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# Economic Capital

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### Economic Capital

1. 1. Credit Portfolio Management -Economic Capital 2007
2. 2. Restricted We cannot direct the wind but can adjust the sail. We don’t know when it will rain, but we know it will. AGENDA OF TODAY •Economic Capital Concept •Economic Capital Model 20070709 Weller, Amber,Eric — Confidential 2
3. 3. Restricted Basel estimate a general form of unexpected loss formula for banks to calculate the capital requirement. Basel estimates Factors in Basel2 A General formula For banks 1 Year PD is considered, •PD instead of cumulative PD K= Based on historical data ⎡ ⎤ ⎡ ⎤ 0.5 ⎛R⎞ •LGD ⎢ LGD× N ⎢(1 − R) × G(PD) + ⎜ ⎟ × G(0.999)⎥ − PD × LGD⎥ −0.5 ⎝1− R ⎠ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎢ ⎥ ⎣ ⎦ × (1 − 1.5 × b ) × [1 + (M − 2.5) × b ] Current status of EAD −1 •EAD RWA = K * 12.50 * EAD [0.11852 − 0.05478 × ln(PD)]2 •Tenor B= Capital = RWA * BIS Ratio ⎡1 − e (−50× PD ) ⎤ ⎡ ⎛ 1 − e (−50× PD ) ⎞ ⎤ ⎥ + 0 .24 ⎢1 − ⎜ ⎜ 1 − e − 50 ⎟ ⎥ •Correlation 0 .12 × ⎢ ⎟ 1 − e (− 50 ) ⎦ ⎣ ⎣⎝ ⎠⎦ 20070709 Weller, Amber,Eric — Confidential 3
4. 4. Restricted Basel estimate a general form of unexpected loss formula for banks to calculate the capital. Factors in Basel2 10th = 3.15% •PD EL = PD * LGD * EAD = 3.15% * 85% * 827,557,500 = 22 Million 9th = 85% •LGD AIRB K = 0.1987 NTD 827 Million •EAD RWA = K * 12.50 * EAD = 0.1987 * 12.5* 827,557,500 = 2,055 Million •Tenor 6 Years Capital = RWA * BIS Ratio =2,055 * 10% =205 Million 0.1048 •Correlation 20070709 Weller, Amber,Eric — Confidential 4
5. 5. Restricted Regulatory capital capture the unexpected loss which based on our target ‘Rating’, usually disregard the tail loss. Probability of loss BIS = 10% ~ A Rating Grade Expected loss Extreme loss (Tail loss) Unexpected loss A B 22 Million 600 Million 205 Million Cost of Capital doing consumption business Potential Max Loss = Total lending amount = 827 Million 20070709 Weller, Amber,Eric — Confidential 5
6. 6. Restricted Economic Capital estimate more accurate ‘Credit Risk’ than AIRB. AIRB Capital is a simplify version of Economic Capital AIRB : Internal Rating AIRB = CTCB Internal Rating Migration LGD Variance D •L •P GD •N ese SIZE Pr lue et nt Va n Correlation tio la re r Concentration Co • R = 0.12 *(1-EXP(-50*PD))/(1-EXP(-50)) Risk Neutral Discount + 0.24*(1-(1-EXP(-50*PD))/(1-EXP(-50))) Economic Capital Source: Basel Committee on banking supervision Basel adjusts correlation based on the size. AIRB :Advanced Internal Rating Based for Basel 2 accord. 20070709 Weller, Amber,Eric — Confidential 6
7. 7. Restricted MKMV uses 120 factors based on the global economy, region, sector, industry, and country, providing high resolution on sources of correlation. Systematic Risk Country Risk Industry Risk US Electronic UK Manufacturing Taiwan Service Korea Real estate . . 45 Countries’ 61 Industries stock index • Moodys’ KMV model each firm’s return as a function of factors: Common Firm Specific Countries Industries Risk 14 45 61 rk = ∑ βkf rf + ∑βkcεc +∑βkiεi + εk f =1 c=1 i =1 20070709 Weller, Amber,Eric — Confidential 7
8. 8. Restricted Economic capital capture the Diversification Effect and estimate the risk contribution of each obligor. - Illustrative - This portion of the 26 % Case1 :Different industry but in same country risk has been Saving diversified away Diversified within the portfolio. Basel 2 5.2 MM 19.7 MM Firm’s total Diversifiable 11.5 MM + Economic Capital Firm Specific Economic Capital = 14.5 MM (stand-alone) 8.2 MM Risk Contribution of Systematic China Airline =3 MM Airline Bank 29.5 % This portion of the Case2 :Different industry and different country Saving risk has been diversified away Diversified within the portfolio. 4.1 MM 13.9 + Firm’s total Diversifiable Economic Capital 8.2 MM Economic Capital = 9.8 MM 5.7 MM Firm Specific (stand-alone) Systematic Risk Contribution of Insurance (US) Airline Insurance Auto = 1.6 MM Assume : Lend NT 100 MM to each borrowers at LGD=45% of collateral, given their different PD. 20070709 Weller, Amber,Eric — Confidential 8
9. 9. Restricted Firm specific risk can be further diversified through adding more credit name. Systematic Risk Can be Further Diversified Through Firm Specific Add more risk obligors 20070709 Weller, Amber,Eric — Confidential 9
10. 10. Restricted Regulatory capital is a simplified version of Economic capital and doesn’t consider the repay effect of a loan and timing of insolvency. Cash flow of a loan without default 11 1 1 1 1 1 -10 Net Present Sophisticated Discounted Value Math, Stat Cash flow of a loan with default Economic Capital 1 1 1 1 0 0 •Rating Migration -10 Defaulted •Default timing Discounted •Correlation Recovery Net •Concentration Present Value •Simulation Discounted 20070709 Weller, Amber,Eric — Confidential 10
11. 11. Restricted Case study Expected loss provides information on cost of doing business. Example Exposure AIRB Expected Loss X X = Probability of Default * Loss Given Default 0.0022 0.15 TSMC 1 Million 330 0.0022 Acer 1 Million 0.55 1,210 Hon Hai 1 Million 0.0014 0.75 1,050 •Utilize KMV’s EDF (Expected Default Frequency) •Assume 1 year tenor for all exposures 20070709 Weller, Amber,Eric — Confidential 11
12. 12. Restricted Economic capital captures the portfolio concentration effect. Example Exposure FIRB Capital * AIRB Capital Economic Capital 364,309 83,935 149,964 TSMC * 1 Million 364,309 307,762 Acer 383,826 1 Million Hon Hai 748,911 1 Million 283,185 309,882 Total=1,282,701 Total= 701,579 Total= 1,011,803 * Hon Hai is classified as electronic equipment industry,Acer is computer hardware,TSMC is Semi-con 20070709 Weller, Amber,Eric — Confidential 12
13. 13. Restricted Using Economic capital to estimate the risk/performance is more accurate. Probability of loss BIS = 10% ~ A Rating Grade Extreme loss (Tail loss) Expected loss Unexpected loss Taiwan exposures 2,298,421 AIRB Cap =701,579 Taiwan exposures 1,717,299 ECap =1,282,701 Max Loss = Total lending amount = 3 Million 20070709 Weller, Amber,Eric — Confidential 13
14. 14. Restricted Now, let’s consider a case of adding 3 US obligors into the current Taiwan asset pool.. Example Before Adding it …. Economic Capital Industry AIRB Capital Exposure PD Utility, Electric 333,372 0.0106 AES 1 Million 685,004 Consumer durable AGCO 1 Million 0.0048 158,431 447,173 & Machinery AEP 654,117 Paper & Plastic 0.0119 396,761 1 Million Total = 888,564 Total = 1,786,294 Note : Assume LGD = 50% . 20070709 Weller, Amber,Eric — Confidential 14
15. 15. Restricted Diversification effect significantly reduce the required capital for unexpected loss. Adding a 3 million exposure of portfolio, only increasing 0.1 Economic Capital Diversification Effect million of credit risk. US Exposure Taiwan Exposure 2,171,265 888,564 632,899 AES 333,372 149,964 TSMC Reduce 1,538,366 1,282,701 AGCO 158,431 + = 383,826 Acer Hon Hai AEP 396,761 748,911 Diversified Final Taiwan US Add Total Total = 888,564 Total= 1,282,701 Effect ECap 20070709 Weller, Amber,Eric — Confidential 15
16. 16. Restricted Correlation acts an important role in estimating economic capital. Taiwan’s GNP is deeply influenced by global economics. Example Even though, the Taiwan exposures have lower PD than US ‘s Taiwan Exposure US Exposure Stand-alone Added together R-Squared Stand-alone Added together R-Squared 149,964 65% 149,964 AES 333,372 TSMC 226,616 39.65% 93,526 61.27% 18.73% Acer AGCO 158,431 383,826 82,158 Hon Hai 748,911 AEP 396,761 748,911 61.15% 237,191 13.97% Total =1,455,502 Total = 888,564 Total = 545,965 Total= 992,401 Higher R-Squared Lower R-Squared represents represents for easier to be for less easier to be influenced by global influenced by global economics economics * FIRB applies 45% of LGD 20070709 Weller, Amber,Eric — Confidential 16
17. 17. Restricted Regulatory capital is a method of addition which sum all the risk up . Example Implication Taiwan Portfolio US Portfolio Total portfolio •Exposure increased double . 3 Million 3 Million 6 Million Exposure •Regulatory capital is a Method of addition. •While as Economic capital AIRB taking into ‘diversification’ , + = 1.8 Mn 2.5 Mn 0.7 Mn Capital ‘concentration’ , ‘ Rating transition’ , ‘ pay-off ‘ and ‘NPV’ 1.5 Mn into account to better estimate Economic 1.3 Mn 0.9 Mn 2.2 Mn the credit risk. Capital 0.6 Mn diversification effect 20070709 Weller, Amber,Eric — Confidential 17
18. 18. Restricted Example Ecap is a better indicator of risk estimation than regulatory capital. Before Adding portfolio into together After Adding portfolio into together The chart below demonstrates a clear effect of Acer benefits the most from the diversification effect industry concentration and correlation . All three whose ECap drop dramatically, While as all the US Taiwan exposures are classified as electronics portfolio reduce the Ecap. This analysis also shows related industry and have strong relationship with that the AIRB Capital over estimated the credit risk global economics which result in a phenomenon of because of all the three US names have lower Ecap higher economic capital than AIRB capital. than its corresponding Rcap. Economic Capital Economic Capital 800,000 800,000 Hon Hai Hon Hai 700,000 700,000 600,000 600,000 500,000 500,000 AEP Acer 400,000 400,000 300,000 AES AEP 300,000 TSMC TSMC 200,000 AES 200,000 AGCO Acer 100,000 AGCO 100,000 0 0 0 200,000 400,000 600,000 800,000 0 200,000 400,000 600,000 800,000 20070709 Weller, Amber,Eric — Capital AIRB Confidential AIRB Capital 18
19. 19. Restricted Concentration risk Economic capital increased even more than the exposure’s. Example Exposure Economic Capital Exposure Economic Capital 149,964 149,964 TSMC * 1 Million 1 Million Increased 4.6 X Acer 383,826 1,766,596 1 Million 4 Million Hon Hai 748,911 748,911 1 Million 1 Million Total=1,282,701 Total= 2,665,472 Increased by 2.08 X * The AIRB Cap of Acer is 1,231,049, increase 4 X . 20070709 Weller, Amber,Eric — Confidential 19
20. 20. Restricted Take away Risk is not additive,correlation is an important driver of portfolio credit risk. Since credit quality is dynamic, exposure value correlation changes, but can be managed. Portfolio Risk Mgmt Obligor Risk Mgmt •Focus on internal ratings •EL + Risk Contribution (post-diversification) reflected in pricing •Expected Loss reflected in pricing •Correlations reflected •No consideration of correlations •Total portfolio can be managed •No view of total portfolio •Active management or balance sheet exposures •No active management through CDS, trading, syndications Separate Assessments of risks by obligor / Unified, coherent portfolio-level analysis, businesses / assets incorporating correlations Capital Strategy Economic Capital RC RC RC RC Risk EL EL EL EL Contribution Portfolio Analysis Rating Rating Rating Rating 1A 2A 3A 4A 1A 2A 3A 4A Obligor 1, Obligor 1, Facility A Facility A 1B 3B 4B 1B 3B 4B 20070709 Weller, Amber,Eric — Confidential 20
21. 21. Restricted We cannot direct the wind but can adjust the sail. We don’t know when it will rain, but we know it will. AGENDA OF TODAY •Economic Capital Concept •Economic Capital Model 20070709 Weller, Amber,Eric — Confidential 21
22. 22. Restricted Portfolio model is a idea of securitization. •Fitch’s Vector Model •CSFB’s Credit Risk+ •KMV’s Portfolio Manager 20070709 Weller, Amber,Eric — Confidential 22
23. 23. Restricted Introduction to MKMV Portfolio Manager™ PM is the most widely used portfolio model among surveyed banks 20070709 Weller, Amber,Eric — Confidential 23
24. 24. Restricted 16 % of clients account for 37% of total exposure and consume 42.7% of capital. Portfolio Facts 100 % = •Economic Capital take the industry correlation , concentration and re- 52 % payment into account. •Most of our asset is concentrated 57 % Un-public 62.8 % 85 % on certain industry with higher correlation with the global economics , therefore, it is inevitably for bank that the Ecap is higher than AIRB Cap. 35.6% 27.6% 23.0% TSE 2.8% 7.0% ROTC 5.3% 2.0% Public Offering 2.0% 7.9% 6.5% 3.0% 5.7% OTC 4.0% 4.3% 3.5% 3.2% # of Client EAD AIRB Capital Economic Capital 20070709 Weller, Amber,Eric — Confidential 24
25. 25. Restricted Certain industries have over concentrated that results in a higher risk capital than IRB’s 100 % = 466 Billion AIRB Capital 100%= 34 Billion Economic Capital 100%= 46 Billion EAD B2C 4% 5% 7% 12% 9% 11% 不 6% 7% 5% 5% 4% 5% 3% 12% 9% 14% 9% 7% 11% 16% 10% 3% 2% 3% 金 11% 6% 13% 行金 2% 3% 7% 4% 2% 3% 4% 4% & 4% 7% 4% 5% 路 6% 5% 5% 零 2% 2% 2% 2% 2% 3% 行 3% 2% 3% & 4% 4% 金 Avg.= 5.8% Equally allocate to each industry = 5.6 %25 20070709 Weller, Amber,Eric — Confidential
26. 26. Restricted Utilizing the Ecap to identify the risk level and as an important component for capital allocation. Unit:Billion ORR Industry It may be inappropriate to apply ‘Concentration Risk’ Higher ECap than RCap in ‘ ’ is an good concept into Rating grade analysis. illustration of ‘high correlation’industry. accounts However, we can use Ecap & Rcap comparison to demonstrate if we over-estimate the credit risk through for 7% of EAD, but it consumes 9% of total Rcap and compare the Ecap and Rcap. As shows in the chart has a 14% share of Ecap. that the 8th, 2nd , 12th Grade have higher Ecap than RCap Economic Capital Economic Capital 8 Others ECap > RCap Zone ECap > RCap Zone 8 Reduce 6 risk 2 RE exposure 12 11 4 4 7 Increase 5 B2C & risk 6 10 exposure Non-Bank 13 Shoes 零 9 2 3 PS 路 1 Bank AIRB Capital AIRB Capital 金 0 20070709 Weller, Amber,Eric — Confidential 26