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- 1. Internal Rating linked to Limit Control Introduction 2007 Eric
- 2. Restricted 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 2
- 3. Restricted 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 3
- 4. Restricted 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 4
- 5. Restricted 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 .
- 6. 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 6
- 7. Restricted 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 Copyright © 2007 ERIC KUO — Confidential 7
- 8. Restricted 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 Copyright © 2007 ERIC KUO — Confidential 8
- 9. Restricted 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 9
- 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 10
- 11. Restricted 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 11
- 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 12
- 13. Restricted 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 13
- 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 14
- 15. Restricted 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 15
- 16. Restricted 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 16
- 17. Restricted 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 17
- 18. Restricted 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 18

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Thanks

Very interesting approach. I would also like a copy of the Limit settings methodology and formulas used to following mail: fyunus@aol.com. Thanks in advance

regards

Farah

Very nice and helpful for limits setting approach. Would it be possible if I could get a copy of the Limit settings methodology and formulas used to following mail: kostasn23@gmail.com? Thank you in advance for your time

Thanks advance