1. Internal Rating linked to
Limit Control
Introduction
2007
Eric

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From regulator’s viewpoint, bank should have a formal system of limits, to
ensure that the credit risk is properly managed.
Single name Limit control linked to internal rating system
LGD 0 1A 1B 2 3 4 5 6 7 8 9 10
ORR_Grade PD 0.001% 2.50% 7.50% 15% 25% 35% 45% 55% 65% 75% 85% 95%
1 0.03%
BOMA
2 0.10%
preliminary
Industry limit control mechanism
3 0.16%
approved control
4 0.26%
at Portfolio Level
•Credit
•AA •CCC
5 0.42%
rating
and
6 0.61% •and Portfolio Level
below
7 0.90% •Industry above •A •BBB •BB •B
Internal rating limit control
8 1.35%
9 2.04% •Telecom •2 •4 •6 •6 •6 •4
Rating Grade EAD
10 3.15%
11 4.93% 1
12 7.82%
2
•Banks and •1 •2 •3 •3 •3 •2
13 12.61%
diversified
3
financials
4
5
•All other •1 •3 •5 •5 •5 •3
6
industries
7
8
9
10
11
12
13
Copyright © 2007 ERIC KUO — Confidential
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To determine an appropriate limit structure, need to take into account both
of the ‘risk/return’ and capital availability.
•Check the current capital.
•Lending business can grow if there is sufficient
Risk capital.
appetite •Lending business need to be constrained when
capital is limited.
• Standard deviation •AP
Limit setting for Rating
of RAROC.
Risk Return •RAROC
•Max loss if down- Factors Factors
- Setting limit at EAD Level •dated from 2005 to
graded by 1 notch.
current.
Utilize
Optimization
•Excel’s linear programming function.
•Pegged max loss at the amount that
can sustain our BIS Ratio = 8 %.
Copyright © 2007 ERIC KUO — Confidential
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Examine current portfolio.
•Examine •Decide
•Return •Risk •Limit
Current Risk •Optimization
structure
Analysis Analysis
Portfolio appetite.
Consider the Divided the capital
Utilize EXCEL ‘s
Bank’s current Risk appetite for Analyze return
with current capital
‘Linear
bank is billion of information from • Standard
•clients . to EAD ratio to
Programming’ to
capital or billion of Jan. 2005 to Mar. deviation of
come up with Max
analyze the
RWA. 2007, in terms of
• billion credit RAROC as
limit by Rating
optimize capital
exposure . earning
Bank has •Accounting profit grade.
structure by
volatility .
•Result in a billion Rating.
• billion of capital . •RAROC
RWA in terms of • Stress Max
AIRB approach. •The max loss At AIRB treatment. loss
tolerance is billion, scenario :
•The average
at which level Bank
capital to EAD ratio 1. Downgrade
can still maintain at
is % each grade.
8 % of BIS Ratio.
2. The worst
grade and
the ‘Early
warming’gra
de goes to
default.
To see if can
sustain BIS =8 %
Copyright © 2007 ERIC KUO — Confidential
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The current capital consumption of lending is around Billion.
# of Clients Usage of Capital EAD Capital as % of EAD
16 16 16 16
15 15 15 15
14 14 14 14
13 13 13 13
12 12 12 12
11 11 11 11
10 10 10 10
9 9 9 9
8 8 8 8
7 7 7 7
6 6 6 6
5 5 5 5
4 4 4 4
3 3 3 3
2 2 2 2
1 1 1 1
Total = Total = Total = Average =
4,406 Bn Bn %
Copyright © 2007 ERIC KUO — Confidential
Note : Basel EL DB, April 2007.Capital is estimated by based on BIS Ratio =10% 5
.

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Examine current portfolio.
•Examine •Decide
•Return •Risk •Limit
Current Risk •Optimization
structure
Analysis Analysis
Portfolio appetite.
Consider the Utilize EXCEL ‘s Divided the capital
Bank’s current Risk appetite for Analyze return
‘Linear with current capital
bank is billion of information from • Standard
•clients . Programming’ to to EAD ratio to
capital or billion of Jan. 2005 to Mar. deviation of
analyze the come up with Max
RWA. 2007, in terms of
• billion credit RAROC as
optimize capital limit by Rating
exposure . earning
Bank has •Accounting profit structure by grade.
volatility .
•Result in a billion Rating.
• billion of capital . •RAROC
RWA in terms of • Stress Max
AIRB approach. •The max loss At AIRB treatment. loss
tolerance is billion, scenario :
•The average
at which level Bank
capital to EAD ratio 1. Downgrade
can still maintain at
is % each grade.
8 % of BIS Ratio.
2. The worst
grade and
the ‘Early
warming’gra
de goes to
default.
To see if can
sustain BIS =8 %
Copyright © 2007 ERIC KUO — Confidential
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The risk appetite of a bank can be linked back to stress testing through the
understanding of specific downside events to be avoided through the use of limits
Objectives
Illustrative earnings distribution
1. Avoid shareholders’aversion
towards ‘ unacceptable’
individual (Event) losses that
Case 1 wipe-out a significant
proportion of profits –
absolute level of risk
2. ‘Extreme’loss relative to
overall profit base
Case 2
3. Average return levels
compared to the volatility of
Case 3
the credit losses inevitably
linked to them
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But the skill of finding risk appetite is above our current capitability we
choose to use available capital on hands to proxy the risk appetite.
Unit : Billion
Current
Total
Capital
xx
BIS Ratio = = xx%
xx
Total =c cc
The lending RWA of
CBG = xx Billion
FIRB
Capital Debt Capital Assume
Capital Sub
Current
Required
Debt available adding
to
Available raising Mat-
maintain ured for Additional
Lending capital to
at 10%
Capital
of BIS support
Market Op Credit RWA CBG’s
lending
Risk Risk Risk
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The Max loss tolerance is set at xx billion, beyond it the BIS may not be
able to maintain at 8%.
Unit : Billion
Min Capital to
maintain at 8%
Exposure increases
based on capital
xx
allocation BIS Ratio = = 8%
xxx
Credit
Market Op Credit Current Potential
RWA
Risk Risk Risk RWA increasing RWA
Set Max loss
tolerance = cc
Billion
Current 8%
Capital Debt Max
Sub
Capital Loss
Available Available Matured
Debt of BIS
Capital raising Copyright © 2007 ERIC KUO — Confidential
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10. Restricted
Examine current portfolio.
•Examine •Decide
•Return •Risk •Limit
Current Risk •Optimization
structure
Analysis Analysis
Portfolio appetite.
Consider the Utilize EXCEL ‘s Divided the capital
Bank’s current Risk appetite for Analyze return
‘Linear with current capital
bank is billion of information from • Standard
•clients . Programming’ to to EAD ratio to
capital or billion of Jan. 2005 to Mar. deviation of
analyze the come up with Max
RWA. 2007, in terms of
• billion credit RAROC as
optimize capital limit by Rating
exposure . earning
Bank has •Accounting profit structure by grade.
volatility .
•Result in a billion Rating.
• billion of capital . •RAROC
RWA in terms of • Stress Max
AIRB approach. •The max loss At AIRB treatment. loss
tolerance is billion, scenario :
•The average
at which level Bank
capital to EAD ratio 1. Downgrade
can still maintain at
is % each grade.
8 % of BIS Ratio.
2. The worst
grade and
the ‘Early
warming’gra
de goes to
default.
To see if can
sustain BIS =8 %
Copyright © 2007 ERIC KUO — Confidential
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RAROC is high ,yet volatile for the first 2 grades.
Average RAROC 2005~2007 Standard Deviation of RAROC
2005~2007 (Cross-Sell Included)
(Cross-Sell Included)
16 16
15 15
14 14
13 13
12 12
11 11
10 10
9 9
8 8
7 7
6 6
5 5
4 4
3 3
2 2
1 1
Avg.=% S.D. %
Copyright © 2007 ERIC KUO — Confidential
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12. Restricted
Examine current portfolio.
•Examine •Decide
•Return •Risk •Limit
Current Risk •Optimization
structure
Analysis Analysis
Portfolio appetite.
Consider the Utilize EXCEL ‘s Divided the capital
Bank’s current Risk appetite for Analyze return
‘Linear with current capital
bank is billion of information from • Standard
•clients . Programming’ to to EAD ratio to
capital or billion of Jan. 2005 to Mar. deviation of
analyze the come up with Max
RWA. 2007, in terms of
• billion credit RAROC as
optimize capital limit by Rating
exposure . earning
Bank has •Accounting profit structure by grade.
volatility .
•Result in a billion Rating.
• billion of capital . •RAROC
RWA in terms of • Stress Max
AIRB approach. •The max loss At AIRB treatment. loss
tolerance is billion, scenario :
•The average
at which level Bank
capital to EAD ratio 1. Downgrade
can still maintain at
is % each grade.
8 % of BIS Ratio.
2. The worst
grade and
the ‘Early
warming’gra
de goes to
default.
To see if can
sustain BIS =8 %
Copyright © 2007 ERIC KUO — Confidential
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Stress the max loss to see if Bank can sustain at BIS =8% minimum
requirement.
=Current Exposure
Down-graded
X X
Current EAD LGD by 1 notch Max Loss
As
su
m
eD
ef
au
lte
d
PD of 2nd Grade
Bn
Bn
Total = Total stress loss=
Copyright © 2007 ERIC KUO — Confidential
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14. Restricted
Examine current portfolio.
•Examine •Decide
•Return •Risk •Limit
Current Risk •Optimization
structure
Analysis Analysis
Portfolio appetite.
Consider the Utilize EXCEL ‘s Divided the capital
Bank’s current Risk appetite for Analyze return
‘Linear with current capital
bank is billion of information from • Standard
•clients . Programming’ to to EAD ratio to
capital or billion of Jan. 2005 to Mar. deviation of
analyze the come up with Max
RWA. 2007, in terms of
• billion credit RAROC as
optimize capital limit by Rating
exposure . earning
Bank has •Accounting profit structure by grade.
volatility .
•Result in a billion Rating.
• billion of capital . •RAROC
RWA in terms of • Stress Max
AIRB approach. •The max loss At AIRB treatment. loss
tolerance is billion, scenario :
•The average
at which level Bank
capital to EAD ratio 1. Downgrade
can still maintain at
is % each grade.
8 % of BIS Ratio.
2. The worst
grade and
the ‘Early
warming’gra
de goes to
default.
To see if can
sustain BIS =8 %
Copyright © 2007 ERIC KUO — Confidential
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Conditions for estimating capital optimization.
=Current Capital Distribution
Allow at least larger Unit : Billion
than current capital
consumption,due to
2
capital is sufficient.
Risk /Return
Moreover, not to
impact current
business. Apply the historical RARAOC
to the current portfolio :
1
- AP = Billion per annual .
Pegged ‘Earning
warming’ grades at - S.D = %
current exposure.
31 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
4
1. Estimate the down- grade expected loss.
1. Assume all default
2. Down grade 1 notch .
2. Estimate recovery
5
Capped at 30 Billion Copyright © 2007 ERIC KUO — Confidential
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Applying the linear programming in Excel and try to find a optimized
capital structure for limit setting.
Current Credit Portfolio Information
Basic Information
Target
3 Year
OR # of % of % of Voliatity of Capital
EAD Current Capital Avg LGD PD
R Client Client Cap RAROC to EAD
RAROC
1. Find Optimization of
1 10 0.2% 29,077,551,718 432,964,610 1% 22.5% 13.7% 1.5% 85% 0.03%
2 20 0.5% 24,933,158,348 903,243,602 3% 9.3% 23.9% 3.6% 84% 0.10% Capital Allocation .
3 88 2.0% 27,892,834,841 1,577,486,326 5% 15.2% 5.7% 5.7% 83% 0.16%
2. Max Profit
4 161 3.7% 45,325,735,870 3,090,370,820 9% 18.0% 7.6% 6.8% 71% 0.26%
5 264 6.0% 29,381,975,774 2,108,935,717 6% 18.1% 7.0% 7.2% 70% 0.42%
3. Lower S.D than current
6 286 6.5% 30,741,266,984 2,281,840,549 7% 18.1% 9.2% 7.4% 62% 0.61%
7 390 8.9% 38,693,823,532 3,224,231,451 9% 13.4% 4.2% 8.3% 57% 0.90%
portfolio.
8 654 14.8% 44,446,337,628 4,230,117,358 12% 11.4% 4.2% 9.5% 57% 1.35%
9 636 14.4% 36,220,446,127 3,307,225,124 10% 9.4% 3.7% 9.1% 47% 2.04%
10 772 17.5% 36,051,184,650 2,695,813,151 8% 4.8% 2.1% 7.5% 34% 3.15%
11 381 8.6% 44,351,078,692 2,816,069,080 8% -0.5% 3.9% 6.3% 30% 4.93%
12 132 3.0% 7,855,700,017 919,705,224 3% -7.0% 3.2% 11.7% 41% 7.82%
-13.2%
13 424 9.6% 31,021,006,357 4,070,146,132 12% 4.5% 13.1% 35% 12.61%
14 122 2.8% 6,976,469,776 1,505,782,028 4% -20.0% 19.6% 21.6% 57% 12.61%
15 38 0.9% 3,522,171,522 471,551,733 1% -7.0% 110.4% 13.4% 65% 12.61%
16 28 0.6% 2,542,820,824 538,166,583 2% -6.9% 157.3% 21.2% 74% 12.61%
NA & X-Sell 0% 206.0% 2624.4%
4,406 100% 439,033,562,660 34,173,649,490 100% 13.1% 3.5% 7.8% 42% 2.07%
Copyright © 2007 ERIC KUO — Confidential
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Linear programming solved the optimized capital allocation.
Business Max Loss is
grows,due to Capital Max AP under Earning limited below
sufficient capital distribution conditions volatility 30 billion
Limit ceiling
Linear
Linear
program Curren
% of progra
Linar ming t 3 Year
Voliatity of Orig Down grad1 CapAll Down
Cap mming
ORR Preliminary AP Current Capital Programming - growth portfoli Cap Allocation AP Final Limit -EAD Avg notch Max Loss Graded 1 notch EL
Increas Capital RAROC
Allocated Cap rate ol Cap RAROC
e distribu
conditio Distrib
tion
ns ution
24,766,053 29,719,263
1 86,631,852 432,964,610 519,557,532 20% 1% 1% 117,023,049 34,893,062,062 22.5% 13.7%
= 20%
33,600,002 40,320,003
2 34,834,945 903,243,602 1,083,892,322 20% 3% 2% 101,309,147 29,919,790,018 9.3% 23.9%
60,319,091 73,539,892
3 232,954,709 1,577,486,326 1,923,241,405 >=20% 22% 5% 4% 292,401,610 34,006,415,138 15.2% 5.7%
135,705,410 192,312,643
4 765,850,829 3,090,370,820 4,379,467,125 42% 9% 10% 790,493,275 64,232,605,628 18.0% 7.6%
124,921,157 178,069,732
5 385,416,022 2,108,935,717 3,006,197,095 43% 6% 7% 545,405,551 41,882,741,851 18.1% 7.0%
171,839,351 244,594,144
6 708,965,643 2,281,840,549 3,247,945,433 42% 7% 7% 587,967,840 43,756,763,704 18.1% 9.2%
>=40%
295,920,802 415,726,049
7 450,673,438 3,224,231,451 4,529,580,194 40% 9% 10% 605,688,894 54,359,241,695 13.4% 4.2%
519,102,453 805,313,334
8 529,785,129 4,230,117,358 6,562,423,069 55% 12% 15% 748,630,824 68,952,146,401 11.4% 4.2%
530,660,760 742,925,064
9 392,447,971 3,307,225,124 4,630,115,174 40% 10% 10% 436,237,929 50,708,624,577 9.4% 3.7%
598,799,662 718,559,594
10 117,221,522 2,695,813,151 3,234,975,781 20% 8% 7% 156,433,073 43,261,421,580 4.8% 2.1%
1,049,407,637 1,259,289,165
11 58,651,897 2,816,069,080 3,379,282,896 20% 8% 8% - 15,810,130 53,221,294,430 -0.5% 3.9%
>=20%
410,170,757 492,204,908
12 - 85,821,269 919,705,224 1,103,646,269 20% 3% 2% - 77,175,649 9,426,840,020 -7.0% 3.2%
10,717,490,313 12,860,988,375
13 - 397,997,525 4,070,146,132 4,884,175,359 20% 12% 11% - 644,685,320 37,225,207,628 -13.2% 4.5%
3,957,519,606 3,957,519,606
14 - 193,176,036 1,505,782,028 1,505,782,028 0% 4% 3% - 301,220,666 6,976,469,776 -20.0% 19.6%
2,302,330,146 2,302,330,146
0%
15 - 29,007,158 471,551,733 471,551,733 0% 1% 1% - 32,988,464 3,522,171,522 -7.0% 110.4%
1,893,509,588 1,893,509,588
16 - 52,787,014 538,166,583 538,166,583 0% 2% 1% - 37,385,864 2,542,820,824 -6.9% 157.3%
NA & X- 2,650,009,937 2,650,009,937 206.0% 2624.4%
22,826,062,788 26,206,921,508
5,654,654,893 34,173,649,490 45,000,000,000 32% 100% 100% 5,922,335,036 578,887,616,855 13.1% 3.5%
Current capital The Max capital
consumption target
7.1%
Original Portfolio Std Dev= Standard deviation is lower than current portfolio
After allocation Portfolio S.D= 7.0%
Copyright © 2007 ERIC KUO — Confidential
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The core of limit setting lies in how are we going to manage our risk under
stressed situation.
Major
•Risk Factor •Return / Business decision
components
Sufficient capital can support more lending business.
AIRB Treatment
Capital Capital allocation is business decision at the top
A function of PD, LGD, EAD, Tenor level.(How much capital should be allocated to CBG,
RBG)
Set limit control at EAD for easier to manage
EAD Sufficient capital can support more lending
risk.
business.
Examine if all grades are down-graded by 1
Stressed notch. •Must not exceed our max loss tolerance.
scenario Increased EL is absorbed by capital. •Maintain at least 8% of BIS Ratio.
th
Assume the 13 – grade and the ‘earning
warning’ are all defaulted.
A top management decision.
Max Loss The cushion to maintain at BIS Ratio at 8%
Can be lower or higher.
Tolerance
The minimum business growth rate can be set
Lending will be charged more EL.,If allocate
Business by BU, due to strategic plan.
more resource in Non-investment grades.
growth If there is not sufficient capital, business will be
constrained.
RAROC is one of the performance indicator for
Consider the profit after the EL.
RAROC
BU to decide where to grow.
Return over the UL .
S.D of Indicator of earning volatility.
RAROC
Capital allocation needs to take market size
Market size
into account.
Copyright © 2007 ERIC KUO — Confidential
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