1. 1 The Use of Internal Models Comparison of the New Basel Proposals with Internal Credit Portfolio Models Michel Crouhy Canadian Imperial Bank of Commerce The Advanced IRB Forum BBA ISDA RMA New York - June 19, 2003

2. 2 IBIS 2006+ for Credit Risk IIInternal Models vs. Regulatory Approaches Agenda

3. 3 BIS 2006+ for Credit Risk I

4. 4 BIS 2006+: Regulatory Credit Risk Capital Computation - Pillar One Standardized approach Standardized approach (external ratings) Internal ratings-based approach Internal ratings-based approach – Foundation approach – Advanced approach Credit risk modeling Credit risk modeling (Sophisticated banks in the future) Minimum Capital Requirement

5. 5 Evolutionary Structure of the Accord Credit Risk Modeling ? Standardized Approach Foundation IRB Approach Advanced IRB Approach Increased level of sophistication

6. 6 Standardized Approach

7. 7 Standardized Approach: New Risk Weights 1 B- is the cut-off rating for sovereigns an banks. It is BB- for corporates. 2 Risk weighting based on risk weighting of sovereign in which the bank is incorporated. Banks incorporated in a given country will be assigned a risk weight one category less favourable than that assigned to claims on the sovereign with a cap of 100% for claims to banks in sovereigns rated BB+ to B- 3 Risk weighting based on the assessment of the individual bank. 4 Claims on banks of a short original maturity, for example less than three months, would receive a weighting that is one category more favourable than the usual risk weight on the bank’s claims subject to a floor of 20%. 5 Supervisory authorities may increase the risk weight above 100% if warranted by default experience in their juridiction.

8. 8 Standardized Approach Retail and retail SMEs exposures are risk weighted at 75% (vs. 100% today) - loan value less than Euro 1 million. Residential mortgages are risk weighted at 35% (vs. 50% today). Commitments under 1 year are risk weighted at 20% (vs. 0 today). Commitments over 1 year are risk weighted at 50% (no change). Unconditionally cancellable commitments are risk weighted at 0% (no change).

9. 9 Shortcomings of the Standardized Approach

10. 10 Shortcomings of the Standardized Approach 1. Not enough differentiation among credit categories in the Standardized Approach (i.e. 6 credit categories are not sufficient). 2. In the Standardized Approach too much capital (e.g. AA at 1.6%) is attributed to investment grade facilities and not enough (e.g. B at 12%) to non-investment grade debt (Banks will have the same incentive as before to play the regulatory arbitrage game).

11. 11 BIS 2006+ 0 1.6 8 16 PER CENT AAA AA A+ A- BBB BB+ BB- B CCC RATING New standardized model Internal rating system & Credit VaR 12 S & P : Note: LGD = 40%

12. 12 Shortcomings of the Standardized Approach Altman et al. (2002) simulated loss distributions for periods 1981-1999 and 1989 - 1991 (recession) Loss rates at the 99.5% confidence levels are: 81-9989-91 AAA to AA- 0% 0% vs. 1.6% A0.35% 0.99% vs. 4% BBB to BB1.7% 2.3% vs. 8% Below BB 11% 13.1% vs. 12% 3. The unrated category receives a risk weight of 100% which is less than what is attributed to non-investment grade facilities rated below BB-.

13. 13 Internal Ratings Based Approach

14. 14 Risk Components Foundation Approach – PD (floor: 3bp) set by Bank – LGD, EAD, M set by Regulator – 45% LGD for Senior Unsecured – 75% LGD for subordinated claims – LGD will be reduced by collateral (Financial or Physical) – EAD = 75% for irrevocable undrawn commitments 1 – M = 2.5 years Advanced Approach – PD (floor: 3 bp), LGD, EAD, M (floor: 1 year - cap: 5 years) all set by Bank Floor – IRB capital requirements for credit risk together with OR and market risk cannot fall below 90% of the current minimim required for credit and market during the first year (80% in the second year) Notes 1 0% credit conversion factor applies for unconditionally and immediately cancelable commitments Internal Ratings-Based Approach

15. 15 Internal Ratings-Based Approach Banks can distinguish separately exposures to large corporates and SMEs (sales of less than Euro 50 million) - SMEs will benefit from a firm- size adjustment in IRB formula with a reduction in capital up to 20%. Within the corporate asset class there are 5 sub- classes of specialized lending: – project finance, – object finance, – commodities finance, – income-producing real estate, and – high-volatility commercial real estate.

16. 16 Standardized vs. Foundation IRB The Foundation Approach charges more capital for non-investment grade facilities and less for investment grade debt than the Standardized Approach BRW = Benchmark Risk Weight Note: 1 Formula supplied by BIS Capital Charge for Standard and Poor’s Rating Categories

17. 17 Risk Weights Standardized vs. Foundation IRB Approach Note: 1 Benchmark set at 0.7% PD, 50% LGD, M=3 years 1

18. 18 Internal Models vs. Regulatory Approaches II

19. 19 Internal Models CreditMetrics (JP Morgan) KMV (KMV Corp.) CreditRisk+ (Credit Suisse First Boston)

20. 20 Comparison of Models Credit migration approachContingent claim approach Actuarial approachReduced-form approach SoftwareCreditMetricsCreditPortfolio- View KMVCreditRisk+Kamakura Definition of Risk Δ Market Value Δ Δ Default losses Credit events Downgrade /default Downgrade /default Δ Continuous default probabilities (EDFs) Δ Actuarial default rate Δ Default intensity Risk driversAsset valuesMacro-factorsAsset valuesExpected default rates Hazard rate Transition probabilities ConstantDriven by macro factors Driven by: -Individual term structure of EDF -Asset value process N/A Correlation of credit events Standard multivariate normal distribution (equity- factor model) Conditional default probabilities function of macro- factors Standard multivariate normal asset returns (asset factor model) Conditional default probabilities function of common risk factors Conditional default probabilities function of macro- factors Recovery rates Random (beta distribution Random (empirical distribution) Random (beta distribution) Loss given default deterministic Loss given default deterministic Interest rates Numerical approach Constant Simulation /analytic Econometric Constant Simulation Econometric Constant Analytic /simulation Econometric Constant Analytic Stochastic Tree-based /simulation Econometric

21. 21 ISDA Experiment

22. 22 ISDA proposed “standard approach” Example: Relative Capital Weights: 99.5% - BBB 3yr = 3.45% - LGD = 100% Weights are average values derived by 6 international banks (Barclays, Chase, CSFB, CIBC, Dresdner and JP Morgan)

23. 23 Foundation IRB attributes more than twice as much capital as Internal Models (ISDA) - 99.5% conf. level BRW = Benchmark Risk Weight

24. 24 Shortcomings of the IRB Approach The capital charge according to the Foundation Approach is twice (1.5 - 2.5) as big as the average economic capital produced by internal models (e.g. ISDA: B at 17.4% vs. FA: B at 27.4%). Inclusion of a 1.5 multiplier in the IRB function (CP2).

25. 25 Calibration in the IRB approach The IRB approach is calibrated to 150% of “model” capital requirements ä the capital requirement (CP2, Paragraph 173) is LGD 50  976.5  N(1.118G(PD) + 1.288)  (1 + 0.047(1 – PD)/PD 0.44 )Capital = 8%  ä the “purely theoretical” capital, as a proportion of LGD, would be just the last two terms ä therefore, there is a multiplier of 0.08  976.5 / (50  100) = 1.5624 ä but, 4% of this is rebated against the granularity adjustment (New Accord, paragraph 515) ä therefore, the real multiplier is 1.5624  (100% - 4%) = 1.499904, i.e. 1.5 Theoretical 99.5% loss contribution Adjusts to 3 years maturity Capital ratio

26. 26 Results of the Second Quantitative Impact Study (QIS2): Percentage change in capital requirements (credit risk only)  Standardized approach: + 6%  IRB Foundation: + 14% (no incentive to adopt IRB Foundation)  IRB Advanced: - 5% Proposed Modifications (November 5, 2001 - no change in CP3):  New corporate risk weight curve: No explicit scaling factor but increased confidence level from 99.5% to 99.9%; asset correlations as inverse function of PD to accomodate SMEs with only one curve (proposed range: 0.1-0.2) - flattening effect on the curve.  New residential mortgage risk weight curve: No explicit scaling factor; same confidence level of 99.5%; no maturity adjustment; fixed correlation of 15%.  Other retail exposures risk weight curve: similar to residential mortgages but correlation decreasing function of PD (proposed range: 0.04-015). Calibration in the IRB approach

27. 27 Results of QIS3: Percentage change in capital requirements  Standardized approach: 0% (11% with OR)  IRB Foundation: -7% (+3% with OR)  IRB Advanced: - 13% (-2% with OR) Results by portfolio: FIRBAIRB  Corporate -9%-14%  Retail-45%-49%  SMEs-15%-13%  Equity+115%+114%  Securitized assets+104%+130% Calibration in the IRB approach

28. 28 Foundation IRB (Modified November 2001) and Internal Models (ISDA) -99.9% conf. level

29. 29 Portfolio Specifications and Input Parameters

30. 30 Benchmark Portfolio 22 Bonds / loans (2 facilities per rating category) Obligors diversified across industries Same correlation matrix for CreditMetrics and KMV Stochastic LGD (mean = 50%, std dev = 25%) Maturity of 1 year and 3 years

31. 31 Credit Rating and Default Rates

32. 32 Transition Matrix Initial Rating Rating at Year End (%) 1234567891011D 187.7012.060.24000000000.01 20.5089.579.710.140.070000000.02 30.041.8992.303.381.690.390.190.030.01000.08 40.020.205.3286.003.202.991.490.320.160.0700.24 50.110.253.844.1882.473.011.502.141.070.800.080.54 60.290.340.871.523.0576.335.255.792.892.270.251.14 70.320.400.871.262.516.9670.147.483.743.883.702.07 80.380.520.870.721.445.4410.8759.378.757.110.613.92 90.350.480.710.601.194.358.6910.7054.4310.021.487.00 100.280.39 0.350.712.154.295.2610.5258.753.2213.69 110.350.170.520.230.461.152.302.535.079.8448.0229.36 D00000000000100.00

33. 33 Zero-coupon Credit Curves

34. 34 Capital Attribution under the Standardized and IRB approaches

35. 35 Summary Comparison of Capital Attributions under the New Basel Accord and the Internal Models 7.4 11.3 17.7 15.3 S&P Equivalent Internal Rating Default Probability AAA10.01 1.6 0.6 0.2 0.5 AA20.02 1.6 1.2 0.4 0.7 A30.08 4.0 2.4 0.9 1.5 BBB40.24 8.0 4.2 2.4 2.8 BBB-50.54 8.0 6.2 5.1 5.9 Investment Grade Portfolio4.6 2.9 1.8 2.3 BB61.14 8.0 8.4 8.7 9.8 BB-72.07 8.0 10.4 13.7 16.3 B83.92 12.0 13.3 19.1 20.0 B-97.00 12.0 17.4 31.1 33.2 CCC1013.70 12.0 24.8 44.6 34.7 CCC-1129.40 12.0 35.8 68.2 43.2 Sub-Investment Grade Portfolio9.7 18.3 30.9 26.2 Standardized Approach IRB - Nov. KMV - 99.9 (%) CreditMetrics - 99.9 Portfolio Facility Rating (%)

36. 36 Conclusion CreditMetrics and KMV produce results that are very close both at the portfolio and at the facility level CreditRisk+ produces results that are dramatically different from CreditMetrics and KMV Capital attribution of the regulatory approaches for investment grade facilities is too high compared with internal models, especially for the Standardized Approach Opposite is true for sub-investment grade facilities - internal models are more onerous than the regulatory models Only for BB rated facilities all the various approaches produce the same capital charge