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Transcript of 1 The Use of Internal Models Comparison of the New Basel Proposals with Internal Credit Portfolio...
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