1

The Use of Internal ModelsComparison of the New Basel Proposals with Internal Credit Portfolio Models

Michel CrouhyCanadian Imperial Bank of Commerce

The Advanced IRB ForumThe Advanced IRB ForumBBA ISDA RMABBA ISDA RMA

New York - June 19, 2003New York - June 19, 2003

2

I BIS 2006+ for Credit Risk

II Internal Models vs. Regulatory

Approaches

Agenda

3

BIS 2006+ for Credit Risk

I

4

BIS 2006+: Regulatory Credit Risk Capital Computation - Pillar One

Standardized approachStandardized approach

(external ratings)

Internal ratings-based approachInternal ratings-based approach– Foundation approach

– Advanced approach

Credit risk modeling Credit risk modeling

(Sophisticated banks in the future)

Minimum Capital

Requirement

5

Evolutionary Structure of the Accord

Credit Risk Modeling ?Credit Risk Modeling ?

Standardized ApproachStandardized Approach

Foundation IRB ApproachFoundation IRB Approach

Advanced IRB ApproachAdvanced IRB Approach

Increased level of sophistication

6

Standardized Approach

7

Standardized Approach:New Risk Weights

Assessment

Claim AAA

to

AA-

A+ to A- BBB+

to

BBB-

BB+ to

BB- (B-)1

Below BB-

(B-)1

Unrated5

Sovereigns 0% 20% 50% 100% 150% 100%

Option 12 20% 50% 100% 100% 150% 100%

Banks Option 23 20% 50%4 50%3 100%3 150% 50%3

Corporates 20% 50% 100% 100% 150% 100%

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

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

Shortcomings of the Standardized Approach

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

BIS 2006+

0

1.6

8

16

PER CENT

AA

A

AA

A+ A-

BB

B

BB

+

BB

- B

CC

C

RATING

New standardized model Internal rating system & Credit VaR

12

S & P :

Note: LGD = 40%

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:

81-99 89-91 AAA to AA- 0% 0% vs. 1.6% A 0.35% 0.99% vs. 4% BBB to BB 1.7% 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

Internal Ratings Based Approach

14

Risk ComponentsRisk Components

• Foundation ApproachFoundation 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 ApproachAdvanced Approach– PD (floor: 3 bp), LGD, EAD, M (floor: 1 year - cap: 5 years) all set by Bank

• FloorFloor– 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)

Notes1 0% credit conversion factor applies for unconditionally and immediately cancelable commitments

Internal Ratings-Based Approach

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

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

Standardized Foundation

S&P Rating

1 YearHistorical

DefaultProbability

%

RiskWeight

%

Capitalcharge Per

$100 ofAsset Value

CorporateBRW RiskWeight1%

IRB CapitalCharge per

$100 of AssetValue

(LGD = 50%)

FoundationCapitalCharge

Divided by

StandardizedCapitalCharge

AAA .01 20 1.6 7 0.56 .35

AA .03 20 1.6 14 1.12 .70

A .04 50 4 17 1.34 .34

BBB .22 100 8 48 3.83 .48

BBeenncchhmmaarrkk ..7700 110000 88 110000 88 11

BB .98 100 8 123 9.87 1.23

B 5.30 150 12 342 27.40 2.28

CCC 21.94 150 12 625 50.00 4.17

17

Risk WeightsStandardized vs. Foundation IRB Approach

Risk weights for corporates under IRB

0

8

16

24

32

40

48

56

Ca

pit

al C

ha

rge

Foundation Standardised

Note: 1 Benchmark set at 0.7% PD, 50% LGD, M=3 years

1

18

Internal Models vs. Regulatory Approaches

II

19

Internal Models

CreditMetrics (JP Morgan)

KMV (KMV Corp.)

CreditRisk+ (Credit Suisse First Boston)

20

Comparison of ModelsComparison of ModelsCredit migration approach Contingent claim

approachActuarial approach Reduced-form

approach

Software CreditMetrics CreditPortfolio-View

KMV CreditRisk+ Kamakura

Definition ofRisk

Δ Market Value Δ Market Value Δ Market Value Default losses Default losses

Creditevents

Downgrade/default

Downgrade/default

Δ Continuous defaultprobabilities (EDFs)

Δ Actuarial defaultrate

Δ Default intensity

Risk drivers Asset values Macro-factors Asset values Expected defaultrates

Hazard rate

Transitionprobabilities

Constant Driven by macrofactors

Driven by:

-Individual termstructure of EDF

-Asset value process

N/A N/A

Correlationof creditevents

Standardmultivariate normaldistribution (equity-

factor model)

Conditional defaultprobabilities

function of macro-factors

Standard multivariatenormal asset returns(asset factor model)

Conditional defaultprobabilities

function of commonrisk factors

Conditional defaultprobabilities

function of macro-factors

Recoveryrates

Random (betadistribution

Random(empirical

distribution)

Random (betadistribution)

Loss given defaultdeterministic

Loss given defaultdeterministic

Interestrates

Numericalapproach

Constant

Simulation/analytic

Econometric

Constant

Simulation

Econometric

Constant

Analytic/simulation

Econometric

Constant

Analytic

Stochastic

Tree-based/simulation

Econometric

21

ISDA Experiment

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)

Prob. Def. % 0.5 Yr 0.5-1 Yr 1-2 Yr 2-3 Yr 3-4 Yr 4-5 Yr 5-6 Yr 6-7 Yr 7-8 Yr 8-9 Yr > 9 Yr

6 8 12 17 21 25 28 32 36 40 43

9 12 17 23 29 35 40 46 51 56 60

13 17 24 31 38 46 52 58 66 73 80

16 20 28 36 44 52 59 65 74 81 89

18 24 32 41 49 58 65 73 81 89 98

22 29 38 47 56 65 73 81 91 100 109

27 34 45 56 66 76 85 94 104 114 123

36 46 59 72 86 97 108 119 130 140 151

48 60 80 100 118 134 149 164 178 191 203

72 86 108 130 150 168 186 202 216 230 241

100 119 145 172 195 216 236 254 269 283 294

140 163 190 215 238 257 275 292 305 317 327

181 207 231 253 273 290 307 321 331 342 351

240 271 293 312 330 345 359 371 379 388 395

370 409 420 430 440 450 457 463 466 473 476

662 716 719 721 724 726 727 727 727 727 727

1083 1163 1164 1166 1166 1168 1168 1168 1168 1168 1168

1619 1718 1718 1718 1718 1718 1718 1718 1718 1718 1718

0.00 0.025

0.025 0.035

0.03 5 0.045

0.04 5 0.055

0.055 0.065

0.065 0.085

0.085 0.115

0.115 0.165

0.165 0.255

0.255 0.405

0.405 0.635

0.635 0.915

0.915 1.335

1.335 1.945

1.945 3.875

3.875 7.705

7.705 14.995

14.995 20.000

23

Foundation IRB attributes more than twice as much capital as Internal Models (ISDA) - 99.5% conf. level

BRW = Benchmark Risk Weight

Foundation IRB ISDA

S&P Rating 1 Year

Historical

Default

Probability

%

Corporate

BRW Risk

Weight1

%

IRB Capital

Charge per

$100 of Asset

Value

(LGD=50%)

Capital

Charge

(LGD=50%)

Foundation

IRB Capital

Charge

Divided by

ISDA Capital

Charge

AAA 0.01 7 0.56 0.22 2.5

AA 0.03 14 1.12 0.43 2.7

A 0.04 17 1.34 0.57 2.4

BBB 0.22 48 3.83 1.95 2.0

Benchmark 0.70 100 8 4.41 1.8

BB 0.98 123 9.87 5.34 1.8

B 5.30 342 27.40 17.74 1.5

CCC3 21.94 694 50 50 1

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

Calibration in the IRB approachThe IRB approach is calibrated to 150% of “model” capital requirements the capital requirement (CP2, Paragraph 173) is

LGD

50976.5 N(1.118G(PD) + 1.288) (1 + 0.047(1 – PD)/PD0.44)Capital = 8%

the “purely theoretical” capital, as a proportion of LGD, would be just the last two terms

therefore, there is a multiplier of 0.08 976.5 / (50 100) = 1.5624 but, 4% of this is rebated against the granularity adjustment (New Accord,

paragraph 515) therefore, the real multiplier is 1.5624 (100% - 4%) = 1.499904, i.e. 1.5

Theoretical 99.5% loss

contribution

Adjusts to 3 years

maturityCapital ratio

26

Results of the Second Quantitative Impact Study (QIS2):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 Proposed Modifications (November 5, 2001 - no change in CP3): 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

Results of QIS3: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: Results by portfolio: FIRB AIRB

Corporate -9% -14%

Retail -45% -49%

SMEs -15% -13%

Equity +115% +114%

Securitized assets +104% +130%

Calibration in the IRB approach

28

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

Foundation IRB ISDA

S&P Rating 1 Year

Historical

Default

Probability

%

Corporate

BRW Risk

Weight1

%

IRB Capital

Charge per

$100 of Asset

Value

(LGD=50%)

Capital

Charge2

(LGD=50%)

Foundation

IRB Capital

Charge

Divided by

ISDA Capital

Charge

AAA 0.01 10 (7) 0.83 0.33 2.5

AA 0.03 18 (14) 1.45 0.57 2.5

A 0.04 21 (17) 1.68 0.74 2.3

BBB 0.22 50 (48) 4.00 2.49 1.6

Benchmark 0.70 86 (100) 6.88 5.40 1.3

BB 0.98 99 (123) 7.90 6.46 1.2

B 5.30 190 (342) 15.20 21.75 0.7

CCC3 21.94 392 (694) 31.30 50 0.6

29

Portfolio Specifications and Input Parameters

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

Credit Rating and Default RatesDefault Rate

CreditRating

S&PEquivalent

Mean (%) StandardDeviation (%)

0 Sovereign 0 0

1 AAA 0.01 0

2 AA 0.02 0.01

3 A 0.08 0.04

4 BBB 0.24 0.12

5 BBB- 0.54 0.27

6 BB 1.14 0.57

7 BB- 2.07 1.03

8 B 3.92 1.96

9 B- 7.0 3.50

10 CCC 13.7 6.85

11 CCC- 29.4 14.68

Default 100 N/A

InvestmentGrade

Sub-investmentGrade

32

Transition Matrix

InitialRating

Rating at Year End (%)

1 2 3 4 5 6 7 8 9 10 11 D

1 87.70 12.06 0.24 0 0 0 0 0 0 0 0 0.01

2 0.50 89.57 9.71 0.14 0.07 0 0 0 0 0 0 0.023 0.04 1.89 92.30 3.38 1.69 0.39 0.19 0.03 0.01 0 0 0.084 0.02 0.20 5.32 86.00 3.20 2.99 1.49 0.32 0.16 0.07 0 0.245 0.11 0.25 3.84 4.18 82.47 3.01 1.50 2.14 1.07 0.80 0.08 0.546 0.29 0.34 0.87 1.52 3.05 76.33 5.25 5.79 2.89 2.27 0.25 1.147 0.32 0.40 0.87 1.26 2.51 6.96 70.14 7.48 3.74 3.88 3.70 2.078 0.38 0.52 0.87 0.72 1.44 5.44 10.87 59.37 8.75 7.11 0.61 3.929 0.35 0.48 0.71 0.60 1.19 4.35 8.69 10.70 54.43 10.02 1.48 7.0010 0.28 0.39 0.39 0.35 0.71 2.15 4.29 5.26 10.52 58.75 3.22 13.6911 0.35 0.17 0.52 0.23 0.46 1.15 2.30 2.53 5.07 9.84 48.02 29.36D 0 0 0 0 0 0 0 0 0 0 0 100.00

33

Zero-coupon Credit Curves

Credit Rating

Term 1 2 3 4 5 6 7 8 9 10 11

1 6.8 6.8 7.0 7.3 7.5 8.0 8.8 9.5 11.8 13.2 19.7

2 6.8 6.8 7.1 7.3 7.5 8.2 9.2 9.7 12.0 13.4 20.03 6.8 6.9 7.1 7.4 7.6 8.4 9.4 9.9 12.2 13.6 20.45 6.9 7.0 7.3 7.6 7.8 8.5 9.5 10.3 12.6 14.0 21.27 6.9 7.1 7.4 7.7 8.0 9.0 9.7 10.5 12.8 14.2 21.510 7.0 7.3 7.9 8.1 8.4 9.5 11.2 12.1 14.4 15.8 24.615 7.0 7.3 7.8 8.1 8.4 9.8 11.6 12.5 14.8 16.2 25.420 7.0 7.3 7.9 8.2 8.5 10.1 12.3 13.4 15.7 17.1 27.130 7.1 7.4 7.9 8.4 8.8 11.6 16.6 20.3 22.6 24.0 40.9

34

Capital Attribution under the Standardized and IRB approaches

Exposure

S&P Equivalent

Internal Rating

Default Probability

(%) ($) ($) (%) ($) (%) ($)

AAA 1 0.01 2 MM 1.6 32,000 0.4 8,000 0.6 12,000

AA 2 0.02 2 MM 1.6 32,000 0.9 18,000 1.2 23,600

A 3 0.08 2 MM 4.0 80,000 2.0 40,000 2.4 48,000

BBB 4 0.24 2 MM 8.0 160,000 4.0 80,000 4.2 84,000

BBB- 5 0.54 2 MM 8.0 160,000 6.8 136,000 6.2 123,000

Investment Grade Portfolio 4.6 464,000 2.8 282,000 2.9 290,600

BB 6 1.14 2 MM 8.0 160,000 10.9 213,000 8.4 167,400

BB- 7 2.07 2 MM 8.0 160,000 15.8 316,000 10.4 208,000

B 8 3.92 2 MM 12.0 240,000 23.0 460,000 13.3 265,200

B- 9 7.00 2 MM 12.0 240,000 32.0 640,000 17.4 347,600

CCC 10 13.70 2 MM 12.0 240,000 45.1 902,000 24.8 495,200

CCC- 11 29.40 2 MM 12.0 240,000 50.0 1,000,000 35.8 715,400

Sub-investment Grade Portfolio 9.7 1,160,000 29.5 3,536,000 18.3 2,198,800

Total Portfolio 7.4 1,624,000 17.3 3,818,000 11.3 2,489,400

IRB - Nov.

(%)

Facility Rating Standardized Approach IRB - Jan.

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

AAA 1 0.01 1.6 0.6 0.2 0.5 AA 2 0.02 1.6 1.2 0.4 0.7 A 3 0.08 4.0 2.4 0.9 1.5 BBB 4 0.24 8.0 4.2 2.4 2.8 BBB- 5 0.54 8.0 6.2 5.1 5.9 Investment Grade Portfolio 4.6 2.9 1.8 2.3

BB 6 1.14 8.0 8.4 8.7 9.8 BB- 7 2.07 8.0 10.4 13.7 16.3 B 8 3.92 12.0 13.3 19.1 20.0 B- 9 7.00 12.0 17.4 31.1 33.2 CCC 10 13.70 12.0 24.8 44.6 34.7 CCC- 11 29.40 12.0 35.8 68.2 43.2

Sub-Investment Grade Portfolio 9.7 18.3 30.9 26.2

Standardized Approach IRB - Nov. KMV - 99.9

(%) (%)

CreditMetrics - 99.9

Portfolio

Facility Rating

(%) (%)

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