1. Credit Portfolio
Management
-Economic Capital
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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

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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
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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
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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
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Portfolio model is a idea of securitization.
•Fitch’s Vector Model
•CSFB’s Credit Risk+
•KMV’s Portfolio Manager
20070709 Weller, Amber,Eric — Confidential
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Introduction to MKMV Portfolio Manager™
PM is the most widely used portfolio model among surveyed banks
20070709 Weller, Amber,Eric — Confidential
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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
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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

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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
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