Toward Credit Portfolio Management

Toward
Credit Portfolio Management

Part I
A Rudimentary Guide to Credit Portfolio Modeling:
Theory Introduction
Model Development
Applications

Draft Edition
Eric Kuo

Toward

Credit Portfolio Management

Part I

A Rudimentary Guide to Credit Portfolio Modeling:

Theory Introduction

Model Development

Applications

Draft Edition

Eric Kuo

ii
Copyright @ Eric Kuo 2008

All rights reserved

No part of this document may be reproduced in any form,
by Photostat, microfilm, xerography or any other means,
or incorporated into any information retrieval system,
electronic or mechanical, without the written permission
of the copyright owner.

iii

To Liwen, for her patience and support

To Tiffany, with joy and pride

iv
Preface

Banks may fail for a lot of reasons. It may fail to compete with peers and gradually lose the
market share. Or it may adopt wrong strategies and target at riskier segments. Or it may fail
to manage the market risk and incur massive trading losses. Or it may underestimate the
interest rate risk, liquidity risk and unable to manage the funding gap. Of all the possible
reasons of failure, the most threatening risk, in my opinion, may be the credit risk.

The massive credit losses arise from the credit risk that wipe out bank capital and cause bank
failure. In my opinion, these credit losses sometimes are a result of concentration risk, such as
single name concentration that one or few obligors account for significant portion of total
portfolio. It also may be a result of industry concentration, product concentration or segment
concentration, that several losses appear simultaneous during the economic malaise.
Moreover, sometimes the credit losses may be the consequence of the problem of miss-pricing
that the credit revenue cannot cover the credit losses.

Although bankers conceited themselves as credit risk professionals, the banking industry in
general doesn’t generate any profit to the shareholders, simply counting the credit losses
occurred in the past decade. All theses lead us to conclude that the banking industry is a highly
vulnerable, highly competitive and highly regulated business. The business that banks do is
risk-taking; however, the amount of potential credit risk is almost unknown – both of the
investors and bankers themselves.

As banks have moved in the direction of new Basel Accord, the credit risk has become more
important and will be more transparent to the investors. However, the measurement of credit
risk parameters (such as probability of default, loss given default and exposure at default) is
only just the first step toward the credit risk management. The estimation of the credit
portfolio risk further allows bankers to understand the unexpected loss. Banks can apply the
economic capital into many management applications, such as capital allocation,
performance management and business strategic planning.

This document is an overture of credit portfolio management.
Part 1: Credit portfolio modeling – measuring the unexpected loss of portfolio. (Discussed in
this document)
Part 2: Credit correlation modeling- estimating the asset correlation among obligors.

v
Part 3: Credit portfolio analysis- diagnosing the performance of portfolio – assessing whether
if risk and return is balanced.
Part 4: Credit concentration risk management- managing the credit concentration risk
through setting the limit boundary.

This document provides a simple credit portfolio model for readers to estimate the credit
portfolio unexpected loss. One important message that I’d like to deliver is that if you cannot
measure risk, then you should not expect to manage the risk.

This document is not aimed at technicians or quants. There are already many excellent
books explore the technique of portfolio modeling. Instead, this document focuses on the
application of the credit portfolio risk. How can bank leverage the simple model provided in
this document to better understand the unexpected loss of bank’s credit portfolio. In my
opinion, the efforts of risk measurement are vanity without promoting the measurement into
management.

In summary, sound credit risk management must be transparent and well perceived. Only
when the board, CEO, rating agencies, equity analysts and the investors are well-informed
and are confident at the bank’s risk management- they will not expect bankers perform
miracles and they won’t be surprised by the losses in a economic recession. After all,
banking business is a cyclical business with frequent expected loss and threatening
unexpected losses.

I could point out that the most opaque black box in many financial institutions is the quality of
credit asset. The figures that bank provided in the annual report only depicts the past and
have no value regarding the future asset quality. The disclosure of economic capital will give
outsiders a clue. Also is an action of risk governance that will distinguish bank from her
peers.

Any error and unintentional deviation from the best practices remain my own responsibility.

Eric Kuo, Sep, 2008

Table of content

Section 1: Foreword and Introduction .......................................................................... 1
Section 2: Why banks need capital .............................................................................. 3
The IRB capital equation...................................................................................... 4
Differences between AIRB capital and Economic Capital .................................... 9
Section 3: Theory & vendor models introduction ....................................................... 17
Portfolio Models Introduction.............................................................................. 18
KMV’s Portfolio manager ................................................................................... 19
Creditmetrics ...................................................................................................... 24
CreditRisk+ ........................................................................................................ 31
Creditportfolioview.............................................................................................. 32
Section 4: Methodology of simple portfolio model development ................................ 37
Unconditional and conditional PD ...................................................................... 37
Loss based or value based ................................................................................ 39
Correlation Model............................................................................................... 40
Model Design Methodology................................................................................ 42
Section 5: Model manual instruction .......................................................................... 47
Data requirement ............................................................................................... 47
Model screenshot............................................................................................... 47
Example ............................................................................................................. 48
Joint default observation .................................................................................... 51
Charts................................................................................................................. 52
Section 6: Applications of in-house credit portfolio model.......................................... 54
Effect of correlation ............................................................................................ 54
Effect of concentration ....................................................................................... 59
Effect of PD ........................................................................................................ 60
Effect of LGD...................................................................................................... 61
Section 7: Future improvements ................................................................................ 64
Correlation.......................................................................................................... 64
Risk contribution................................................................................................. 65
Section 8: Economic capital as management applications ........................................ 67
Risk governance ................................................................................................ 67
External communication..................................................................................... 69
Internal management ......................................................................................... 72

Performance metrics .................................................................................. 72
Capital allocation ........................................................................................ 75
Limit setting ................................................................................................ 76
Section 9: Beyond economic capital .......................................................................... 77
Revisit the commercial banking business model ............................................... 77
Credit portfolio management as a business model ............................................ 79
Section 10: Helping the CEO’s sleep quality.............................................................. 82
Reference .................................................................................................................. 83
Appendix .................................................................................................................... 85
Interpreting the IRB capital equation.................................................................. 85
1. The Vasicek formula............................................................................... 86
2. Correlation estimation: R........................................................................ 88
3. The expected loss .................................................................................. 91
4. Maturity adjustment: ............................................................................... 91
VBA code ........................................................................................................... 93

1

Section 1: Foreword and Introduction

Credit portfolio modeling is one of the most important topics in risk management and finance
theory today. The last decade has seen the development of models to compute portfolio credit
losses for bonds and loan portfolios. The important output from the credit portfolio model is so
called economic capital which is used to gauge how many amount of potential unexpected loss
a bank is exposed to given the current credit portfolio constitution. Banks hold ‘Economic
Capital’ (or “Risk” Capital) to protect against “Unexpected Loss”.

It is opposed to the Basel 1 and is different from the AIRB approach under Basel 2. Although,
the Basle 2 has taken the first steps to amend the capital requirement and to promote banks to
implement the internal credit risk models for better estimating the unexpected loss (regulatory
capital). In the BIS regulatory model, the potential exposures are given by an add-on factor
multiplying the notional of each transaction. It is simple to implement, but the model has been
widely criticized because it does not accurately capture the diversification effect and
concentration risk of portfolio.

By contrast, credit portfolio models measure credit economic capital and are specifically
designed to capture the portfolio effects, specifically obligor correlations. These models include
the pioneers: KMV’s Portfolio Manager (1993), CreditMetrics (JP Morgan 1997), CreditRisk+
(Credit Suisse Financial Products 1997) and Credit Portfolio View (Mckinsey, Wilson 1997a
and 1997b). Although superficially they appear quite different—the models differ in their
distributional assumptions, restrictions, calibration and solution1.

The major limitations, in my point of view, are: the vendor models are expensive and
complexity. Expensive means the subscriber needs to pay for the software expense each year,
unless bank has a big commitment on the use of economic capital. Most of the model
comprises sophisticated mathematic modeling and are difficult to explain in a simple
spreadsheet. For the user who is less trained in math will have an impression of ‘Black box’.
Both of the above are the motivation of this document. In addition, it is vital for banks to
estimate the unexpected loss of their credit portfolio to better understand the uncertainty.

1
Gordy (1998) and Koyluoglu and Hickman (1998) show an underlying mathematical equivalence
among these models.

2

This document will begin at revisit the role of bank capital; why is it essential to the bank
management- it is definitely not only to meet the regulatory compliance. Then, review the
portfolio theory and introduce several vendors’ portfolio models. In the following, this document
will explain the method that grounded on this simple credit portfolio model. There is one section
elaborates how to leverage the model provided in this document to simulate the economic
capital and gauge the sensitivity of portfolio loss based on bank’s internal risk parameters. The
limitation of this model and directions of future improvement are also discussed. I also briefly
introduce the management applications and the concept of active credit portfolio management
in this document as well.

3

Section 2: Why banks need capital

Banks as chartered financial intermediary institutions require taking many responsibilities and
needs to meet many regulations. To prevent from the insolvency and result in financial crisis,
banks need to reserve a certain amount of capital to protect from unexpected loss except for
the provision reserve. Therefore, the estimation of bank capital is essential for the regulator to
gauge the riskiness of bank’s asset and is important for bank itself to do business.

In principle, the maximum amount of the credit loss a bank might face is the ‘Credit Exposure’
multiplying by the ‘Loss Given Default’.

Maximum Loss = Exposure at Default * Loss Given Default

Take a portfolio contains 500 billions of exposure and has an average 40 % of LGD as an
example. The maximum loss is equal to 500 Bn*40% = 200 Bn. If the regulator takes a
conservative stance in the regulatory capital policy, then bank needs to hold 200 billion for this
500 billion of loan portfolio.

However, the occurrence of this maximum loss is close to zero. The event implies that all
obligors are going to be insolvent in the same time. The essence of credit portfolio
management is to establish portfolio balance with adequate diversification2. This mitigates the
consequences of the portfolio's volatility of value (sometimes termed unexpected losses) to a
level where an institution can survive such losses given its reserves and capital.

The Basel committee, therefore, investigated the existed credit portfolio models and assistance
from the best practices3. Finally, Basel committee decided to apply the Merton’s concept and
come up with equation4 to estimate the risk weight for bank’s credit asset.

2
Usually comes from the correlation which is to estimate the default event relationship among the
obligors.
3
Such as, J.P Morgan, CSFB, Bank of America and other pioneers in credit portfolio management.
4
Basel Committee on Banking Supervision,2004.An Explanatory Note on the Basel II IRB Risk Weight
Functions. Page 5, page 6.

4

The IRB capital equation5

The calculation of AIRB capital requires a bank to utilize the past historical loss information to
estimate the PD, LGD and EAD - the same concept as developing a credit scoring card or
utilizing the data mining skills to find the customer behaviors.
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Bank capital is reserved as a cushion to absorb unexpected loss.
Conceptual
Generate risk parameters (PD,LGD,EAD) Bank capital (risk or economic capital)
from historical loss data. is prepared as cushion to absorb the
The expected loss estimation is the cost unexpected credit losses.
of doing loan business.

Target
1. Basel
Capital is used to rating
cover these Credit loss generates a
Credit Loss
extraordinary loss
general form of
Risk Appetite formula to
A
proxy the
Bank’s actual loss ‘unexpected
Risk
Unexpec-
experience
Capital loss’ and as
ted loss
Average
capital
credit loss
requirement.

2. It might over or
EL
under
estimated the
Time Probability
risk.

Note : Expected Loss = PD*LGD *EAD
EL doesn’t necessary equal to the historical loss experience, due to the portfolio component may change. 2008 Eric Confidential
1

The EL is a concept of average credit losses based on the past experience and should be able
to cover the credit losses in the most of the time6. The capital requirement is reserved for the
losses that exceed the expected loss. Ideally, the capital requirement estimation should link to
bank’s desire rating grade. The Basel committee generates a general form of formula to proxy
the ‘unexpected loss’ and as capital requirement. It might over or under estimated the risk.

For the corporate exposure, the Basel suggests the following formula:

5
Please refer to the appendix ‘Interpreting the IRB capital formula’ for more detail mathematics
deduction.
6
The historical expected loss usually doesn’t equal to the current expected loss of the portfolio, for the
following reasons :
1. The portfolio mix is different from the past portfolio : The PD and LGD of a portfolio may change
over time. If the PD becomes better than the past, the expected loss ratio might be lower and visa’
versa.
2. The exposure may be different: for example the average credit loss is 100 out of 1,000 of exposure,
while as the exposure may be expand to 2,000. To compare the absolute amount of expected loss
may not be appropriate.

5
Restricted
Basel committee generates a general form of unexpected loss formula for
banks to calculate the capital. –”a simplified version of EC”.
Basel estimates
A General formula
Inverse of the
Factors in Basel2 For banks
standard normal
Standard normal distribution
distribution (G)
(N) applied to threshold and
applied to PD to
1 Year PD is considered, conservative value of
PD derive default
systematic factor
instead of cumulative PD
threshold
Subtract EL
based
Correlation
K= provision
Based on historical data
LGD
⎡ ⎤
⎡ ⎤
0.5
⎛R⎞
⎢LGD× N ⎢(1 − R) × G(PD) + ⎜ ⎟ × G(0.999)⎥ − PD × LGD⎥
−0.5

⎝1− R ⎠
⎢ ⎥
⎢ ⎥
⎣ ⎦
⎢ ⎥
⎣ Inverse of the ⎦
standard normal
Current status of EAD
EAD distribution (G)
× (1 − 1.5 × b ) × [1 + (M − 2.5) × b ]
−1
applied to
confidence level
to derive
Tenor adjustment conservative
value of
systematic factor
[0.11852 − 0.05478 × ln(PD)]2
Tenor RWA = K * 12.50 * EAD
B=

R=
⎡1 − e (−50× PD ) ⎤ ⎡ ⎛ 1 − e ( −50× PD ) ⎞ ⎤
Asset
Capital = RWA * BIS Ratio
⎥ + 0.24 ⎢1 − ⎜ ⎟⎥
0 .12 × ⎢ ⎜ ⎟
1 − e (− 50 ) ⎦ − 50
⎣ ⎝ 1− e
Correlation ⎣ ⎠⎦
2008 Eric Confidential
1

Restricted

Basel 2 Capital estimation is a simplified version of EC (or Credit VaR)

Basel set at 99.9% of confidence

Subtract EL
based
Correlation provision

⎡ ⎤
⎡ ⎤
0.5
⎛R⎞
⎢ LGD× N ⎢(1 − R) × G(PD) + ⎜ ⎟ × G(0.999)⎥ − PD × LGD⎥ × (1 − 1.5 × b )−1 × [1 + (M − 2.5) × b ]
−0.5

K= ⎝1− R ⎠
⎢ ⎥
⎢ ⎥
⎣ ⎦
⎢ ⎥
⎣ ⎦
Tenor adjustment
Source : An Explanatory Note on the Basel II IRB Risk Weight Functions, Basel 2
1

Higher the target BIS ratio, larger the capital required to reserve. The Basel 2 AIRB capital is a
simplified version of VaR model 7 . From Basel committee’s perspectives, the confidence

7
An Explanatory Note on the Basel II IRB Risk Weight Functions, Basel 2.

6
interval for protecting the risk of insolvency is set at 99.9%. This implies that there is only
0.1% of possibility that the loss will exceed ‘expected loss + unexpected loss’ within 1 year.

The major difference between wholesale and retail bank’s capital computation can be further
explained by the below chart:
Restricted

The major difference in Basel 2 capital estimation between Corporate and
Retail Banking is ‘Correlation’.
Retail example Corporate example
Frequency Frequency

Credit Loss Credit Loss

1. UL more important than EL (small number
1. EL more important than UL (large number of
of relatively good quality loans)
loans minimises Impact of fluctuations)
2. High correlation
2. Low correlation
3. Significant capital requirements
3. Capital required is relatively low:

Constant correlation = 15% for Mortgage Correlation =
= 4% for Revolving
Correlation = 23.8% for obligor with 0.03% (AA-)of PD

K=
K=

RWA= K * 12.5*EAD
1

As illustrated in the chart, the Basel committee considered the retail products have a lower
asset correlation than wholesales banking. Based on the equation; the asset correlation for the
AA grade8 is around 23.82%. By contrary, the correlation for the B- grade is less than half of
the 1st grade – 12%. We can find that the asset correlation function is built of two boundaries:
correlations of 12% and 24% for very high and very low PDs. Correlations between these
boundaries are modeled by an exponential weighting function that displays the dependency on
PD. The exponential function decreases rather fast; its pace is determined by the risk weight
equation; the so-called “k-factor”. The upper and lower bounds for the correlations and the
functions are based on the empirical studies.

On the other hand, the mortgage asset has a 15% of constant correlation; while as the
revolving product has a 4% of correlation. Both of the above retail products’ correlations are
lower than most of the corporate rating’s. The reason that the retail products have lower

8
PD of AA grade is 0.03%. PD of B- grade is 12.61%.

7
correlations is that the retail products are viewed as more diversified portfolio compare to
corporate obligors. Several studies also confirmed the same result9. On the other hand, the
mortgage has higher dependency with the real estate industry and is deeply influenced by the
economy; therefore, the mortgage has higher asset correlation compare with other retail
products10.
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Better grade has higher asset correlation under Basel committee’s
assumption.

ORR_Grade PD Correlation
AA 0.03% 23.82%
25%
23.82% A+~A- 0.10% 23.41%
BBB+ 0.16% 23.08%
20%
BBB 0.26% 22.54%
Mortgage
BBB- 0.42% 21.73%
15%
BBB-
Negative 0.61% 20.85%
Asset 12%
Correlation perspective
10%
BB+ 0.90% 19.65%
Resolving Product
BB 1.35% 18.11%
5%
BB- 2.04% 16.33%
11

BB-Negative
3.15% 14.48%
perspective
0%
1 2 3 4 5 6 7 8 9 10 11 12 13
B+ 4.93% 13.02%
B 7.82% 12.24%
CTCB Rating Grates
B- 0.1261 12.02%

1

The Basel deployed the correlation effect on the rating grade instead of on the country, industry.
The difficulty that the Basel committee faces is that it’d be challenge to estimate average
correlation for different country and different industry. Therefore, they turn to implement the
correlation into the probability of default. The rational is that better rating obligor usually has
larger asset size; larger asset usually has a higher dependency with the state of economy11.

For example, the Honhai company has conducted many business across the world and is a
major export contributor to Taiwan’s GNP. Therefore, if the economic declines, the Honhai
company will be easier influenced by the economic downturn than SMEs or retail products may
have.

9
Asset correlation of mortgage is range from 7% ~ 10% and 2%~5% for the retailing products, based on
MKMV’s survey, Technical note. ‘Including non-corporate credit risk’, 2007.
10
Paul Calem and James Follain also found the 15% of correlation is reasonable and is supported by
their empirical test.
11
Lopez,2002. The empirical relationship between average asset correlation,firm probability of default
and asset size.

8
We can use the following example to illustrate the effect of correlation on the capital
estimation.
Restricted

Same lending amount, different capital charge are result from correlation.

Both have the same
EL = PD * LGD * EAD Mortgage
Corporate Clients
= 1.35% * 45% * 100 Mn
= 0.61 Million 1.35%
1.35%
PD
While as mortgage has
Corporate has higher lower ‘K’ , due to lower
‘K’ correlation
45%
K = 0.082 K = 0.0549
45%
LGD

RWA = K * 12.50 * EAD RWA = K * 12.50 * EAD
NTD 100 Million
NTD 100 Million
EAD = 0.082 * 12.5* 100 Mn = 0.0549 * 12.5* 100 Mn
= 102 Million = 68.7 Million

2.5 Years
2.5 Years
Tenor

Capital = RWA * BIS Ratio Capital = RWA * BIS Ratio
=102 Mn * 10% =68.7 Mn * 10%
15 %
18.11%
Correlation =10.2 Million =6.87 Million

1

In this example, the PD, LGD, EAD and loan maturity are the same for both of the corporate
loan and retail mortgage. As a result, the EL is the same for both exposures.12. Given the
correlation formula, the corporate client has an 18.11% of asset correlation and result in a
capital charge of 10.2 million higher than the 6.87 million of mortgage’s. Even though, the
correlation difference between this corporate client and mortgage is merely 3.11% but this tiny
variation result in a 3.15 million of capital divergence.

12
EL = PD * LGD* EAD

9
Restricted

It also implies that Mortgage will faces longer tail risk of uncertainty.

Probability of
loss
98.65%
Mortgage Corporate
Case Case

Best effort
estimation
if default
1.35%
1.35%

Loss
Most likely loss If default = Max loss
=100million
EAD * LGD =100mn*45% =45 Million
Expected loss Unexpected loss Tail Risk
Corporate
0.61 89.19 Million
10.2 Million Case
Million

Expected loss Tail Risk
Unexpected loss
Mortgage
0.61 92.52 Million Case
6.87 Million
Million
Total lending amount = 100 Million 2008 Eric Confidential
1

We can further depict the loss assumption under the Basel by using the above chart. The
maximum amount of loss is the total principle, in our case it is 100 million. The most likely loss
in the event of default is the EAD* LGD, in this case is 45 million. If the loan is still performing,
the bank needs to reserve 0.61 million of EL as provision and requires to charge 10.2 million of
capital13 for the unexpected loss in this corporate lending example. In oppose to the corporate
loan, the mortgage also needs to reserve the same provision, but the capital is far lower. The
amount that is not covered by the EL and UL is so called tail risk. The tail risk is a risk that
rarely happens but once it does, it will cost you an arm and a leg. We can easy observe that
the mortgage asset retains a longer tail than corporate client’s. The recent sub-prime credit
lesson is a perfect example to demonstrate the importance of tail risk management.

Differences between AIRB capital and Economic Capital

There are five major differences between economic capital and regulatory capital, in my point
of views:
1. The linkage to bank’s target rating: the AIRB capital is large depends on the BIS ratio,
however, the BIS ratio doesn’t links to bank’s desire rating. The determination of economic
capital requires bank to identify the confidence interval which direct links to bank’s target rating.

13
Assume BIS =10%

10
Restricted

The amount of EC held by a bank reflects the risk appetite of a bank.
Illustrative
EC links to
bank‘s target
Probability of
rating
loss

‘A’ rating ‘AA’ rating
Loss Distribution :Confidence of :Confidence of
=99.9% =99.97%

Better rating requires
increased capital
holding and
Y demonostrates the
appetite of a bank
X

Credit
Losses

0 Loss Tail Risk
Expected Unexpected loss
loss = Economic Capital

Regulator Capital is also used to cover
unexpected loss.The Basel Comittee uses a
general form of formula to proxy the UL

1

In the above chart illustrates that determination of economic capital links to the bank’s target
rating. The X axis represents for the amount of credit losses. On the other hand, the Y axis
stands for the occurrences of the corresponding credit losses. If bank is aiming at ‘A’ rating
grade bank, given the riskiness of the current credit portfolio, this bank requires X amount of
economic capital. If this bank shooting for a better rating, say ‘AA’, then needs Y amount of
economic capital. Better rating grade means bank need to hold more capital for protecting
unexpected loss.

The economic capital represents for risk governance of a bank. As shown in the chart below:
the Winterthur illustrates that their risk exposure in line with risk taking capacity to a confidence
of 99.97% over 1 year period. The 99.97% implies that the possibility of not be able to cover
the losses is 0.03%. The 0.03% equal to the default probability of AA rating grade’s. This
indicates the ‘Risk Appetite’ of Winterthur.

11
Restricted

Risk appetite makes explicit how much risk the institution is willing to
take.
Winterthur

The bank’s current available
Link to its target rating
capital is sufficient to cover
99.7% is equal to ‘AA’ 99.97% ‘s potential unexpected
loss.

The possibility of loss amount
exceeds the current available capital
is 0.03%

Sources: Credit Suisse analyst day presentation 2006 2008 Eric Confidential
1

2. The consideration of diversification effect, which usually refers to the estimation of
customized asset correlation, instead of using the constant correlation suggested by the Basel.
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Higher the correlation will have high relationship with the global
economics, result in a higher impact to obligor’s business.

Higher the correlation higher the UL, therefore,
bank needs to reserve higher capital requirement

Low correlation

High correlation

Basel Committee generates the asset correlation through ‘Reverse
Engineering’ – Empirical experimental through several banks’ EC.
Source : An Explanatory Note on the Basel II IRB Risk Weight Functions, Basel 2
1

12
Higher the asset correlation of a portfolio, usually result in a higher unexpected loss; vice
versa14.
Use a constant correlation (or formula to estimate) doesn’t really capture Restricted
the correlation nature. Different types of loan assets have different asset
correlation.

1

Conceptually, as shown in the above, that the large corporations have higher asset correlation
than SME and retail banking products. Higher correlation usually results in a higher economic
capital requirement under everything being equal. The reason behind this is that: large
corporations generally have better rating and usually have larger amount of financing needs.
Once default, the credit losses may result in a catastrophe.

For example, a bank has a 400 billion on loan exposure- 200 billion lends to one corporate
client and a 200 billion credit card portfolio; and with 100 billion capital reserve. Assuming both
has 50% of LGD. Once the corporate client defaults the bank capital will be wiped out.

Credit loss = 200 billion * 50% =100 billion =total bank capital

Even under economic downturn, the credit card portfolio encounters all card holders claim
insolvency event is rare. This may explain that the retailing products are considered a more
diversified and enjoy a lower correlation.

14
An Explanatory Note on the Basel II IRB Risk Weight Functions, Basel 2 working paper.

13
3. Estimation of concentration risk : concentration risk refer to a bank’s credit portfolio that
concentrated on certain country, industry, rating grade, single name or collaterals. Once the
above encounter systematic risk that will cause banks significant losses. In the worse situation,
bank may not be able to raise capital and turn out to be insolvent.

Credit concentration risk is the largest source of risk to the solvency of a bank. This can occur
in the form of the default of a large customer, and causes the simultaneous default of a few
sizeable customers, or a downturn in the industry the bank is exposed to. Credit expected loss
risk is something that can be priced for in most circumstances, whereas concentration risk is
simply too expensive to price and need to be covered by the bank capital. Paradoxically, banks
tend to have concentrated exposure to their best customers, and hence underwriting standards
alone would not be sufficient to control this form of credit risk.

Below chart illustrates that obligor ‘Y’ has larger exposure with low PD. In the event of default,
bank will suffer large credit loss from obligor ‘Y’ that may jeopardize bank’s operation. Obligor
‘X’ has higher risk but lower exposure, even bank faces the insolvency of obligor ‘X’, the loss
will be covered with the bank’s provision.

Restricted
Paradoxically, banks tend to have concentrated exposure to their best
customers or certain industries that might result in an extreme losses when
Illustrative
economic downturn.

Our view
Illustrative – Impact of concentration on portfolio
loss distribution
• Credit concentration risk is the largest
source of risk to the solvency of a bank,
and this can occur in the form of the
Default
probability
default of a large customer, the
Company X
simultaneous default a few sizeable but
Or industry
weak customers, or a downturn in the
High risk and
high
industry the bank is exposed to
exposure
• Credit expected loss risk is something
that can be priced for in most
Name level
circumstances, whereas concentration
concentration
risk is simply too expensive to price for
Or
Industry
in most cases
Solvency
concentration
• Paradoxically, banks tend to have
Company Y
concentrated exposure to their best
Low risk and
very high
customers, and hence underwriting
exposure
standards alone would not be sufficient
to control this form of credit risk

Provision Capital

1

A good demonstration is Enron event occurred in 2002. J.P Morgan lost a total of perhaps $0.5
billion in the course of Enron meltdown. Yet, as events unfolded, shareholders lost confidence

14
and share price plummeted to all time low. JPMC’s share price fell from about $40-$15
dollars, destroying about $50 billion of market cap. This gives us a good example that the
concentration risk will not only cause bank large credit loss but also result in:
Stock price drops
Market capitalization decline even more than the credit loss
Downgrade by rating agency

The recent sub-prime credit crunch is an example 15 . If banks’ revenue relies on certain
products, industries or obligors in the recession, the concentration risk will penalize banks a lag
and an arm sooner or later. In the worst case, bank may not be able to raise capital from the
capital market, due to investors lose confidence on banks’ future.
Restricted

Usually the low possibility of ‘Large unexpected loses’ not only wiped out
the profits but also results in significant market cap decline…

– In addition to
putting in
danger bank’s
target credit
rating, large
losses can
erode
shareholder
confidence

– Implications for
• JPM Bank lost a total of market
perhaps $0.5 billion in the capitalization
course of Enron meltdown. Yet, can far exceed
as events unfolded, actual losses
shareholders lost confidence
and share price plummeted to
all time low
• XX Bank’s share price fell from
about $40-$15 dollars,
destroying about $50 billion of
market cap
1

4. The estimation of economic capital requires bank to utilize the simulation skill to simulate
the occurrences of loss and its corresponding credit loss amount based on the internal rating
system (PD, LGD,EAD).

The simulation will simulate different state of economy, under which the obligor may defaults or
even results in a joint default event. The simulation result will form the loss distribution of a
portfolio.

15
Several American and British banks have claim insolvent. This event also demonstrates these banks
have over concentrated on the sub-prime segments.

15

5. Objective is different: The last but not least, the major objective of regulator capital is to
assess the capital sufficiency. On the other hand, the regulatory capital is for the measure of
capital sufficiency. The regulator needs to have easier way to estimate the capital requirement
to supervise the banks and to measure whether if banks have sufficient cushion to sustain
against unexpected loss.

The economic capital is a better management tool for bank to demonstrate the capital
efficiency to their shareholder. For example, under the AIRB capital estimation, bank may need
to reserve 30 dollars of capital, after considering the diversification and concentration effect,
the economic capital is only 27 dollars; as illustrate in the blow.
Restricted

The objective of economic capital is to measure the ‘Capital Efficiency’.
While as the objective of regulatory capital is ‘Capital sufficiency’.

Illustrative
Total = 30 Total = 27
5
2
Credit
Regulatory Capital

Diversification Concentration - Economic
Regulatory Bank’s current
Effect- Benefit Punishment , due Capital
Capital available
Requirement from correlation to concentrated on capital
certain name ,
industry…
EC is the maximum amount of unexpected losses
Regulatory capital is the
minimum amount of capital to potentially arising from all sources that could be
Definition
meet regulator’s request. absorbed while remaining solvent, with a given level of
confidence over a given time horizon.
Capital efficiency : Shareholder’s interest, measures if
Capital sufficiency : regulator’s
Objective main concern. capital is utilized efficient. For example, given 100 dollar of
exposure, A portfolio consumes 10 dollar of capital while as
B only consumes 5 dollar. 2008 Eric Confidential
1

The regulator capital is what we need to comply with. By contrast, the economic capital exhibits
the real risk capital given the current portfolio mix and we have enough capital to prevent
against unexpected loss – we are a fine bank with high disciplined in risk management.

We can further use one example to illustrate the capital efficiency: assuming there are 2
portfolios, each has 100 dollar of exposure but the portfolio components are different16 which
result in ‘A’ portfolio has 10 dollar EC while as ‘B’ only consumes 5 dollar of EC. Therefore, we

16
The weights of exposures are different, such as industries, countries, ratings or collaterals.

16
17
find that portfolio ‘A’ has a 10% of capital ratio and portfolio ‘B’ has 5% of capital ratio. We,
then, can conclude that portfolio ‘B’ is more efficient than portfolio ‘A’ in terms of use of bank’s
capital.18

17
Estimated by divided EC with exposure.
18
We can also measure the capital efficiency by using the regulatory capital, such as AIRB approach.
Using economic capital is more accurate in terms of the risk estimation.

17

Section 3: Theory & vendor models introduction

In the past decade, four important credit portfolio models have been introduced to measure the
credit portfolio risk:
1. KMV’s portfolio manager is the first model introduced in 1993
2. J.P Morgan’s Credit metrics in 1997
3. Credit Suisse First Boston introduced CreditRisk+ in 1997
4. Also in 1997, McKinsey brought out portfolioview in different approach
There are other vendors and consulting firms provide solutions in this field. Some banks also
developed their in-house models. According to the survey conducted by the IACPM 19
(International Association of Credit Portfolio Managers), 44% of the IACPM members have
in-house models 20 . In terms of vendor model, the KMV’s portfolio manager is widely
subscribed.
Restricted

Understand your MODEL and what is the ASSUMPTION before further
implementation.

Findings from credit portfolio management Comments
study in 2004
1. Different models may
have different results.
Which models are used?

• Each vendor model
has his own
In-house
features.
developed CSFB Credit Risk+ 6%
44 %
• Understand what
Credit Metric 6%
are you doing when
using vender’s
Vendor
model model.
MKMV 42%
66%

Banks need to understand
Macro Model 2% what methods are you using in
estimating EC and gain
confidence internally before
communicating with regulator
and rating agency.

Source: IACPM -Survey of CPM practices 2004 1

This section provides brief introductions of the vendor models.

19
Source: IACPM -Survey of CPM practices 2004. Wedsite: www.iacpm.org
20
Some banks even maintain 2 models-vendor model and in-house model.

18

Portfolio Models Introduction

In the last decade, a whole range of modeling techniques has been developed to analyze
portfolio credit risk. Broadly viewed, there are three groups of portfolio credit risk models. The
first group is ’structural’ and based on Merton’s21 model of firm capital structure: individual
firms default when their assets’ value fall below the value of their liabilities. Examples of such a
microeconomic causal model are CreditMetrics and KMV’s PortfolioManager. The second
group consists of econometric factor risk models, like McKinsey’s CreditPortfolioView 22 .
McKinsey’s model is basically a logistic model where default risk in ’homogeneous’ subgroups
that determined by a macroeconomic index and a number of idiosyncratic factors. These two
model types apply similar Monte Carlo simulations to calculate portfolio risk, as both
are ’bottom-up’ models that compute default rates at either the individual firm level or at
sub-portfolio level. Both thus require a similar kind of aggregation. The third group contains
actuarial models, like Credit Suisse’s CreditRisk+23, that make no assumptions with regard to
causality.

The credit portfolio models usually construct the portfolio loss density in two stages. First, one
has to derive the credit risk on the level of individual asset. Second, these risks have to be
aggregated to the portfolio level.

The first stage needs to have obligor’s PD and rating transition metrics to capture default and
migration risk. In the event of default, model estimates the credit loss by applying the LGD. If
obligor upgrades or downgrades due to the rating migration instead of insolvent, then estimate
the value of loan correspondingly.24

The second stage requires take the correlation into consideration. Usually leverage the factor
model to capture the default dependency and estimate the joint probability for all obligors. Most
models employ the Monte Carlo simulation technique to derive the portfolio loss.

21
Merton, Robert, (1974), On the pricing of corporate debt: the risk structure of interest rates, Journal of
Finance, Vol 29, pp. 449-470.
22
Wilson, Thomas, (1997), Portfolio credit risk (I), Risk,Vol. 10, No. 9.
23
CreditRisk+ - a credit risk management framework,1997.
24
Similar to the bond valuation. When bond being upgraded, the price goes up and visa’ versa. Models
apply the Net Present Value and risk neutral methodology to evaluate the value of loan. These models
also called ‘Value’ based model.

19

KMV’s Portfolio manager

Portfoliomanager is the most comprehensive tool to accomplish a measurement of three
objectives 25 : diversification, optimization and valuation, though it is complex in terms of
methodology. The estimation of economic capital require user to input the PD, LGD, EAD,
tenor, credit spread26 and obligor’s information: weighting of country, industry as minimum
requirements.27

In the first step, KMV’s model applies Merton’s concept that debt behaves like a short put
option on the value of firm’s asset. In Merton’s world, default occurs when the value of the
firm’s asset falls below default point – determined by the structure of the individual firm and its
asset volatility. KMV modifies the Motern’s model and assumes that asset values follow a
log-normal process with a specific growth rate to calculate the distance to default of obligor.
Combing the simulation, KMV then simulate a credit quality transition table (KMV’s used the
term : Distance to Default Dynamic) of each obligor instead of leveraging the rating transition
metrics that provided by the rating agency.

The loan’s value depends on the financial condition of each facility, such as credit spread,
upfront fee, tenure and payment type. The individual loan or facility can have a range of
possible values at future dates depends on the obligor’s change of default probability. The
following chart provides the logic behind the generation of such value distribution in portfolio
manager.28

KMV assumes that, at some time in the future or the horizon, the value of firm’s asset will follow
a lognormal distribution. Furthermore, individual value for the firm’s assets at the horizon will
correspond to values the facilities (loans or bonds). In other words, if the firm’s asset value
increased, there is a high chance that the firm’s rating will be upgraded and result in a higher
value of the facilities. If the value of the firm’s assets falls below the default point, then the firm
will default and the value of the facilities will be the recovery value.

25
Brian Ranson, Credit risk management,2005. page 10-22. Printed by Sheshunoff.
26
The user can choose to use KMV’s EDF as a measure of PD, or use internal rating system. Credit
spread is used for loan valuation.
27
The more detail can be found from the PM’s preprocess documentation.
28
More detail can be found in the ‘Modeling Portfolio Risk’ and ‘Credit portfolio management’, Charles
Smithson.

20
In the step 1 of the below chart demonstrates how the KMV simulates the firm’s future value
and proxies the firm’s credit quality. Based on the credit quality and the credit related spread,
the KMV estimates the value of the loan (the step 2). Final step is to map the loan value with
probability – the value distribution of a firm’s facilities29.
Restricted

Log( Asset Value) Log( Asset Value)
Step 1 Step 2

Step 3

Probability
Value
distribution

1

To estimate the portfolio value distribution requires to take asset correlation into consideration.
KMV decomposes asset returns into systematic and idiosyncratic factor. The asset return is
derived from equity prices30 and incorporated into the firm’s liability. The correlation model (so
called GCorr ) incorporates 120 factors to capture the macro factor, country factor and industry
factor. This model estimates asset correlation among obligors and can translate into default
correlation and joint probability of default. Please refer to the following chart.

As we can see in the next chart that KMV’s GCorr decomposes the firm’s asset return into
country’s, industry’s, sector’s, globe’s and firm’s specific risk. Moreover, user can easy to see
the asset and default correlation. It is well known that if higher portion of systematic risk, the
easier to be influenced by the macroeconomic fluctuation. The source of the diversification
comes from the firm’s specific risk. The GCorr also contains a feature that can estimate

29
An obligor may have multiple credit lines (facilities) in a bank in the same time for different purpose and
bank charges different rate for the risk taking activities.
30
KMV collects the stock index around the world to calculate the market value of firm, by adding the
liability of firms, KMV can estimate the asset value of firms. Therefore, KMV can utilize these information
and to re-contracture a benchmark index and to estimate the asset return of firms.

21
correlation in matrix.
Restricted

Bank can extend the one factor model into multiple factors model to
estimate the correlation.

Systematic Risk

Country Risk Industry Risk

US Electronic
UK Manufacturing
Taiwan Service
Korea Real estate
. .

• Bank can extend the on factor into multiple factors model

Common Firm Specific
Countries Industries
Risk
14 45 61
rk = ∑ βkf rf + ∑βkcεc +∑βkiεi + εk
f =1 c=1 i=1

1

Restricted

Higher the asset correlation easier to be influenced by the state of the
economy.

Asset correlation between obligor and the
state of the economy Asset correlation between 2 obligors

Joint default
probability
of 2 obligors
Default correlation
between 2 obligors

Systematic
Risk
Can be
Further
Diversified
Through
Firm Specific
Add more
risk
obligors

1

22
Restricted

2008 Prepared by Eric — CTCB Confidential
1

The portfolio value distribution is calculated simply by summing up all the facility values31. Then,
the loss distribution is obtained by using the risk-free rate to calculate the future value of the
portfolio at the horizon and subtracting the simulated value of the portfolio at the horizon:

Portfolio Loss at Horizon = Expected Future Value of Current Portfolio– Simulated Value of the
Portfolio at Horizon

The portfolio value distribution and the loss distribution are mirror images of each other. The
below chart32 in the next page shows how the two distributions that are related graphically.

The value-distribution highlights several reference points and depict the boundary of the
portfolio:
VMax—Maximum possible value of the portfolio at the horizon (assuming there are no defaults
and every obligor upgrades to AAA).
VTS—Realized value of the portfolio if there are no defaults and all borrowers migrate to their
forward EDF (maintain at the same credit rating grade).
VES—Realized value when the portfolio has losses equal to the expected loss (or earns the

31
Considering the correlation effect in this step. For example, all obligors maintain solvency, then A
obligor defaults and causes B obligor defaults and so on. Then evaluate the recovery value of the loan.
32
Source, ‘Modeling Portfolio Risk’ and ‘Credit portfolio management’, Charles Smithson.
Page 117.

23
expected spread over the risk-free rate)—expected value of the portfolio.
VRF—Realized value when credit losses wipe out all the spread income—zero spread value of
the portfolio.
VBBB—Realized value when the losses would consume the entire portfolio’s capital if it were
capitalized to achieve a BBB rating (equivalent to approximately a 15 bps EDF).
Restricted

Portfolio value distribution and the loss distribution are mirror images of
each other.

Expected value

Value
Distribution

VES
VBBB VRF
VTS VMax

Expected loss

Loss
Distribution

1

KMV defines two loss distributions. One is based on the expected spread for the portfolio, so
the loss is that in excess of the expected loss. The other is based on the total spread to the
portfolio, so it is the loss in excess of total spread. Expected loss is expressed as a fraction of
the current portfolio value.

The economic capital estimation requires user to pre-define the target rating before running the
simulation. EC is the difference between unexpected loss and expected loss. This capital value
is calculated at each iteration, and is binned and portrayed graphically as the tail of the loss
distribution.

It answers the question:
“Given the risk of the portfolio, what losses should we be prepared to endure?”33

33
KMV also provide portfolio optimization and trade optimization and can provide information which
obligor should reduce or increase exposure. We won’t spend time to introduce these functions here.

24

Creditmetrics

In April 1997, J.P. Morgan introduced CreditMetrics, a model that first developed by the
banking practitioner and sponsored by the KMV and other financial institutions. Like KMV’s
model is based on Merton’s concept - debt behaves like a short put on the value of the firm’s
assets, the stochastic variable in CreditManager is the value of the firm’s assets.

2 4

1

3

5
Inputs
The approach can be explained as following34:

First, calculate the different exposure profiles and dynamics for each exposure type with the
consideration of the volatility of value due to credit quality migration for each individual
exposure.35

The below chart explains the rating change within 1 year. That the BBB grade has an 86.93%
will remain at the same grade. 6% of possibility will be upgraded and 0.18% of possibility may
be insolvent within 1 year.

34
We summarized the steps into 2 steps to keep it simple and consistent in this paper, although Credit
manager has many, many steps. Please refer to the ‘Introduction of CreditMetrics,1997’ for more details.
35
Source, Creditmertics’s technical note.

25

1

Creditmetrics then estimates the value of the loan corresponding to credit quality of the
obligor – as shown in the below charts.

1

26

2

3

Second, calculate the volatility of value due to credit quality migration across the entire portfolio
and different approaches. The estimation of correlations of credit quality migrations plays the
core. Consequently, portfolio effects – the benefits of diversification and costs of
concentrations – can be properly quantified36.

36
Refer to the ‘4’, ‘5’.

27

4

Similar to KMV’s correlation approach, the major differences are illustrated below:

Moody’s–KMV Model CreditMetrics Group’s Model
37
Asset value driven Equity index proxy
Default correlation derives Systematic risk based on
Default correlation derives Default correlation derives
from asset correlation from correlation in the proxy (equity returns)

Assuming obligor ‘s return is related to 2 systematic factors described as below :

rA= uA+wA1f1+wA2f2+εA
where : f1 ~ N(0,σ21) , f2 ~ N(0,σ22), εA ~ N(0,σ2A)

σ1 ,σ2 is the standard deviation of factor 1 ,2 and σA is the firm-specific risk standard deviation.
The correlation between two obligors A and B’s returns are given by:

37
Equity correlation would be a perfect proxy if the value of the debt remained fixed. The RiskMetrics
Group argues that the approximation is good as long as the firm’s volatility is primarily driven by equity
fluctuations, and the volatility of the debt level is relatively small in comparison to the equity fluctuations.

28

w A1 wB1σ 12 + w A2 wB 2σ 2 + ( w A1 wB 2 + w A 2 wB1 )σ 1σ 2 ρ ( f1 , f 2 )
2

ρ (rA , rB ) =
σr σr
A B

Where σrA=(wA12σ21+ wA22σ22+σ2A)1/2

and similarly for obligor B. What is left is to determine the relationship between the correlation
of the returns and the default event correlation for two obligors. We see that correlation
depends both on the weights on the factors and on the correlation between the factors38.

4

Utilized the correlation model, Creditmetrics measures the joint migration probability based on
the asset correlation, as exhibited above. Next step is to apply the Merton’s model to estimate
the firm’s credit rating based on the joint migration.

4

38
General assumption is the correlation between the factors is zero.

29
The process reiterates many times and then can generate the value distribution of the
portfolio.

5

30
The differences between the Creditmetrics and KMV are as follows:
1. Rating migration : User of KMV can choose to use the Distant to Default Dynamic or
applies the rating agency’s rating transition matrix, whiles as the credit metrics only provide
rating agency’s rating transition matrix to measure the rating migration likelihood.
2. Correlation : KMV constructs index by their own and estimate the asset return. The
creditmetrics utilize the equity index39 to estimate the asset correlation.

A core assumption of both of the KMV and CreditMetrics models is the multivariate normality of
the latent variables. The asset return correlations are calibrated by assuming that asset returns
follow a factor model, where the underlying factors are interpreted as a set of macro-economic
variables40, such as country, industry etc. At each simulation, the return will determine if the
obligor’s credit quality (credit migration) and then estimate the loan value of the obligor. The
result is a value distribution of the portfolio.
Restricted

KMV and Creditmatrics run numerous simulations to generate a ‘Value
Distribution’ and then translate it into loss distribution.
For Each Simulation
Draw
Calculate
Recover
Correlat individual Sum
Calculate y Rate in
ed asset Obligor’s asset across Save the
Obligor’s
Simulati the case
value value return, r, obligors to result
new rating
on of
returns given index get (loss
given asset
#3436 default
for each returns and portfolio #3436)
return and
index ∆I idiosyncratic losses
calculate
component
loss

Portfolio Value Distribution
Tabulated Simulation Results

∆Portfolio
Simulation # Company A Company B Value

1 Default; loss = 100 No Default 100

2 No default No Default 0

3 Default, loss = 60 Default, loss = 50 110

. . . .

. . . .

. . . .

. . . .

1

39
MSCI global index or local equity index. User of creditmetrics needs to estimate the correlation in the
implementation stage, while as KMV embedded the GCorr into the Portfoliomanager already.
40
For further reading see papers by Koyluoglu and Hickman (1998), Gordy (2000) and Crouhy, Galai,
and Mark (2000).

31

CreditRisk+

Creditrisk+ is an actuarial model also called a reduced form model. Economic causality is
ignored—there is no “story” to explain default. Consequently, specific asset values and
leverage details for specific firms are irrelevant. Actuarial models specify a distribution for the
default rate and apply statistics to obtain a closed form expression for the joint distribution of
loss events. By extension the expected severity can be incorporated to arrive at a distribution
of losses.

An attractive feature of Credit Risk+ is that it requires only limited data. There are three
required inputs:
1. PD of the obligor.
2. Volatility of default rate for the obligor—the model is very sensitive to this parameter; and
this parameter is difficult to accurately measure and seldom can be provided by the user.
3. Facility exposure (amount at risk net of recovery)—Credit Risk+ takes the loss given
default as fixed. The user inputs a net figure taking into account usage at default (for
committed lines) and the amount of recovery. Unlike the Moody’s–KMV model and the
RiskMetrics Group’s model, there is no simulation of how much is actually lost when
default occurs for the recovery rate.
Given the data input, it doesn’t require the calculation of individual default risk, and neither
does it look at changes in market value in the even of upgrade or downgrade- as oppose to the
KMV and creditmetrics.

In this model, correlation is handled through the aggregation of like assets sorted by industry
and country or the termed sector. Sectors allow users to influence the degree of default
correlation between obligors:
Specific risk sector—Placing some of an obligor’s risk in the specific risk sector means
that that risk can be fully diversified away.
Systematic sectors (maximum nine)—Within each sector, the default rates of each obligor
are correlated. Across the sectors, the default rates are independent.

For the loss aggregation, Credit Risk+ assumes that the default rate may vary, thus introducing
the concept of “default rate volatility” for each obligor. Because this implies an underlying
distribution for the average default rate, the developers made the assumption that the mean

32
default rate (for each sector) is governed by a gamma distribution. Though there is no upper
bound for the gamma distribution, this is permissible because the default rate for a sector can
be greater than one, as opposed to a default probability.

The actuarial approach has the appearance of precision because results are calculated via
mathematical model rather than a simulation; however, just the opposite is true. Actuarial
models are closed form approximations to the true distribution of defaults. However, Credit
Risk+ is subject to at least two criticizes:
1. It is possible for a credit to default more than once.
2. The approximation used to calculate the portfolio distribution from the individual loss
distributions relies on default rates being small. This means, for example, that
noninvestment grade credits of longer.

Creditportfolioview

The first widely discussed macrofactor model was introduced by McKinsey & Company and
was called CreditPortfolioView.41 The model starts not with the individual obligors’ information
but rather with the view about the situation of the economy. The major difference between is
the structured model ( KMV, CreditMetrics) estimates risk parameters (for example, PD and
migration probabilities) as un-conditional, the Creditportfolioview’s approach focuses on
conditional modeling conditional on the state of economy. The model requires the country risk
of the economy, the industry risk within the economy and the rating of the obligor in order to
predict default. To gauge the diversification, this model segments the portfolio based on the
number of firms in the segment index.

The systematic (non-diversifiable) risk – risk of economy – has a large predictable impact on
credit migration and on default probabilities. That implies that we should use conditional rather
than unconditional models! As an example Wilson42 presents the following table, in which he
has found a linear regression model forecasting defaults and having the highest explaining
power and only one explanatory variable.

41
Designed by the Thomas Wilson
42
Wilson, T. (1997a) Measuring and Managing Credit Portfolio Risk: Part I: Modelling Systematic Default
Risk. The Journal of Lending and Credit Risk Management, July, 61 – 72.
Wilson, T. (1997b) Measuring and Managing Credit Portfolio Risk: Part II: Portfolio Loss Distributions. The
Journal of Lending and Credit Risk Management, August , 67 – 78.

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