32 0.13 0.02 0.06 4.55 BBB 0.01 0.10 3.51 85.56 3.79 0.51 0.12 0.18 6.23 BB 0.01 0.03 0.12 4.97 76.98 6.92 0.61 0.72 9.63 B 0.00 0.03 0.09 0.19 5.15 74.26 4.46 3.76 12.06 CCC to C 0.00 0.00 0.13 0.19 0.63 12.91 43.97 26.78 15.39
  • 31. Copyright © 2018 CapitaLogic Limited 31 Aggregated rating migration matrix From /To (%) AAA AA A BBB BB B CCC to C Default No rating AAA 87.05 96.08 96.61 96.66 96.74 96.77 96.82 96.82 100 AA 0.52 87.34 95.34 95.85 95.90 95.97 95.99 96.01 100 A 0.03 1.80 89.59 94.92 95.24 95.37 95.39 95.45 100 BBB 0.01 0.11 3.62 89.18 92.97 93.48 93.60 93.78 100 BB 0.01 0.04 0.16 5.13 82.11 89.03 89.64 90.36 100 B 0.00 0.03 0.12 0.31 5.46 79.72 84.18 87.94 100 CCC to C 0.00 0.00 0.13 0.32 0.95 13.86 57.83 84.61 100 Example 7.4
  • 32. Copyright © 2018 CapitaLogic Limited 32 Interpolation  Linear interpolation  2 points define a straight line  Cubic interpolation  4 balanced points define a balanced curve 0 1 2 3 0 1 2 3 y = a + a x y = a + a x + a x + a x
  • 33. Copyright © 2018 CapitaLogic Limited 33 ECAI Plus rating scale with rating modifiers Group Rating 3-year DR (%) PD (%) Excellent AAA 0.0300 0.0100 Good AA+ 0.0678 0.0226 AA 0.1000 0.0333 AA- 0.1341 0.0447 A+ 0.1803 0.0601 A 0.2500 0.0834 A- 0.3692 0.1232 Moderate BBB+ 0.5844 0.1952 BBB 1.0000 0.3345 BBB- 2.0598 0.6914 BB+ 4.1162 1.3913 BB 7.5000 2.5652 BB- 11.0869 3.8413 Poor CCC 40.00 15.6567 CC 65.00 29.5270 C 95.00 63.1597 Example 7.5
  • 34. Copyright © 2018 CapitaLogic Limited 34 PD vs FICO in the prime range Middle Probit PD (%) 735 -2.1290 1.6628 730 -2.0854 1.8517 725 -2.0418 2.0585 720 -1.9982 2.2847 715 -1.9546 2.5314 710 -1.9110 2.8000 705 -1.8704 3.0711 700 -1.8301 3.3616 695 -1.7901 3.6722 690 -1.7502 4.0038 685 -1.7107 4.3571 680 -1.6713 4.7329 Example 7.6