1. Capital Requirements Under
Basel II:
Evaluation Of Capital Requirement to Default
Probability, Loss Given Default and Maturity for
SME and Other Retail Asset Classes
Maggie Kriebelt
October 2011

2. Minimum Requirements for Internal
Rating Systems for Basel II
 Minimum 7 rating classes for non-defaulted borrowers
 No excessive concentrations in single rating classes
 Differentiation of risk amongst the rating classes
 Plausible, intuitive and current input data
 All relevant information must be taken into account
 No preference for model methods
Maggie Kriebelt October 2011

3. Risk-Weighted Assets for Small &
Medium Sized Entities: Evaluating
Exposures Not In Default
 Based on the Section 273 of the Basel II Committee
Notes - Rules for Risk Weighted Assets in this Class Are
Determined As Follows:
Correlation = 0.12 * (1-e(-50*pd))/(1-e(-50))+ 0.24 * [1-(1-
e(-50*pd)) / (1-e(-50))] – 0.04*(1-(S-5)/45)
Maturity Adjustment = (0.11852 – 0.05478*ln(pd))^2
Capital Requirement = [LGD * N(1-R)^-0.5 * G(PD) +
(R/(1-R))^0.5 * G(0.999)] – PD * LGD] *(1-1.5*b)^-1
*(1+(M-2.5)*b)
Risk Weighted Assets = 12.5 *Capital Requirement*EAD
Maggie Kriebelt October 2011

4. Risk-Weighted Assets for SME Exposures:
Evaluating Exposures Not In Default
 Risk Weighted Assets for entities with sales under 50
million Euros are likewise stressed at the alpha 0.1%
level to obtain a 99.9% confidence that realizations of
default on the portfolio for each exposure is better
than the stress scenario
 Maturity adjustment remains the same
 Correlation is dependent on Probability of Default and
adjustment for firm size is incorporated
 Required Capital increases for larger SME’s and is more
pronounced at higher maturities as can be seen from
Required Capital surfaces at 1Yr, 5Yr, 10Yr and 20Yr:
response surface and grid illustrations follow
Maggie Kriebelt October 2011

5. Determining Probability of Default
◦ Migration Matrices to calculate PD using
Cohort Method or Hazard Rate Method
from historical credit ratings
Sample Rating Data
Obligor Date Rating
12550 17-Nov-84 AA
12550 1-Feb-00 BBB
12550 21-Mar-04 BB
14770 2-Sep-82 CCC
14770 30-Dec-94 B
14770 14-Apr-96 BB
13426 30-Sep-82 B
13426 3-May-96 BB
Maggie Kriebelt October 2011

6. Cohort Method
 Uses obligors that have a rating at
beginning of evaluation period creating a
transition matrix with frequencies of
rating at end of period
◦ Let Ni,t = # of obligors in category i at
beginning period t
◦ Let Nij,t = # of obligors in cohort i that moved
to grade j at end of period t
◦ Transition frequency in period t
 pˆij,t = Nij,t / Ni,t
Maggie Kriebelt October 2011

7. Cohort Method
◦ Transition frequency averaged over all periods
 pˆij,t=  Ni,t * pˆij,t /  Ni,t
t t
◦ Combining equations and reducing yields the
obligor weighted average as the aggregate of
the transitions from i to j divided by the total
obligors in cohort i at beginning of period
 pˆij,t=  Ni,t * [Nij,t / Ni,t] /  Ni,t
t t
 pˆij,t=  Nij,t /  Ni,t
t t
 pˆij,t= Nij / Ni
Maggie Kriebelt October 2011

8. Cohort Method Portfolio Results
on Hypothetical Credit Data
One Year Transition Probabilities Based On Cohort Approach
Using Historical Credit Ratings Data From 1986 to 2005
From/To AAA AA A BBB BB B CCC D
AAA 93.70606 5.523937 0.602611 0.133914 0.033478 0 0 0
AA 1.778222 93.12687 4.355644 0.579421 0.11988 0 0 0.03996
A 0.110274 2.940636 92.17056 4.208785 0.459474 0.055137 0 0.055137
BBB 0.021418 0.257014 5.225958 90.27629 3.512529 0.471193 0.042836 0.192761
BB 0.023137 0.161962 0.624711 6.362795 88.59324 3.378066 0.254512 0.601573
B 0 0 0.041632 0.749376 7.993339 86.5945 2.622814 1.998335
CCC 0 0 0.095057 0.285171 1.996198 5.038023 82.12928 10.45627
D 0 0 0 0 0 0 0 100
One Year Transition Probabilities Based On Cohort Approach
Using Historical Credit Ratings Data From 1996 to 2005
From/To AAA AA A BBB BB B CCC D
AAA 91.27219 7.544379 0.887574 0.221893 0.073964 0 0 0
AA 2.573808 91.06737 5.412566 0.719152 0.189251 0 0 0.03785
A 0.167729 3.555854 90.00335 5.73633 0.469641 0.033546 0 0.033546
BBB 0.037566 0.413223 6.423742 88.12923 3.869271 0.713749 0.075131 0.338092
BB 0.054915 0.384404 1.043383 9.2257 84.40417 3.953871 0.10983 0.823723
B 0 0 0.120773 1.449275 9.903382 82.72947 2.777778 3.019324
CCC 0 0 0.429185 0.858369 3.433476 6.437768 79.39914 9.44206
D 0 0 0 0 0 0 0 100
Maggie Kriebelt October 2011

9. Cohort Method Portfolio Results
5Yr & 10 Yr Migration
Five Year Transition Probabilities Based On Cohort Approach
Using Historical Credit Ratings Data From 1986 to 2005
From/To AAA AA A BBB BB B CCC D
AAA 73.06543 21.29285 4.284603 1.046794 0.254769 0.023495 0.002075 0.029982
AA 6.847254 71.90163 16.54954 3.600975 0.786187 0.087365 0.007538 0.219519
A 0.847467 11.09027 69.29591 15.13993 2.739804 0.478313 0.040981 0.367323
BBB 0.189815 2.181287 18.61027 63.33793 11.89928 2.346053 0.285521 1.149843
BB 0.128347 0.919461 4.680541 21.11996 58.13473 10.40889 1.276009 3.332054
B 0.019635 0.154885 1.018553 5.993631 24.44986 51.382 6.864434 10.11701
CCC 0.006867 0.064796 0.57572 2.121639 8.0462 13.37377 38.19502 37.61598
D 0 0 0 0 0 0 0 100
Ten Year Transition Probabilities Based On Cohort Approach
Using Historical Credit Ratings Data From 1986 to 2005
From/To AAA AA A BBB BB B CCC D
AAA 54.88218 31.36801 9.830473 2.898558 0.749521 0.119689 0.013522 0.138051
AA 10.07438 55.07772 24.3688 7.618646 1.943656 0.355796 0.041533 0.519475
A 1.998195 16.19584 52.84186 21.09709 5.502486 1.23296 0.155925 0.975646
BBB 0.58174 5.167537 25.63513 45.67485 15.57847 4.059124 0.610572 2.692578
BB 0.313235 2.219682 10.16596 27.04901 39.09302 12.08884 2.00598 7.064282
B 0.086901 0.668082 3.554979 12.34532 28.07138 30.00972 6.47848 18.78514
CCC 0.033936 0.277624 1.537531 4.74466 11.28951 12.86993 15.6156 53.6312
D 0 0 0 0 0 0 0 100
Maggie Kriebelt October 2011

10. Hazard Rate Method
 Incorporates within period transitions
◦ Calculate generator matrix 
◦ Let Nij = # of obligors in cohort i that moved to
grade j
◦ Let Yi (s) = # of obligors rated i at time s
t
◦ Let ij= Nij / ∫ Yi(s) ds for i ≠j
t0
◦ Let ii= -  ij
i≠j
◦ T-year migration P(T)
 k k
 P(T) = exp( T) =  [ T ] / k!
k=0
Maggie Kriebelt October 2011

11. Hazard Rate Portfolio Results on
Hypothetical Credit Data
One Year Transition Probabilities Based On Hazard Rate Approach
Using Historical Credit Ratings Data From 1986 to 2005
From/To AAA AA A BBB BB B CCC D
AAA 91.48377 7.143391 1.025835 0.261321 0.080607 0.002547 0.00015 0.002381
AA 2.39916 91.58535 4.966863 0.80533 0.196159 0.007226 0.000435 0.039473
A 0.196455 3.394196 90.40769 5.318108 0.577465 0.058286 0.002858 0.044939
BBB 0.043742 0.357067 6.251844 88.62991 3.613714 0.683256 0.073595 0.346873
BB 0.055308 0.27961 1.156373 8.904006 84.94655 3.559837 0.14485 0.953468
B 0.003317 0.020408 0.310894 1.655158 9.166305 83.65436 2.321998 2.867557
CCC 0.0012 0.006633 0.05653 0.98391 3.376531 6.418202 80.43506 8.72193
D 0 0 0 0 0 0 0 100
One Year Transition Probabilities Based On Hazard Rate Approach
Using Historical Credit Ratings Data From 1996 to 2005
From/To AAA AA A BBB BB B CCC D
AAA 91.48377 7.143391 1.025835 0.261321 0.080607 0.002547 0.00015 0.002381
AA 2.39916 91.58535 4.966863 0.80533 0.196159 0.007226 0.000435 0.039473
A 0.196455 3.394196 90.40769 5.318108 0.577465 0.058286 0.002858 0.044939
BBB 0.043742 0.357067 6.251844 88.62991 3.613714 0.683256 0.073595 0.346873
BB 0.055308 0.27961 1.156373 8.904006 84.94655 3.559837 0.14485 0.953468
B 0.003317 0.020408 0.310894 1.655158 9.166305 83.65436 2.321998 2.867557
CCC 0.0012 0.006633 0.05653 0.98391 3.376531 6.418202 80.43506 8.72193
D 0 0 0 0 0 0 0 100
Maggie Kriebelt October 2011

12. Hazard Rate Portfolio Results
5Yr & 10 Yr Migration
Five Year Transition Probabilities Based On Hazard Rate Approach
Using Historical Credit Ratings Data From 1986 to 2005
From/To AAA AA A BBB BB B CCC D
AAA 73.38483 20.65001 4.454501 1.149504 0.28702 0.032235 0.003147 0.03875
AA 6.550769 72.95027 15.67757 3.639123 0.836047 0.107379 0.010417 0.228424
A 0.881035 10.75132 70.0775 14.47197 2.857795 0.516373 0.049304 0.3947
BBB 0.20045 2.032838 18.31537 64.33316 11.35115 2.289411 0.285357 1.192264
BB 0.126529 0.77568 4.776965 20.6913 58.97102 9.928518 1.223181 3.506811
B 0.025236 0.170192 1.319722 6.304139 23.7213 52.30527 6.173526 9.980614
CCC 0.006923 0.046348 0.376048 2.167411 7.2824 13.67692 39.42811 37.01584
D 0 0 0 0 0 0 0 100
Ten Year Transition Probabilities Based On Hazard Rate Approach
Using Historical Credit Ratings Data From 1986 to 2005
From/To AAA AA A BBB BB B CCC D
AAA 55.24799 30.72278 9.852635 3.040695 0.81819 0.140936 0.016679 0.160091
AA 9.73258 56.33635 23.423 7.520052 2.009072 0.385311 0.046882 0.546757
A 2.001007 15.87657 53.62746 20.47819 5.549173 1.265583 0.163269 1.038746
BBB 0.585547 4.893365 25.51896 46.61364 15.10129 3.933185 0.585521 2.768485
BB 0.304434 2.001088 10.21716 26.88666 39.71213 11.71463 1.878023 7.285881
B 0.097573 0.675289 3.953918 12.59257 27.60057 30.70927 5.971997 18.39881
CCC 0.03117 0.21777 1.344712 4.674156 10.66734 13.32095 16.48556 53.25834
D 0 0 0 0 0 0 0 100
Maggie Kriebelt October 2011

13. Default Probability from Empirical Data
for Cohort & Hazard Rate Methods
Default Probabilities Based On Cohort Approach
Using Historical Credit Ratings Data From 1986 to 2005
From/To 1Yr 2Yr 3Yr 4Yr 5Yr 6Yr 7Yr 8Yr 9Yr 10Yr
AAA 0.001498 0.005996 0.013517 0.024101 0.037807 0.054708 0.074885 0.098427 0.12543 0.155991
AA 0.040788 0.083544 0.128718 0.176724 0.227944 0.282727 0.341385 0.404199 0.471415 0.543248
A 0.059614 0.128384 0.206552 0.294276 0.391638 0.498653 0.615271 0.741389 0.876854 1.021472
BBB 0.202292 0.423177 0.661822 0.917261 1.188434 1.474216 1.773451 2.084972 2.407621 2.740265
BB 0.619709 1.271857 1.950739 2.650864 3.367084 4.09468 4.829397 5.567462 6.305568 7.040864
B 2.018484 4.050252 6.063012 8.033479 9.945363 11.78777 13.55391 15.24014 16.84515 18.36934
CCC 9.629118 17.78827 24.71842 30.61973 35.65858 39.97344 43.67962 46.87324 49.63454 52.03053
Default Probabilities Based On Hazard Rate Approach
Using Historical Credit Ratings Data From 1986 to 2005
From/To 1Yr 2Yr 3Yr 4Yr 5Yr 6Yr 7Yr 8Yr 9Yr 10Yr
AAA 0.001535 0.006144 0.01385 0.024698 0.03875 0.056084 0.076787 0.100955 0.128688 0.160091
AA 0.040797 0.083582 0.128829 0.176975 0.228424 0.283542 0.342658 0.406067 0.474026 0.546757
A 0.059362 0.128286 0.207046 0.295821 0.3947 0.503696 0.622747 0.751731 0.890472 1.038746
BBB 0.200529 0.421073 0.660641 0.91811 1.192264 1.481835 1.785528 2.102046 2.430113 2.768485
BB 0.649443 1.330547 2.03753 2.764734 3.506811 4.258847 5.016422 5.775631 6.533084 7.285881
B 2.014358 4.052683 6.076586 8.058813 9.980614 11.8297 13.59863 15.28358 16.88339 18.39881
CCC 10.17111 18.6966 25.86297 31.90512 37.01584 41.35351 45.04838 48.20775 50.92006 53.25834
Maggie Kriebelt October 2011

14. Capital Requirement for Hypothetical SME Portfolio
Maggie Kriebelt October 2011

15. Capital Requirement for Hypothetical SME Portfolio
Maggie Kriebelt October 2011

16. Required Capital Levels for SME Exposures
Required Capital By SME Size Factor Level 10YR Maturity
5MM Euro
0.30
0.30
0.25
0.25
0.20
0.20
Req'd Capital
0.15
0.10 0.15
0.05
0.10
0.5
0.4
0.3
0.05
0.2 0.1
Probability Default 0.2
0.1 0.3
0.4
0.5
0.6
Loss Given Default
0.00
Kriebelt 2011
Maggie Kriebelt October 2011

17. Required Capital Levels for SME Exposures
Required Capital By SME Size Factor Level 10YR Maturity
20MM Euro
0.35
0.30
0.30
0.25
0.25
0.20
Req'd Capital 0.20
0.15
0.10
0.15
0.05
0.10
0.5
0.4
0.3
0.2 0.1 0.05
Probability Default 0.2
0.1 0.3
0.4
0.5
0.6
Loss Given Default
0.00
Kriebelt 2011
Maggie Kriebelt October 2011

18. Required Capital Levels for SME Exposures
Required Capital By SME Size Factor Level 10YR Maturity
50MM Euro
0.40
0.35
0.30
0.3
0.25
Req'd Capital
0.2
0.20
0.1
0.15
0.5 0.10
0.4
0.3
0.2 0.1
Probability Default 0.2 0.05
0.1 0.3
0.4
0.5
0.6
Loss Given Default
0.00
Kriebelt 2011
Maggie Kriebelt October 2011

19. Required Capital Levels for SME Exposures
Required Capital SME 10MM Euros Maturity 10Yrs
lgd_0.1 lgd_0.2 lgd_0.3 lgd_0.4 lgd_0.5 lgd_0.6 lgd_0.7
pd_0.1 0.039 0.046 0.047 0.044 0.040 0.034 0.078
pd_0.2 0.091 0.093 0.089 0.080 0.069 0.117 0.137
pd_0.3 0.140 0.133 0.120 0.103 0.157 0.183 0.186
pd_0.4 0.177 0.160 0.137 0.196 0.228 0.233 0.222
pd_0.5 0.200 0.171 0.235 0.274 0.279 0.266 0.240
pd_0.6 0.206 0.274 0.319 0.326 0.310 0.280 0.240
Required Capital SME 20MM Euros Maturity 10Yrs
lgd_0.1 lgd_0.2 lgd_0.3 lgd_0.4 lgd_0.5 lgd_0.6 lgd_0.7
pd_0.1 0.042 0.048 0.049 0.046 0.042 0.035 0.084
pd_0.2 0.097 0.098 0.093 0.083 0.071 0.126 0.145
pd_0.3 0.147 0.139 0.125 0.106 0.168 0.193 0.196
pd_0.4 0.186 0.167 0.142 0.209 0.242 0.245 0.232
pd_0.5 0.208 0.177 0.251 0.290 0.294 0.278 0.250
pd_0.6 0.213 0.293 0.339 0.343 0.325 0.292 0.248
Required Capital SME 30MM Euros Maturity 10Yrs
lgd_0.1 lgd_0.2 lgd_0.3 lgd_0.4 lgd_0.5 lgd_0.6 lgd_0.7
pd_0.1 0.045 0.051 0.051 0.048 0.043 0.037 0.089
pd_0.2 0.102 0.103 0.097 0.086 0.073 0.134 0.153
pd_0.3 0.154 0.145 0.130 0.110 0.178 0.204 0.205
pd_0.4 0.193 0.173 0.146 0.223 0.255 0.256 0.241
pd_0.5 0.216 0.183 0.267 0.306 0.308 0.290 0.259
pd_0.6 0.219 0.312 0.357 0.359 0.338 0.302 0.256
Maggie Kriebelt October 2011

20. Required Capital Levels for SME Exposures
Required Capital SME 40MM Euros Maturity 10Yrs
lgd_0.1 lgd_0.2 lgd_0.3 lgd_0.4 lgd_0.5 lgd_0.6 lgd_0.7
pd_0.1 0.047 0.054 0.053 0.050 0.045 0.038 0.094
pd_0.2 0.107 0.107 0.100 0.089 0.075 0.142 0.161
pd_0.3 0.160 0.150 0.134 0.113 0.189 0.214 0.214
pd_0.4 0.200 0.178 0.150 0.236 0.268 0.267 0.250
pd_0.5 0.223 0.188 0.283 0.321 0.321 0.300 0.267
pd_0.6 0.225 0.330 0.375 0.374 0.350 0.312 0.263
Required Capital SME 50MM Euros Maturity 10Yrs
lgd_0.1 lgd_0.2 lgd_0.3 lgd_0.4 lgd_0.5 lgd_0.6 lgd_0.7
pd_0.1 0.050 0.056 0.056 0.052 0.046 0.038 0.099
pd_0.2 0.112 0.111 0.103 0.092 0.077 0.149 0.168
pd_0.3 0.167 0.155 0.138 0.115 0.199 0.224 0.222
pd_0.4 0.207 0.183 0.154 0.249 0.280 0.278 0.259
pd_0.5 0.229 0.192 0.298 0.336 0.333 0.310 0.275
pd_0.6 0.231 0.348 0.391 0.389 0.362 0.321 0.269
Generally, required capital increases over higher SME size ,with
larger default probabilities and greater loss given default, however
the parabolic functions determining the required capital
incorporates higher probability of default lowers possibility of
upgrade: result is a relatively lower required capital when pd and
lgd closer to 1.0 with the pattern continuing over higher
maturities as well.
Maggie Kriebelt October 2011

21. Required Capital Levels for SME Exposures
Required Capital By SME Size Factor Level 1YR Maturity
30MM Euro 35MM Euro 40MM Euro 45MM Euro 50MM Euro
0.30
0.25 0.25 0.25 0.25 0.25
0.20 0.20 0.20 0.20 0.20
0.25
Req'd Capital
0.15 Req'd Capital
0.15 Req'd Capital
0.15 Req'd Capital
0.15 Req'd Capital
0.15
0.10 0.10 0.10 0.10 0.10
0.05 0.05 0.05 0.05 0.05
0.20
0.5 0.5 0.5 0.5 0.5
0.4 0.4 0.4 0.4 0.4
0.3 0.3 0.3 0.3 0.3
0.2 0.1 0.2 0.1 0.2 0.1 0.2 0.1 0.2 0.1
Probability Default 0.3 0.2 Probability Default 0.3 0.2 Probability Default 0.3 0.2 Probability Default 0.3 0.2 Probability Default 0.3 0.2
0.1 0.4 0.1 0.4 0.1 0.4 0.1 0.4 0.1 0.4
0.5 0.5 0.5 0.5 0.5
0.6 0.6 0.6 0.6 0.6
Loss Given Default Loss Given Default Loss Given Default Loss Given Default Loss Given Default
0.15
5MM Euro 10MM Euro 15MM Euro 20MM Euro 25MM Euro
0.25 0.25 0.25 0.25 0.25 0.10
0.20 0.20 0.20 0.20 0.20
Req'd Capital
0.15 Req'd Capital
0.15 Req'd Capital
0.15 Req'd Capital
0.15 Req'd Capital
0.15
0.10 0.10 0.10 0.10 0.10
0.05 0.05 0.05 0.05 0.05 0.05
0.5 0.5 0.5 0.5 0.5
0.4 0.4 0.4 0.4 0.4
0.3 0.3 0.3 0.3 0.3
0.2 0.1 0.2 0.1 0.2 0.1 0.2 0.1 0.2 0.1
Probability Default 0.2 Probability Default 0.2 Probability Default 0.2 Probability Default 0.2 Probability Default 0.2
0.1 0.4 0.3 0.1 0.4 0.3 0.1 0.4 0.3 0.1 0.4 0.3 0.1 0.4 0.3
0.5 0.5 0.5 0.5 0.5
0.6 0.6 0.6 0.6 0.6 0.00
Loss Given Default Loss Given Default Loss Given Default Loss Given Default Loss Given Default
Kriebelt 2011
Maggie Kriebelt October 2011

22. Required Capital Levels for SME Exposures
Required Capital By SME Size Factor Level 5YR Maturity
30MM Euro 35MM Euro 40MM Euro 45MM Euro 50MM Euro 0.35
0.30 0.30 0.30 0.30 0.30
0.25 0.25 0.25 0.25 0.25
0.30
0.20 0.20 0.20 0.20 0.20
Req'd Capital Req'd Capital Req'd Capital Req'd Capital Req'd Capital
0.15 0.15 0.15 0.15 0.15
0.10 0.10 0.10 0.10 0.10
0.25
0.05 0.05 0.05 0.05 0.05
0.5 0.5 0.5 0.5 0.5
0.4 0.4 0.4 0.4 0.4
0.3 0.3 0.3 0.3 0.3
0.2 0.2 0.2 0.2 0.2
Probability Default
0.1 0.4
0.3 0.2 0.1
Probability Default
0.1 0.4
0.3 0.2 0.1
Probability Default
0.1 0.4
0.3 0.2 0.1
Probability Default
0.1 0.4
0.3 0.2 0.1
Probability Default
0.1 0.4
0.3 0.2 0.1
0.20
0.5 0.5 0.5 0.5 0.5
0.6 0.6 0.6 0.6 0.6
Loss Given Default Loss Given Default Loss Given Default Loss Given Default Loss Given Default
5MM Euro 10MM Euro 15MM Euro 20MM Euro 25MM Euro
0.15
0.30 0.30 0.30 0.30 0.30
0.25 0.25 0.25 0.25 0.25
0.10
0.20 0.20 0.20 0.20 0.20
Req'd Capital Req'd Capital Req'd Capital Req'd Capital Req'd Capital
0.15 0.15 0.15 0.15 0.15
0.10 0.10 0.10 0.10 0.10
0.05 0.05 0.05 0.05 0.05
0.05
0.5 0.5 0.5 0.5 0.5
0.4 0.4 0.4 0.4 0.4
0.3 0.3 0.3 0.3 0.3
0.2 0.1 0.2 0.1 0.2 0.1 0.2 0.1 0.2 0.1
Probability Default 0.2 Probability Default 0.2 Probability Default 0.2 Probability Default 0.2 Probability Default 0.2
0.1 0.4 0.3 0.1 0.4 0.3 0.1 0.4 0.3 0.1 0.4 0.3 0.1 0.4 0.3
0.5 0.5 0.5 0.5 0.5
0.6 0.6 0.6 0.6 0.6 0.00
Loss Given Default Loss Given Default Loss Given Default Loss Given Default Loss Given Default
Kriebelt 2011
Maggie Kriebelt October 2011

23. Required Capital Levels for SME Exposures
Required Capital By SME Size Factor Level 10YR Maturity
30MM Euro 35MM Euro 40MM Euro 45MM Euro 50MM Euro
0.40
0.3 0.3 0.3 0.3 0.3 0.35
Req'd Capital
0.2 Req'd Capital
0.2 Req'd Capital
0.2 Req'd Capital
0.2 Req'd Capital
0.2
0.1 0.1 0.1 0.1 0.1 0.30
0.5 0.5 0.5 0.5 0.5
0.4 0.4 0.4 0.4 0.4
0.3 0.3 0.3 0.3 0.3
0.25
0.2 0.1 0.2 0.1 0.2 0.1 0.2 0.1 0.2 0.1
Probability Default 0.3 0.2 Probability Default 0.3 0.2 Probability Default 0.3 0.2 Probability Default 0.3 0.2 Probability Default 0.3 0.2
0.1 0.4 0.1 0.4 0.1 0.4 0.1 0.4 0.1 0.4
0.5 0.5 0.5 0.5 0.5
0.6 0.6 0.6 0.6 0.6
Loss Given Default Loss Given Default Loss Given Default Loss Given Default Loss Given Default
0.20
5MM Euro 10MM Euro 15MM Euro 20MM Euro 25MM Euro
0.15
0.3 0.3 0.3 0.3 0.3
Req'd Capital
0.2 Req'd Capital
0.2 Req'd Capital
0.2 Req'd Capital
0.2 Req'd Capital
0.2 0.10
0.1 0.1 0.1 0.1 0.1
0.05
0.5 0.5 0.5 0.5 0.5
0.4 0.4 0.4 0.4 0.4
0.3 0.3 0.3 0.3 0.3
0.2 0.1 0.2 0.1 0.2 0.1 0.2 0.1 0.2 0.1
Probability Default 0.2 Probability Default 0.2 Probability Default 0.2 Probability Default 0.2 Probability Default 0.2
0.1 0.4 0.3 0.1 0.4 0.3 0.1 0.4 0.3 0.1 0.4 0.3 0.1 0.4 0.3
0.5 0.5 0.5 0.5 0.5
0.6 0.6 0.6 0.6 0.6 0.00
Loss Given Default Loss Given Default Loss Given Default Loss Given Default Loss Given Default
Kriebelt 2011
Maggie Kriebelt October 2011

24. Required Capital Levels for SME Exposures
Required Capital By SME Size Factor Level 20YR Maturity
30MM Euro 35MM Euro 40MM Euro 45MM Euro 50MM Euro
0.5
0.5 0.5 0.5 0.5 0.5
0.4 0.4 0.4 0.4 0.4
0.3 0.3 0.3 0.3 0.3
Req'd Capital Req'd Capital Req'd Capital Req'd Capital Req'd Capital
0.2 0.2 0.2 0.2 0.2
0.4
0.1 0.1 0.1 0.1 0.1
0.5 0.5 0.5 0.5 0.5
0.4 0.4 0.4 0.4 0.4
0.3 0.3 0.3 0.3 0.3
0.2 0.1 0.2 0.1 0.2 0.1 0.2 0.1 0.2 0.1
Probability Default 0.3 0.2 Probability Default 0.3 0.2 Probability Default 0.3 0.2 Probability Default 0.3 0.2 Probability Default 0.3 0.2
0.1 0.1 0.1 0.1 0.1
0.6
0.5 0.4
0.6
0.5 0.4
0.6
0.5 0.4
0.6
0.5 0.4
0.6
0.5 0.4 0.3
Loss Given Default Loss Given Default Loss Given Default Loss Given Default Loss Given Default
5MM Euro 10MM Euro 15MM Euro 20MM Euro 25MM Euro
0.5 0.5 0.5 0.5 0.5
0.2
0.4 0.4 0.4 0.4 0.4
0.3 0.3 0.3 0.3 0.3
Req'd Capital Req'd Capital Req'd Capital Req'd Capital Req'd Capital
0.2 0.2 0.2 0.2 0.2
0.1
0.1 0.1 0.1 0.1 0.1
0.5 0.5 0.5 0.5 0.5
0.4 0.4 0.4 0.4 0.4
0.3 0.3 0.3 0.3 0.3
0.2 0.1 0.2 0.1 0.2 0.1 0.2 0.1 0.2 0.1
Probability Default 0.2 Probability Default 0.2 Probability Default 0.2 Probability Default 0.2 Probability Default 0.2
0.1 0.4 0.3 0.1 0.4 0.3 0.1 0.4 0.3 0.1 0.4 0.3 0.1 0.4 0.3
0.5 0.5 0.5 0.5 0.5
0.6 0.6 0.6 0.6 0.6
0.0
Loss Given Default Loss Given Default Loss Given Default Loss Given Default Loss Given Default
Kriebelt 2011
Maggie Kriebelt October 2011

25. Risk-Weighted Assets of Other Retail Exposures:
Evaluating Exposures Not In Default
 Based on the Section 330 of the Basel II Committee
Notes - Rules for Risk Weighted Assets in this Class Are
Determined As Follows:
Correlation = Correlation = 0.03 * (1-e(-35*pd))/(1-e(-35))+
0.16 * [1-(1-e(-35*pd)) / (1-e(-35))]
Capital Requirement = [LGD * N(1-R)^-0.5 * G(PD) +
(R/(1-R))^0.5 * G(0.999)] – PD * LGD]
Risk Weighted Assets = 12.5 *Capital Requirement*EAD
Maggie Kriebelt October 2011

26. Risk-Weighted Assets of Other Retail Exposures :
 Required Capital increases for with LGD and is
parabolic with respect to PD, but is smaller than for
both mortgage and revolving retail lines exposures
 No maturity adjustment
 Correlation is dependent on default probability
 Response surface and grid illustrations compare the
required capital requirements
Maggie Kriebelt October 2011

27. Capital Requirement for Hypothetical Other Retail
Portfolio
Maggie Kriebelt October 2011

28. Risk-Weighted Assets of Other Retail Exposures
Required Capital For Other Retail Exposures
0.20
0.15
0.15
Req'd Capital
0.10
0.10
0.05
0.8
0.05
0.6
0.4
0.2
Probability Default 0.4
0.2 0.6
0.8
Loss Given Default
0.00
Kriebelt 2011
Required Capital Other Retail Exposures
lgd_0.1 lgd_0.2 lgd_0.3 lgd_0.4 lgd_0.5 lgd_0.6 lgd_0.7 lgd_0.8 lgd_0.9
pd_0.1 0.013 0.018 0.020 0.021 0.021 0.019 0.016 0.012 0.007
pd_0.2 0.027 0.036 0.041 0.043 0.041 0.038 0.032 0.024 0.013
pd_0.3 0.040 0.053 0.061 0.064 0.062 0.057 0.048 0.036 0.020
pd_0.4 0.054 0.071 0.082 0.085 0.083 0.075 0.064 0.048 0.027
pd_0.5 0.067 0.089 0.102 0.106 0.103 0.094 0.080 0.059 0.034
pd_0.6 0.081 0.107 0.123 0.128 0.124 0.113 0.095 0.071 0.040
pd_0.7 0.094 0.125 0.143 0.149 0.145 0.132 0.111 0.083 0.047
pd_0.8 0.107 0.143 0.164 0.170 0.165 0.151 0.127 0.095 0.054
pd_0.9 0.121 0.160 0.184 0.191 0.186 0.170 0.143 0.107 0.061
Maggie Kriebelt October 2011

29. Risk-Weighted Assets of Other Retail Exposures
Required Capital For Other Retail Exposures
0.20
0.15
0.15
0.10
Req'd Capital
0.10
0.05
0.8 0.05
0.6
0.4
Probability Default
0.2 0.2
0.4
0.6
0.8
Loss Given Default
0.00
Kriebelt 2011
Maggie Kriebelt October 2011