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18.2 internal ratings based approach
1.
Copyright © 2018
CapitaLogic Limited This presentation file is prepared in accordance with Chapter 18 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 18 Internal Ratings Based Approach
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 Theory of the IRB approach Retail IRB approach Advanced IRB approach Foundation IRB approach Implementation of the IRB approach
4.
Copyright © 2018
CapitaLogic Limited 4 The IRB theory A bank holds a well diversified debt portfolio A large number of debts Smaller EAD Many debt issuers RMs unified to 1 year Portfolio XCL = Portfolio EAD × LGD × XCDR Portfolio 1-year EL = Portfolio EAD × LGD × PD Portfolio UL = Portfolio XCL - Portfolio 1-year EL
5.
Copyright © 2018
CapitaLogic Limited 5 Single debt UL For each debt k, define A total of NOB debts k k k k k k k k k k k 1-year EL = EAD × LGD × PD XCL = UL EAD × LGD × = XCL - X DR EL C NOB k k=1 EAD = Portfolio EAD k k k LGD LGD XCDR XCDR PD PD
6.
Copyright © 2018
CapitaLogic Limited 6 Portfolio UL NOB NOB k k k=1 k=1 NOB k k=1 Portfolio UL = Portfolio XCL - Portfolio 1-year EL = Portfolio EAD × LGD × XCDR - Portfolio EAD × LGD × PD = EAD × LGD × XCDR - EAD × LGD × PD = EAD × LGD × XCDR - EAD NOB k k=1 NOB NOB k k k k k k k=1 k=1 NOB k k k=1 NOB k k=1 × LGD × PD EAD × LGD × XCDR - EAD × LGD × PD = XCL - 1-year EL = UL
7.
Copyright © 2018
CapitaLogic Limited 7 Exposure at default On balance sheet debt Term loan, mortgage, bond EAD = Principal + Accrued Interest Commitment A promise to lend up to a certain amount Credit card, card line EAD = Drawdown amount + (Credit limit - Drawdown amount) × CCF CCF estimated by bank’s internal model
8.
Copyright © 2018
CapitaLogic Limited 8 Loss given default Estimated by Bank’s internal quantitative model Taking into account collaterals Particularly important for residential mortgage When property value goes up continuously LGD = 0 => Default loss = 0 LGD floor is set artificially to 10%
9.
Copyright © 2018
CapitaLogic Limited 9 Probability of default Estimated by Bank’s internal ratings system PD floor Minimum 0.03% except for a country which has sole discretion on its currency policy
10.
Copyright © 2018
CapitaLogic Limited 10 Residual maturity Effective RM Expected cash flow weighted RM; or Contractual maturity RM floor one year RM cap five years N k k k=1 N k k=1 CF × Tenor RM = CF Example 18.1
11.
Copyright © 2018
CapitaLogic Limited 11 IRB formulas by exposure IRB approach Retail IRB Residential mortgage Other retail exposure A-IRB and F-IRB SME corporate exposure Large financial institution exposure Institution exposure Qualifying revolving retail exposure
12.
Copyright © 2018
CapitaLogic Limited 12 Outline Theory of the IRB approach Retail IRB approach Advanced IRB approach Foundation IRB approach Implementation of the IRB
13.
Copyright © 2018
CapitaLogic Limited 13 Retail exposures Retail Individual person Small business with annual revenue < EUR 5 mn lending from a bank < EUR 1 mn Managed and calculated on a pool basis A large finite homogenous portfolio At least 300 debt issuers per pool EAD, LGD and PD estimated for each pool
14.
Copyright © 2018
CapitaLogic Limited 14 A pool of residential mortgages Example 18.2 -1 -1 CCC = 0.15 Φ PD + Φ 99.9% CCC XCDR = Φ 1 - CCC XCL = EAD × LGD × XCDR 1-year EL = EAD × LGD × PD UL = XCL - 1-year EL CP = 1-year EL CC = 1.06UL
15.
Copyright © 2018
CapitaLogic Limited 15 A pool of qualifying revolving retail exposures Example 18.3 -1 -1 Φ PD + Φ 99.9% CCC XCDR = Φ 1 - CCC XCL = EAD × LGD × XCDR 1-year EL = EAD × LGD × PD UL = XCL - 1-year EL CP = 1-y CCC = ear EL CC = 1.06UL 0.04
16.
Copyright © 2018
CapitaLogic Limited 16 A pool of other retail exposures Example 18.4 -1 -1 Φ PD + Φ 99.9% CCC XCDR = Φ 1 - CCC XCL = EAD × LGD × XCDR 1-year EL = EAD × LGD × PD UL = XCL - 1- CCC = 0.03 + 0. year EL CP = 1-year EL CC = 1.06 13exp -3 U 5PD L
17.
Copyright © 2018
CapitaLogic Limited 17 Outline Theory of the IRB approach Retail IRB approach Advanced IRB approach Foundation IRB approach Implementation of the IRB
18.
Copyright © 2018
CapitaLogic Limited 18 Institution exposure Example 18.5 2 b = 0.11852 - 0.05478ln PD 1 + RM - CP = 1-yea 2.5 b M r AF = 1 EL CC = 1.06UL × - 1.5b MAF -1 -1 Φ PD + Φ 99.9% CCC XCDR = Φ 1 - CCC XCL = EAD × LGD × XCDR 1-year EL = E C A CC = 0.12 1 D × LGD × + exp - PD UL = XCL - 1-year EL 50PD
19.
Copyright © 2018
CapitaLogic Limited 19 SME corporate exposure Example 18.6 2 b = 0.11852 - 0.05478ln PD 1 + RM - 2.5 b MAF = 1 - 1.5b CP = 1-year EL CC = 1.06UL × MAF -1 -1 CCC = 0.12 1 + exp -50PD Φ PD + Φ 99.9% CCC XCDR = Φ 1 - CCC XCL = EAD × LGD × XCDR 1-year EL = EAD S - 5 × LGD × PD UL = XCL - 1-y 0 + 112 ear EL 5 For a SME with total annual revenue < EUR 50 mn S: Total annual revenue in EUR mn
20.
Copyright © 2018
CapitaLogic Limited 20 Large financial institution exposure Example 18.7 2 b = 0.11852 - 0.05478ln PD 1 + RM - 2.5 b MAF = 1 - 1.5b CP = 1-year EL CC = 1.06UL × MAF -1 -1 CCC = 1 + exp -50PD Φ PD + Φ 99.9% CCC XCDR = Φ 1 - CCC XCL = EAD × LGD × XCDR 1-year EL = EAD × LGD × PD UL = XCL - 1-year 0.15 EL For a financial institution with total assets > USD 100 bn
21.
Copyright © 2018
CapitaLogic Limited 21 Credit risk mitigation Reduction of EAD On balance sheet netting Reduction of LGD Collaterals Reduction of PD Default insurance Credit guarantee CDS
22.
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CapitaLogic Limited 22 On balance sheet netting Bilateral netting agreement in place Net EAD Lending EAD = Max - Borrowing EAD 1 - Currency haircut , 0
23.
Copyright © 2018
CapitaLogic Limited 23 Default insurance Credit guarantor/protection independent of debt issuer Substitution framework For both retail and advanced IRB approaches Credit guarantor/protection seller with higher credit quality PD of credit guarantor/protection seller adopted in the calculations of CP and CC Double default framework For advanced IRB approach only CP and CC calculated by double default IRB formulas Example 18.8
24.
Copyright © 2018
CapitaLogic Limited 24 Double default framework Example 18.9 o g g 2 b = 0.11852 - 0.05478ln 1 + RM - 2.5 b Min PD , PD DDF = 0.15 + 160PD CP MAF = 1 - 1.5b CC = 1.06UL × MAF = 0 DDF× o o o -1 -1 o o CCC = 0.12 1 + exp -50PD or S - 50 CCC = 0.12 1 + exp -50PD + or 1125 CCC = 0.15 1 + exp -50PD Φ PD + Φ 99.9% CCC XCDR = Φ 1 - CCC XCL = EAD × LGD × XCDR 1-year EL = EAD × LGD × PD UL = XC L - 1-year EL
25.
Copyright © 2018
CapitaLogic Limited 25 Currency and maturity mis-matches Currency mis-match Protected part reduced by 8% Maturity mis-match Protected part reduced to RM > 0.25 RM < 0.25 Credit risk control ignored simply EAD of the protected part without maturity mis-match Min Protection period of credit risk control, 5 - 0.25 × Min RM of debt, 5 - 0.25 Example 18.10 Example 18.11
26.
Copyright © 2018
CapitaLogic Limited 26 Outline Theory of the IRB approach Retail IRB approach Advanced IRB approach Foundation IRB approach Implementation of the IRB
27.
Copyright © 2018
CapitaLogic Limited 27 Exposure at default Type of commitment CCF (%) 1. Direct credit substitutes 100 2. Transaction related contingencies 50 3. Trade related contingencies 20 4. Asset sales with recourse 100 5. Forward asset purchases 100 6. Partly paid-up securities 100 7. Forward forward deposits placed 100 8. Note issuance and revolving underwriting facilities 75 9. Commitments that are unconditionally cancellable without prior notice 0 10. Other commitments 75* * Different from the standardized approach
28.
Copyright © 2018
CapitaLogic Limited 28 Loss given default 45% for senior debt 75% for subordinated debt Recognized collaterals Financial collaterals in standardized approach IRB collaterals Financial receivables Real estate Physical assets
29.
Copyright © 2018
CapitaLogic Limited 29 Financial collaterals Collateral and credit rating Constituent / residual maturity Corporation and bank (%) Country (%) Debt AAA and AA Up to 1 year 1 0.5 From 1 to 5 years 4 2 Longer than 5 years 8 4 A and BBB Up to 1 year 2 1 From 1 to 5 years 6 3 Longer than 5 years 12 6 BB 15 Equity of a listed company Constituent of a major equity index 15 Not a constituent of major equity indices 25 Others 100 Mutual fund The largest haircut among the investment components
30.
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CapitaLogic Limited 30 Senior debt with financial collaterals EAD - Collateral value 1 - Collateral haircut Max × - Currency haircut 0 LGD = 45% × EAD
31.
Copyright © 2018
CapitaLogic Limited 31 IRB collaterals Lower bound C* (%) Upper bound C** (%) Collateral LGD (%) Financial receivables 0 125 35 Real estate 30 140 35 Physical assets 30 140 40
32.
Copyright © 2018
CapitaLogic Limited 32 Senior debt subject to IRB collaterals * ** ** ** Collateral value C = EAD 45% C less than C LGD = Collateral LGD C greater than C C C 45% × 1 - + Collateral LGD × C in between C C
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CapitaLogic Limited 33 Probability of default and residual maturity PD Following the advanced IRB approach RM 2.5 years; or Following the advanced IRB approach, subject to regulatory approval
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CapitaLogic Limited 34 Outline Theory of the IRB approach Retail IRB approach Advanced IRB approach Foundation IRB approach Implementation of the IRB approach
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CapitaLogic Limited 35 Capital charge calculation approaches Sophist -ication Approach Internal model Regulatory rule High Retail IRB* Advanced IRB EAD, LGD, PD, RM Medium Foundation IRB PD, RM EAD, LGD PD EAD, LGD, RM Low Standardized EAD, CCR * RM not applicable
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CapitaLogic Limited 36 Benefits of the IRB approach Savings on regulatory capital Less capital charge for debts of higher credit quality Material savings on retail lending An exhibition of advanced credit risk management expertise
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CapitaLogic Limited 37 Comparison: capital charge ratio Exposure LGD (%) RM (yr) Approach AA (%) A (%) BBB (%) BB (%) B (%) Retail 90 IRB 0.82 1.66 4.32 10.38 11.79 Standardized 6 6 6 6 6 Institute 45 1 IRB 0.70 1.39 3.52 8.43 12.95 Standardized 1.6 4 4 8 8 75 1 IRB 1.16 2.32 5.86 14.73 21.58 Standardized 1.6 4 4 8 8 Example 18.12, 18.13, 18.14
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CapitaLogic Limited 38 Internal ratings system A consolidated opinion from PD derived from quantitative model Agency credit rating Specialist judgment Internal rating => average PD 7-level AAA, AA, A, BBB, BB, B, C 19-level AAA, AA (+/-), A (+/-), BBB (+/-), BB (+/-), B (+/-), CCC, CC, C
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CapitaLogic Limited 39 IRB system Credit data Rating systems Capital charge engine Regulatory reports EAD, LGD, PD, RM CP, CC
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CapitaLogic Limited 40 Capital charge engine