Credit risk management

1. Example Index
Copyright 2018 CapitaLogic Limited
Example Description Excel technique
1 Samples 100 good and 100 bad borrowers
2 Explanative variables identification with 4 variables Multiple linear regression
3 Explanative variables identification with 3 variables Multiple linear regression
4 Statistical distance Array function
5 Statistical distance with three groups Array function
6 Linear discriminant analysis Solver
7 Mis-classification cost Solver
8 Probit transformation Multiple linear regression
9 Probit regression Solver
This Excel workbook is prepared in accordance with
Chapter 9 of the text book
"Managing Credit Risk Under The Basel III Framework, 3
rd
ed"
Authored by :Dr. LAM Yat-fai (林日辉)
Principal, Structured Products Analytics, CapitaLogic Limited
Adjunct Professor of Finance, City University of Hong Kong
Doctor of Business Administration
CFA, CAIA, CAMS, FRM, PRM
Website: https://sites.google.com/site/crmbase
E-mail: crmbasel@gmail.com
Copyright 2018 CapitaLogic Limited

2. Example 1 100-100 samples
Borrower Monthly
income
Outstanding
loan
No. of
dependents
University
graduate
Defaulted in
1 year
1 3750 3160 1 0 No
2 1497 2156 0 0 No
3 1878 4450 0 0 No
4 2085 5856 0 1 No
5 1420 3095 0 0 No
6 1696 4455 0 0 No
7 2967 3492 1 1 No
8 2247 638 1 0 No
9 3935 7477 0 0 No
10 1022 4022 0 1 No
11 1068 5683 0 1 No
12 3327 9795 1 0 No
13 2265 5341 1 0 No
14 3684 11888 1 1 No
15 3973 4857 1 0 No
16 3147 10548 1 0 No
17 3928 5131 1 1 No
18 3274 2399 1 0 No
19 1825 6041 1 0 No
20 3777 6516 1 1 No
21 1244 4223 0 0 No
22 3514 23724 0 0 No
23 3139 14500 1 0 No
24 3712 17445 1 0 No
25 1172 6019 1 1 No
26 2731 11872 0 0 No
27 3559 24955 0 1 No
28 1117 7229 1 1 No
29 1818 1387 1 1 No
30 3524 9166 1 0 No
Copyright 2018 CapitaLogic Limited

3. Example 2 EVI 4 variables
Borrower Monthly
income
Outstanding
loan
No. of
dependents
University
graduate
Defaulted in
1 year
Coded PD
1 3750 3160 1 0 No 0 SUMMARY OUTPUT
2 1497 2156 0 0 No 0
3 1878 4450 0 0 No 0 Regression Statistics
4 2085 5856 0 1 No 0 Multiple R 0.805417
5 1420 3095 0 0 No 0 R Square 0.648697
6 1696 4455 0 0 No 0 Adjusted R Square0.641491
7 2967 3492 1 1 No 0 Standard Error0.30013
8 2247 638 1 0 No 0 Observations 200
9 3935 7477 0 0 No 0
10 1022 4022 0 1 No 0 ANOVA
11 1068 5683 0 1 No 0 df SS MS F Significance F
12 3327 9795 1 0 No 0 Regression 4 32.43484 8.108711 90.01904 3.25E-43
13 2265 5341 1 0 No 0 Residual 195 17.56516 0.090078
14 3684 11888 1 1 No 0 Total 199 50
15 3973 4857 1 0 No 0
16 3147 10548 1 0 No 0 CoefficientsStandard Error t Stat P-value Lower 95%Upper 95%Lower 95.0%Upper 95.0%
17 3928 5131 1 1 No 0 Intercept -0.03103 0.084166 -0.36865 0.712787 -0.19702 0.134965 -0.19702 0.134965
18 3274 2399 1 0 No 0 Monthly income-0.00014 2.43E-05 -5.80425 2.58E-08 -0.00019 -9.3E-05 -0.00019 -9.3E-05
19 1825 6041 1 0 No 0 Outstanding loan2.76E-05 1.89E-06 14.55216 5.8E-33 2.38E-05 3.13E-05 2.38E-05 3.13E-05
20 3777 6516 1 1 No 0 No. of dependents0.175738 0.017588 9.992167 3.02E-19 0.141051 0.210424 0.141051 0.210424
21 1244 4223 0 0 No 0 University graduate-0.01164 0.042869 -0.27144 0.786343 -0.09618 0.07291 -0.09618 0.07291
22 3514 23724 0 0 No 0
23 3139 14500 1 0 No 0
24 3712 17445 1 0 No 0
25 1172 6019 1 1 No 0
26 2731 11872 0 0 No 0
27 3559 24955 0 1 No 0
28 1117 7229 1 1 No 0
29 1818 1387 1 1 No 0
30 3524 9166 1 0 No 0
Copyright 2018 CapitaLogic Limited

4. Example 3 EVI 3 variables
Borrower Monthly
income
Outstanding
loan
No. of
dependents
Defaulted in
1 year
Coded PD
1 3750 3160 1 No 0
2 1497 2156 0 No 0
3 1878 4450 0 No 0 Regression Statistics
4 2085 5856 0 No 0
5 1420 3095 0 No 0
6 1696 4455 0 No 0
7 2967 3492 1 No 0
8 2247 638 1 No 0
9 3935 7477 0 No 0
10 1022 4022 0 No 0
11 1068 5683 0 No 0
12 3327 9795 1 No 0
13 2265 5341 1 No 0
14 3684 11888 1 No 0
15 3973 4857 1 No 0
16 3147 10548 1 No 0
17 3928 5131 1 No 0
18 3274 2399 1 No 0
19 1825 6041 1 No 0
20 3777 6516 1 No 0
21 1244 4223 0 No 0
22 3514 23724 0 No 0
23 3139 14500 1 No 0
24 3712 17445 1 No 0
25 1172 6019 1 No 0
26 2731 11872 0 No 0
27 3559 24955 0 No 0
28 1117 7229 1 No 0
29 1818 1387 1 No 0
30 3524 9166 1 No 0
Copyright 2018 CapitaLogic Limited

5. Example 4 Statistical distance
Borrower Monthly
income
Outstanding
loan
No. of
dependents
Defaulted in
1 year
Defaulted in
1 year
Monthly
income
Outstanding
loan
No. of
dependents
Monthly
income
Outstanding
loan
No. of
dependents
Statistical
distance
1 3750 3160 1 No No 2702.95 12220.71 1.46 1047.05 -9060.71 -0.46 1.47007352
2 1497 2156 0 No Yes 2235.09 26454.33 2.54 -1205.95 -10064.71 -1.46 2.05896046
3 1878 4450 0 No -824.95 -7770.71 -1.46 1.69440576
4 2085 5856 0 No -617.95 -6364.71 -1.46 1.51912991
5 1420 3095 0 No -1282.95 -9125.71 -1.46 2.08717415
6 1696 4455 0 No -1006.95 -7765.71 -1.46 1.82312967
7 2967 3492 1 No Monthly incomeOutstanding loanNo. of dependents 264.05 -8728.71 -0.46 0.902019
8 2247 638 1 No Monthly income766824.934 -138482.86 -30.485 -455.95 -11582.71 -0.46 1.21982025
9 3935 7477 0 No Outstanding loan-138482.86 126058538 339.28 1232.05 -4743.71 -1.46 1.86662191
10 1022 4022 0 No No. of dependents-30.485 339.28 1.46 -1680.95 -8198.71 -1.46 2.41050911
11 1068 5683 0 No -1634.95 -6537.71 -1.46 2.32677471
12 3327 9795 1 No 624.05 -2425.71 -0.46 0.82254647
13 2265 5341 1 No Discrepancy -437.95 -6879.71 -0.46 0.88252075
14 3684 11888 1 No No. 16 981.05 -332.71 -0.46 1.17330649
15 3973 4857 1 No Ratio 8.00% 1270.05 -7363.71 -0.46 1.61617564
16 3147 10548 1 No 444.05 -1672.71 -0.46 0.63947473
17 3928 5131 1 No 1225.05 -7089.71 -0.46 1.56121844
18 3274 2399 1 No 571.05 -9821.71 -0.46 1.13615571
19 1825 6041 1 No -877.95 -6179.71 -0.46 1.21685227
20 3777 6516 1 No 1074.05 -5704.71 -0.46 1.36255451
21 1244 4223 0 No -1458.95 -7997.71 -1.46 2.2028662
22 3514 23724 0 No 811.05 11503.29 -1.46 1.84227342
23 3139 14500 1 No 436.05 2279.29 -0.46 0.65597309
24 3712 17445 1 No 1009.05 5224.29 -0.46 1.29962788
25 1172 6019 1 No -1530.95 -6201.71 -0.46 1.88772953
26 2731 11872 0 No 28.05 -348.71 -1.46 1.20830812
27 3559 24955 0 No 856.05 12734.29 -1.46 1.93288593
28 1117 7229 1 No -1585.95 -4991.71 -0.46 1.91803693
29 1818 1387 1 No -884.95 -10833.71 -0.46 1.45917691
30 3524 9166 1 No 821.05 -3054.71 -0.46 1.0329256
Covariance matrix
Historical record Centre Distance to centre of Good
Copyright 2018 CapitaLogic Limited

6. Example 5 Stat dist with 3 groups
Borrower Monthly
income
Outstandin
g loan
No. of
dependent
Status Status Monthly
income
Outstanding
loan
No. of
dependents
Monthly
income
Outstanding
loan
No. of
dependents
Statistical
distance
1 2857 19783 2 Good Good 2739.02 8189.26 1.18 117.98 11593.74 0.82 1.45209403
2 1493 16873 2 Good Moderate 2638.74 16301.53 1.74 -1246.02 8683.74 0.82 2.23356744
3 4012 6578 0 Good Bad 2235.09 26454.33 2.54 1272.98 -1611.26 -1.18 2.15341344
4 3935 7477 0 Good 1195.98 -712.26 -1.18 2.04437647
5 4413 5005 1 Good 1673.98 -3184.26 -0.18 2.13304307
6 3756 2176 1 Good 1016.98 -6013.26 -0.18 1.51428981
7 3831 3045 1 Good Monthly incomeOutstanding loanNo. of dependents 1091.98 -5144.26 -0.18 1.5499808
8 3750 3160 1 Good Monthly income811942.832 1478739.24 297.7152 1010.98 -5029.26 -0.18 1.45430415
9 3973 4857 1 Good Outstanding loan1478739.24 120123029 -2842.6017 1233.98 -3332.26 -0.18 1.62800235
10 4068 5505 1 Good No. of dependents297.7152 -2842.6017 1.44093333 1328.98 -2684.26 -0.18 1.71306505
11 3928 5131 1 Good 1188.98 -3058.26 -0.18 1.5650998
12 3274 2399 1 Good 534.98 -5790.26 -0.18 1.00323099
13 3777 6516 1 Good Discrepancy 1037.98 -1673.26 -0.18 1.33850126
14 2967 3492 1 Good No. 30 227.98 -4697.26 -0.18 0.65071308
15 1878 4450 0 Good Ratio 10.00% -861.02 -3739.26 -1.18 1.28423985
16 2085 5856 0 Good -654.02 -2333.26 -1.18 1.14244158
17 3166 11729 0 Good 426.98 3539.74 -1.18 1.25284096
18 1696 4455 0 Good -1043.02 -3734.26 -1.18 1.39804373
19 1420 3095 0 Good -1319.02 -5094.26 -1.18 1.64006775
20 2091 6569 0 Good -648.02 -1620.26 -1.18 1.12156735
21 1355 3162 0 Good -1384.02 -5027.26 -1.18 1.69177538
22 2620 3369 1 Good -119.02 -4820.26 -0.18 0.5065225
23 3304 7108 1 Good 564.98 -1081.26 -0.18 0.77049532
24 2143 1192 1 Good -596.02 -6997.26 -0.18 0.86557578
25 1667 5198 0 Good -1072.02 -2991.26 -1.18 1.40187087
26 1227 3048 0 Good -1512.02 -5141.26 -1.18 1.80415026
27 3524 9166 1 Good 784.98 976.74 -0.18 0.97366596
28 3844 10931 1 Good 1104.98 2741.74 -0.18 1.32897287
29 3712 10307 1 Good 972.98 2117.74 -0.18 1.17975769
30 1244 4223 0 Good -1495.02 -3966.26 -1.18 1.76836399
Covariance matrix
Historical record Centre Distance to centre of Good
Copyright 2018 CapitaLogic Limited

7. Example 6 Linear discrminant analysis
Borrower Monthly
income
Outstanding
loan
No. of
dependents
Defaulted in
1 year
Defaulted in
1 year
Monthly
income
Outstanding
loan
No. of
dependents
Z Class
ification
Discrepancy
1 3750 3160 1 No No 2702.95 12220.71 1.46 111.574522 No 0
2 1497 2156 0 No Yes 2235.09 26454.33 2.54 63.5107094 No 0
3 1878 4450 0 No 59.5453906 No 0
4 2085 5856 0 No 55.5496226 No 0
5 1420 3095 0 No 48.1348603 No 0
6 1696 4455 0 No 48.7431357 No 0
7 2967 3492 1 No Average S.D. 61.5200249 No 0
8 2247 638 1 No Good -88.489933 99.0308064 51.930898 No 0
9 3935 7477 0 No Bad -359.50985 101.461754 146.070591 No 0
10 1022 4022 0 No 13.946797 No 0
11 1068 5683 0 No -2.4948691 No 0
12 3327 9795 1 No 10.0766923 No 0
13 2265 5341 1 No -1.2490316 No 0
14 3684 11888 1 No Monthly incomeOutstanding loanNo. of dependents 7.01276101 No 0
15 3973 4857 1 No Initial value 1 -1 -1 105.167052 No 0
16 3147 10548 1 No Alpha 0.05903619 -0.0115336 -73.364979 -9.2346327 No 0
17 3928 5131 1 No Maximize 3.65402933 99.3502136 No 0
18 3274 2399 1 No 92.2503745 No 0
19 1825 6041 1 No -35.298485 No 0
20 3777 6516 1 No 74.4616949 No 0
21 1244 4223 0 No Discrepancy 24.7345753 No 0
22 3514 23724 0 No Cutoff -223.99989 -66.170254 No 0
23 3139 14500 1 No No. 16 -55.28776 No 0
24 3712 17445 1 No Ratio 8.00% -55.426512 No 0
25 1172 6019 1 No -73.595378 No 0
26 2731 11872 0 No 24.3007876 No 0
27 3559 24955 0 No -77.711502 No 0
28 1117 7229 1 No -90.79804 No 0
29 1818 1387 1 No 17.9656959 No 0
30 3524 9166 1 No 28.9614645 No 0
Classification
Maximization (using Solver add-in)
Historical record Centre
Z
Copyright 2018 CapitaLogic Limited

8. Example 7 Mis-classification cost
Loan Monthly
income
Outstanding
loan
No. of
dependents
Defaulted in
1 year
Defaulted in
1 year
Monthly
income
Outstanding
loan
No. of
dependents
Z Class
ification
Discrepancy
1 3750 3160 1 No No 2702.95 12220.71 1.46 111.574522 No 0
2 1497 2156 0 No Yes 2235.09 26454.33 2.54 63.5107094 No 0
3 1878 4450 0 No 59.5453906 No 0
4 2085 5856 0 No 55.5496226 No 0
5 1420 3095 0 No 48.1348603 No 0
6 1696 4455 0 No 48.7431357 No 0
7 2967 3492 1 No Average S.D. 61.5200249 No 0
8 2247 638 1 No Good -88.489933 99.0308064 51.930898 No 0
9 3935 7477 0 No Bad -359.50985 101.461754 146.070591 No 0
10 1022 4022 0 No 13.946797 No 0
11 1068 5683 0 No -2.4948691 No 0
12 3327 9795 1 No 10.0766923 No 0
13 2265 5341 1 No -1.2490316 No 0
14 3684 11888 1 No Monthly incomeOutstanding loanNo. of dependents 7.01276101 No 0
15 3973 4857 1 No Initial value 1 -1 -1 105.167052 No 0
16 3147 10548 1 No Alpha 0.05903619 -0.0115336 -73.364979 -9.2346327 No 0
17 3928 5131 1 No Maximize 3.65402933 99.3502136 No 0
18 3274 2399 1 No 92.2503745 No 0
19 1825 6041 1 No -35.298485 No 0
20 3777 6516 1 No 74.4616949 No 0
21 1244 4223 0 No Discrepancy 24.7345753 No 0
22 3514 23724 0 No Cutoff -223.99989 -66.170254 No 0
23 3139 14500 1 No No. 16 -55.28776 No 0
24 3712 17445 1 No Ratio 8.00% -55.426512 No 0
25 1172 6019 1 No -73.595378 No 0
26 2731 11872 0 No 24.3007876 No 0
27 3559 24955 0 No -77.711502 No 0
28 1117 7229 1 No Mis-classification cost -90.79804 No 0
29 1818 1387 1 No Good as bad 1 17.9656959 No 0
30 3524 9166 1 No Bad as good 10 28.9614645 No 0
Historical record Centre Classification
Z
Maximization (using Solver add-in)
Copyright 2018 CapitaLogic Limited

9. Example 8 Probit transform
Borrower Monthly
income
Outstanding
loan
No. of
dependents
Defaulted in
1 year
Coded PD
1 3750 3160 1 No 0 SUMMARY OUTPUT
2 1497 2156 0 No 0
3 1878 4450 0 No 0 Regression Statistics
4 2085 5856 0 No 0 Multiple R 0.805335
5 1420 3095 0 No 0 R Square 0.648564
6 1696 4455 0 No 0 Adjusted R Square0.643185
7 2967 3492 1 No 0 Standard Error0.299419
8 2247 638 1 No 0 Observations 200
9 3935 7477 0 No 0
10 1022 4022 0 No 0 ANOVA
11 1068 5683 0 No 0 df SS MS F Significance F
12 3327 9795 1 No 0 Regression 3 32.42821 10.8094 120.5707 2.82E-44
13 2265 5341 1 No 0 Residual 196 17.57179 0.089652
14 3684 11888 1 No 0 Total 199 50
15 3973 4857 1 No 0
16 3147 10548 1 No 0 CoefficientsStandard Error t Stat P-value Lower 95%Upper 95%Lower 95.0%Upper 95.0%
17 3928 5131 1 No 0 Intercept -0.03605 0.081911 -0.44014 0.660323 -0.19759 0.125489 -0.19759 0.125489
18 3274 2399 1 No 0 Monthly income-0.00014 2.43E-05 -5.82554 2.3E-08 -0.00019 -9.3E-05 -0.00019 -9.3E-05
19 1825 6041 1 No 0 Outstanding debt2.76E-05 1.89E-06 14.63062 3E-33 2.39E-05 3.13E-05 2.39E-05 3.13E-05
20 3777 6516 1 No 0 No. of dependents0.175568 0.017535 10.01252 2.54E-19 0.140987 0.210149 0.140987 0.210149
21 1244 4223 0 No 0
22 3514 23724 0 No 0
23 3139 14500 1 No 0
24 3712 17445 1 No 0 Total no. of records 10000
25 1172 6019 1 No 0 Probit coefficient 3.719042
26 2731 11872 0 No 0
27 3559 24955 0 No 0 Potential borrowerMonthly incomeOutstanding loanNo. of dependentsUnbound PDProbit Bound PD
28 1117 7229 1 No 0 1001 4,000 15,000 2 20% -2.23107 1%
29 1818 1387 1 No 0 1002 1,600 40,000 3 140% 6.729114 100%
30 3524 9166 1 No 0 1003 2,400 20,000 1 39% -0.8292 20%
Copyright 2018 CapitaLogic Limited

10. Example 9 Probit regression
Borrower Monthly
income
Outstanding
loan
Default in 1
year
Probit PD Likelihood Ln(Likelihood)
1 78 200 No -4.5980272 2.1326E-06 0.99999787 -2.133E-06 β0 -1.125628
2 73 200 No -4.2745184 9.5775E-06 0.99999042 -9.578E-06 β1 -0.0647018
3 73 500 No -1.9130111 0.02787332 0.97212668 -0.0282692 β2 0.00787169
4 71 300 No -3.3579458 0.00039262 0.99960738 -0.0003927
5 68 500 No -1.5895023 0.05597352 0.94402648 -0.0576011 Maximize -6.7153166
6 59 600 No -0.2200173 0.41292884 0.58707116 -0.5326092
7 57 300 No -2.4521211 0.00710084 0.99289916 -0.0071262
8 49 500 No -0.3601688 0.35936046 0.64063954 -0.4452883
9 35 600 No 1.33282499 0.90870538 0.09129462 -2.3936634
10 27 300 No -0.5110682 0.30465164 0.69534836 -0.3633423
11 59 700 Yes 0.5671518 0.71469447 0.71469447 -0.3359001
12 57 600 Yes -0.0906138 0.46389974 0.46389974 -0.7680868
13 44 500 Yes -0.03666 0.48537806 0.48537806 -0.7228272
14 38 500 Yes 0.35155059 0.63741234 0.63741234 -0.4503385
15 36 600 Yes 1.26812322 0.89762303 0.89762303 -0.1080051
16 36 800 Yes 2.84246143 0.99776167 0.99776167 -0.0022408
17 22 400 Yes 0.59960969 0.7256168 0.7256168 -0.3207332
18 22 500 Yes 1.38677879 0.91724539 0.91724539 -0.0863802
19 15 600 Yes 2.62686023 0.99569116 0.99569116 -0.0043181
20 10 400 Yes 1.37603083 0.91559396 0.91559396 -0.0881823
Copyright 2018 CapitaLogic Limited