Basel II – Integrated Risk Capital

Basel II – Integrated Risk Capital
Concentration Risk & Capital
Framework & Analysis
Prepared by: Walid Saafan
Aug 2009

CONCENTRATION RISK & CAPITAL
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Contents
1. Introduction ......................................................................................................................3
2 Concentration Risk Framework.........................................................................................4
2.2 Best Practice Guidance on Concentration Risk Management........................................5
2.3 Effects of Concentration Risk ......................................................................................5
2.3.1 Idiosyncratic risk – Single name exposures.....................................................6
2.3.2 Systematic risk – Country and Industry Concentration.................................9
2.4 Stress Testing Concentration Risk in Industries and Countries .....................................9
3 Analysis of Concentration Effects ................................................................................... 11
3.1 Concentration Limits by Local Regulation ................................................................. 11
3.2 Quantitative Analysis – Benchmarking Basel I and II................................................. 11
3.2.1 Regulatory Capital ......................................................................................... 11
3.2.2 Concentration-Sensitive Capital Requirement for the Top-20 Portfolio ..... 12
4 Link to Portfolio Management......................................................................................... 12
4.1 Fundamentals of Portfolio Management..................................................................... 12
4.2 Setting Concentration Limits, Allocation, and Monitoring.......................................... 13
5. References ...................................................................................................................... 14
A Appendix: CEBS Guidance for Institutions ..................................................................... 15
C Appendix: Credit Portfolio Approach.............................................................................. 18
D Appendix: Parameters ..................................................................................................... 21
E Appendix: Sensitivity Analysis ....................................................................................... 24

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1. Introduction
This document includes:
(i) A brief risk review of national Egyptian banks.
(ii): A framework for concentration risk based on international best-practice requirements
and industry standards
(iii): A quantitative analysis of concentration risk in National Egyptian banks credit
portfolio.
(iv): A link of concentration risk to portfolio management.
This analysis was based on some published information by Central Auditing Organization
about the national Egyptian banks about the available risk from concentrated loan portfolio in
few numbers of customers along with fewer numbers of sectors.
The concentration risk effects in National banks’ current portfolio can be estimated, we can
quantify expected capital requirements with two approaches, an Advanced Foundation Credit
Risk Approach from the Basel II Accord (using the analytic ASRF approximation) and a
credit risk Monte Carlo simulation method sensitive to name and sector concentration. The
difference in capital requirement between the two approaches represents a proxy for a
concentration risk add-on.
Concentration risk triggers an additional capital requirement of roughly 50%, 30% for the
Top-20 respectively total corporate portfolio. These results crucially depend on correlation
parameters that need to be confirmed by real data. Furthermore, it is assumed that the
exposure is not associated with guarantees or collateral (unsecured lending). Apart from the
corporate portfolio, National banks lends a substantial part (in notional) to Financial
Institutions. The risk involved and capital required for this mostly short-term, uncommitted
exposure to good-quality counterparties is expected to be relatively low.
Despite a variety of assumptions, the relative capital increase due to concentration effects
obtained is in line with results from a Basel II publication that investigated effects of
concentration risk on stylised portfolios. Some application are available that enables banks to
estimate capital add-ons reflecting concentration risk.
Best-practice banks commonly have an advanced portfolio management in place to manage
concentration risk effects. Key incentives of portfolio (risk) management are: (i)
safeguarding the bank’s portfolio credit quality, (ii) linking portfolio capital requirements to
down-to-earth credit decision-making, and (iii) indicating profitability aspects of individual

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portfolio constituents. An officially approved portfolio management framework does not
exist in National banks.
Given the size of concentration risk, it is recommended that National banks:
 Reviews this analysis including the tool attached to it, and recalculates
concentration risk effects using the latest, complete portfolio update and a local
correlation update.
 Reviews its current limit setting and related risk appetite
 Formulates an adequate portfolio management framework
 Devises a short- to mid-term tactical approach to cope with concentration risk and
its effects.
2 Concentration Risk Framework
This Section describes the elements of concentration risk and a methodology for measuring
concentration risk taking into account the Bank’s current environment in terms of regulation,
internal management and general characteristics of the Egyptian Banking market.
2.1 Elements of Concentration Risk
The term “Concentration Risk” generally refers to the following definition:
A risk concentration is any single exposure or group of exposure with the potential to
produce losses large enough (relative to a bank’s capital, total assets, or overall risk level) to
threaten a bank’s health or ability to maintain its core operations. Risk concentrations are
arguably the single most important cause of major problems in banks.
While concentration, in principle, refers to any kind of non-diversified risk exposure, the term is
of particular importance in the credit risk area. For most commercial bank’s risks other than
credit risk are significantly smaller and /or well mitigated. Bearing this in mind, the Basel II
Accord has identified the management of credit concentration risk as a crucial component of its
Supervisory Review (as formulated under Pillar 2 of the Accord).
One distinguishes three types of concentration risk:
 Single name concentration: Lending to many smaller customers is less risky than
relying on a few big counterparties.
 Geographic concentration: Local or regional banks tend to carry more risk than global
businesses.

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 Industry concentration: Spreading a business over different sectors results in a more
balanced dependence on a weakening economy and / or
specific industry events.
The definition of concentration risk and the current framework are aligned with the Basel II
Accord. The latter identifies one additional form of concentration under Pillar 2: indirect credit
exposure arising from a bank’s credit risk mitigation activities in form of collateral type or
credit protection provider. National banks currently does not manage this risk explicitly. We
will not further cope with credit risk mitigation concentration effects in the remainder of this
document.
2.2 Best Practice Guidance on Concentration Risk Management
The Committee of European Banking Supervisors (CEBS) defines a high-level guidance, in
particular applicable to banks. These guidelines are the result of a survey across financial
institutions, and set best practice standards within the market.
Such guidelines, advise that banks should:
 Have a clear concentration risk policies (that include limit structures), approved by
management;
 Identify, monitor, manage and report concentration risk;
 Assess capital requirement due to concentration risk.
It is worth noticing that CEBS recognises that market practices are still developing, and
adaptations in the light of future developments in this area are to be expected. Another point of
attention is the fact that “specialised institutions should not necessarily be assumed to be more
risky in comparison with larger institutions doing the same business”: in this respect one should
not forget to compare advantages such as expertise and knowledge of the local market versus
disadvantages such as additional capital requirement.
2.3 Effects of Concentration Risk
Credit concentration risk may arise from three types of imperfect diversification. The first type,
single name concentration, relates to imperfect diversification of idiosyncratic risk in the
portfolio either due to its small size or due to large exposures to specific individual
counterparties. The other two types, geographic and industry concentration relate to

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diversification across systematic components of credit risk, which is to components that are
shared among all counterparties in this geography and industry.
The Internal Ratings Based (IRB) framework as defined in the Basel II Accord is based on the
Asymptotic Single Risk Factor (ASRF) model. This model assumes perfect granularity of the
portfolio, i.e. an infinitely fine-grained and well-diversified portfolio, the systematic risk of
which can be described in terms of one common component. The systematic risk factor
introduces the dependency of all counterparties on one common component like the global
economy. The more weight this component is given the more are correlated are counterparty
defaults.
The assumptions of the ASRF model in terms of perfect diversification may provide a good
approximation to large, global, diversified portfolios as run by the industry leaders, but
commonly show their shortcomings if applied to portfolio of smaller, regional banks. Rather
than suggesting an alternative model, the Basel II Committee introduced capital requirements
for excessive concentration risk to patch the gap with the ASRF model.
As discussed in Section 1, National banks’s portfolio carries substantial concentration risk that
is not in line with the assumptions of the ASRF model. We here refer to:
Name concentration: The 20 biggest groups are responsible for more than 80% of the total
portfolio outstanding.
Sector concentration: More than 84% of portfolio outstanding is lent to the six biggest
sectors of, in particular to Petroleum & Gas, and Contracting.
Geographic concentration: National banks are a mainly domestic player. The Bank is
strongly exposed to downtrends of the Egyptian economy.
Capital estimation must occur by means of an approach that is sensitive to the portfolio
structure; by construction, Basel II formulae do not offer sufficient flexibility.
2.3.1 Idiosyncratic risk – Single name exposures
The effect of single name exposures is measured by comparing the Credit VaR of an infinitely
fine-grained portfolio (ASRF-Model) with National banks’s portfolio with the same exposure
and default probabilities. The ideally diversified portfolio is constructed, by definition, by
distribution of the total exposure over an infinite amount of obligors. Obviously, in reality the
case of an infinite number of counterparties is never reached, but the results are very close to
those obtained for a portfolio with several thousand obligors. For better comparison, we evenly

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distribute total portfolio exposure over a number of counterparties that are supposed to define
the Egyptian level playing field. Hence, we construct three portfolios:
B1: Stylized benchmark portfolio with an infinite amount of counterparties;
P1: Stylized Top-20 portfolio with exposure distributed over 35 obligors.
PR: Stylized Top-20 portfolio, reflecting name and industry concentration effects.
Table 1 and Figure 1 illustrate the effects of diversification among identical counterparties.
Credit VaR is reduced with a growing number of counterparties and uniformity of the exposure
distribution. Vice versa, credit VaR increases with concentration of exposure among fewer
counterparties.
Table 1: Credit VaR as a function of number of loans N. Portfolio is defined as such
that it contains N-1 loans of equal size x and one loan of ten times this amount, i.e.
10*x. Note a misprint: VaR(99.9%) should be VaR(99.5%).

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The effects of concentration on VaR respectively capital are illustrated more vividly in Figure 3
Figure 1: Ratios (VaR(x%)@N=…) / (VaR(x%)@N=3000) as implied by Table 3.
These findings confirm the relevance of concentration risk management. For portfolios of
effectively 50 to 100 counterparties, concentration risk easily induces an increase of capital
requirement of 50% to far more than 100%.
An Alternative Approach: Herfindahl-Hirschman Index
The Herfindahl-Hirschman Index (HHI) represents an alternative approach to the one described
above. The HHI is a straightforward measure of concentration that is calculated as the sum of
squared parts of individual counterparties, defined as:
H = SUMi=1,…,n[si
2
] ,
Where si is the contribution of counterparty i to the total exposure, and n is the number of
counterparties.
The ease of computing the HHI proves useful for applications of portfolio concentration
monitoring. The results could be easily compared with a corresponding limit (this is not
common in the industry though). Despite its simplicity, we do not apply the HHI for our
concentration analysis. This is due to its weaknesses, among which one finds:

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 It does not consider the distribution of exposure across credit ratings. Credit quality, e.g.
in terms of PD is an essential input, however.
 The approach is not sensitive to portfolio effects other than exposure contribution alone.
 It does not connect concentration effects with capital requirement.
2.3.2 Systematic risk – Country and Industry Concentration
The ASRF model—being the standard underlying the Basel II Accord—assumes a single
systematic factor. In reality, groups of obligors may be concentrated in a particular industry or
country and have a high exposure to the risks in that industries while the exposure to the
common factor is small. This mostly leads to an underestimation of obligor correlation and
therefore an underestimation of risk. To study this effect, commonly industry- and country-
specific risk factors are introduced, which results in a multi-factor model with a richer
correlation structure. Factor weights and correlation need to be determined on the basis of
historical evidence or expert judgment.
As governmental banks predominantly operate on a national level, diversification over
countries is (almost) absent. While this in itself might be a perfectly fitting business strategy, it
introduces high vulnerability to Egyptian crises. In a big international portfolio, loss frequency
may be high, but losses generally are restricted to low to medium severity. In a nationally
concentrated portfolio, a crisis situation may be less frequent but of much higher loss potential.
In addition, there are economic effects imported via the international financial and trade
markets (e.g. dependency on natural resources, FX rates, and the like) that have an effect on the
national economy.
2.4 Stress Testing Concentration Risk in Industries and Countries
Credit risk concentrations are based on common or correlated risk factors, which, in times of
stress, have an adverse effect on the creditworthiness of each of the individual counterparties
making up the concentration. Stress tests are used to determine the effect of country and
industry concentrations in exceptional but plausible scenarios.
Economic scenarios describe the integral impact of an event on the portfolio. They describe the
impact of economic (political, social, etc.) circumstances on the specific risks of National banks
as changes in a specific risk seldomly come alone, i.e. the scenarios are developed for
determining the effect of credit concentration risk under stressed circumstances. This section
discusses elements of a stress testing framework. Scenarios used for this purpose, should
comply with the following principles:

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 Plausibility implies credibility of the stress scenario which is necessary to have an
impact on the bank’s risk management. It requires that the stress scenario should be
believable and have a certain probability of actually occurring.
 Stress scenarios should be consistent with historical experience and with the risks
National banks is exposed to. Among others this means that the scenario-implied
changes of the various risk factors are economically sound.
 To assess the impact of a stress test, a base (reference) scenario and performance
measure are required. The impact of the stress scenario is measured by comparing the
performance under this scenario of the performance of the base scenario. The base
scenario is the current situation and portfolio of National banks.
 Stress scenarios should be portfolio specific. Stress testing should not be confined to
global portfolios but should include sector, region, product or portfolio-specific
scenarios to measure the impact of concentration. This means that big changes that have
small effects on the particular portfolio need not to be included, while minor events (on
a macroeconomic scale_ with drastic implications on the particular portfolio should be
addressed.
 Scenarios and the underlying risk drivers should take into account plausible
management reaction on the events.
 Stress scenarios should span among others, retail and corporate credit risk (including
country risk and concentration risk).
 The impact stress testing is, at least, quantified by:
o Expected loss and required capital under adverse macroeconomic circumstances.
The change in expected loss, resulting from changes in PD and/or LGD,
provides a test of the capital adequacy and the effectiveness of the risk limits,
risk appetite definition, hedging and contingency planning.
o Various additional performance measures may be adopted to quantify the
scenario effect, such as the overall (future) performance measure (e.g. RAROC),
the expected provisions (balance sheet), changes in revenue, losses, profits, or
any other element of the future P&L or balance sheet.
 Conceivable scenarios are a devaluation of the Egypt Pound, substantial decrease in
overall credit quality, stock market crisis and the like
We recommend developing stress test scenarios consistent with the guidelines presented above.

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3 Analysis of Concentration Effects
3.1 Concentration Limits by Local Regulation
Local regulation (issued by the Central Bank of Egypt and to be enforced by end of 2008) sets
the following concentration limits for Egyptian banks:
1) A single obligor exposure must not exceed 20% of the bank equity base.
2) Exposure from obligors of the same group must not exceed 25% of the equity capital
base
3)
The sum of the limits granted to all obligors with a limit bigger than 10% of the equity
base, must not exceed eight times the equity base itself
The sum of individual limits bigger than 10% of equity base.
Note that no regulation exists (yet) with respect to industry concentration. Moreover, no
consequences have been detailed in case an Egyptian bank would fail to meet such
requirements. Concentration risk management therefore is an internal key responsibility. Best-
practice banks focus on concentration as part of their overall portfolio management.
3.2 Quantitative Analysis – Benchmarking Basel I and II
The purpose of this quantitative analysis is to estimate the effects of concentration onto capital
requirements. In order to obtain measure concentration effects, we need to compare the capital
requirement of 1) a standard Basel model assuming perfect diversification (i.e. no or hardly any
concentration effects), and 2) a model that is sensitive to the true concentration present in
National banks’s portfolio. We will refer to the two models as regulatory (i.e. Basel I / Basel II
Pillar 1) and portfolio model, respectively.
3.2.1 Regulatory Capital
Under Basel II Standardized Approach Pillar 1 Credit Risk, each of the performing portfolio
exposures is assigned a risk weight. For corporate counterparties1
, the Standardized Approach
assigns risk weights of 100% to 150% for credit ratings corresponding to ORR 1-4, respectively
ORR 5-7. The calculation of capital therewith becomes straightforward, being a weighted sum,
and amounts to 10% of the total risk weighted assets.

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Based on the Top-20 report received, we arrive at utilizations of 13.15 and 9.8 billion EGP for
categories ORR 1-4 and ORR 5-7, respectively. Therefore, projected minimal capital
requirement for National banks Top-20 portfolio exposure would amount to:
Alternatively, for the calculation of regulatory capital we may employ the rules prescribed for
the Foundation Advanced Internal Ratings-Based Approach (FIRB). In the latter, probability of
default is assigned to each ORR and capital calculations are made on the basis of a
mathematical formula assuming perfect portfolio diversification (see also Section 2, ASRF
formula and paragraph 272 of the Basel II Accord).
3.2.2 Concentration-Sensitive Capital Requirement for the Top-20 Portfolio
The Basel II F-IRB capital requirement formula is based on a one-factor model, and assumes
infinitely granular portfolio, i.e. an infinite number of counterparties, each with an infinitely
small exposure. This implies that the systematic risk is completely diversified. A real portfolio
will have, however, a finite number of counterparties; moreover, exposure (EAD) will not be
distributed evenly.
4 Link to Portfolio Management
4.1 Fundamentals of Portfolio Management
Portfolio management is not a new concept to banks. The purpose of portfolio management is
basically to manage concentration risk, to protect the bank from adverse credit events, and –
eventually—to manage portfolio profitability.
It is common for central banks in many countries to impose single customer limits and industry
limits. Usually, single customer limits are set as a percentage of total capital funds, like e.g.
25%, and industry limits are set based on a percentage of total loan exposure. As discussed in
Section 3.1, CBE has single customer and group limits in place. A reference to local regulatory
industry limits has not been found. Nevertheless, the vagaries and customization that are
available around the credit product make it difficult to compare notional exposure across
obligors, sectors, and regions. This is a main criticism of the Basel I Accord and the
conventional forms of concentration limits, mentioned above.
With improvements in the methodology for measuring risk, banks are now able to implement
more complex and accurate portfolio management strategies. This is also the expectation of
central banks around the work in light of Basel 2. Nowadays, banks aim to create a portfolio

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limit framework that is both effective in protecting the institution from single credit events and
practical in its enforcement.
The key to an effective portfolio management framework is the definition of a loan-equivalent
metric that allows banks to differentiate the risks between, for example, a 100 million USD
exposure to a AAA-rated entity versus a 10 million USD exposure to a BB-rated entity; or an
unsecured facility to a single-B obligor versus a secured obligation in the same amount to
another single-B entity.
The importance of managing concentration risk and requirements under Basel 2 can be found in
paragraphs 770 to 777 of the Basel II Accord.
4.2 Setting Concentration Limits, Allocation, and Monitoring
Healthy and effective concentration limit systems are designed to flag pockets of vulnerability.
They create a framework for discussion among risk management, the origination business and
portfolio management. In doing so, they are a key part of a culture that directs the day-to-day
activities of a bank around return and risk optimization.
A good limit system needs to accommodate a wide variety of exposure types and forms a
simple and sound basis for a limit management.
Following the concentration risk aspects discussed in Section 2, an effective limit system is
usually set around three different levels of the portfolio:
Credit portfolio limit: This is a limit on the overall credit portfolio and is a very top-down
type of limit, typically set as part of the capital allocation process.
Sector / regional limits: An institution may determine that it does not like exposure to any one
industry sector or region to exceed a certain amount.
Single obligor limits: To prevent single-name concentration risk, exposure to any single
customer respectively group should not exceed a certain amount or
fraction of equity capital.
A common approach is to set limits as a percentage of capital involved with a variety of
definitions available for capital—for example Tier 1, Tier 2, regulatory capital, market
capitalization, or economic capital. Traditionally, such limits are set with the idea that an
institution is willing to bear losses only to a point where its capital is not impaired.

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5. References
[1]: Basel Committee on Banking Supervision, International Convergence on Capital
Measurement and Capital Standards. A Revised Framework. Comprehensive Version,
June 2006. The document can be downloaded from http://www.bis.org.
[2]: Committee of European Banking Supervisors, Technical aspects of the management of
concentration risk under the supervisory review process, December 14, 2006.

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A Appendix: CEBS Guidance for Institutions
Concentration 1
All institutions should have clear policies and key procedures ultimately approved by the
management body2
in relation to exposure to concentration risk
Institutions should have a clear and transparent concentration risk policy, as part of the broader
credit risk process, which is clearly and properly documented and approved by the management
body. It should be subject to regular review to take account of changes in risk appetite and the
business environment.
When devising their policies and procedures and when carrying out their review, institutions
should bear in mind the CEBS guidelines on internal governance3
.
Concentration 2
In application of Article 22 of the Capital Requirements Directive, institutions should
have appropriate internal processes to identify, manage, monitor and report
concentration risk which are suitable to the nature, scale and complexity of their business.
Institutions should have internal processes that identify, measure and monitor concentration risk
encompassing, for example:
 Individual large exposures to a single counterparty, connected counterparties and
related clusters the definition of connected for these purposes needs to be
sufficiently broad to capture exposures which are connected through, for example,
common ownership / management / guarantors / syndication techniques,
 Exposures to counterparties in the same economic sector or geographic region, or
 CRM techniques, collateral type or single protection seller.
For more complex businesses and for sophisticated institutions, this might also encompass
common or correlated risk factors that reflect more subtle or situation specific factors, that
require more sophisticated analysis for measurement and control. These concentrations may
reflect correlations in underlying risk factors or exposure to common factors that are embedded
in financial structures and may only become apparent in stress situations (see below).
Concentration 3
2
As referred to in Article 11 of the Capital Requirements Directive
3
See CEBS guidelines on the Application of the supervisory review process under Pillar 2, Chapter 2.1

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Institutions should use internal limits, thresholds or similar concepts, as appropriate,
having regard to their overall risk management and measurement.
Institutions should establish, as appropriate, a set of limits thresholds or similar concepts for
credit risk management. Procedures should be in place for the utilisation of such limits
thresholds or similar concepts ensuring that the degree of credit risk stipulated by the
management body is not exceeded.
Institutions should carry out analyses of the credit portfolio, including estimates of its trends,
and should take account of the results of these analyses in setting and verifying the adequacy of
the procedures and limits, thresholds or similar concepts for credit risk management.
The following sets out some examples for the expression of limits thresholds or similar
concepts:
 Size of top `x´ large exposures relative to relevant numeraire (e.g. balance sheet/own
funds/net profit numeraire);
 Size of top `x´ connected exposures relative to relevant numeraire;
 Size of key sectoral/geographical concentrations relative to relevant numeraire;
 As contributory factors in economic capital model: Portfolio concentration ratios,
Diversity scores, Concentration curves, Gini coefficients4
; Portfolio correlations and
variance/ covariance measures.
Concentration 4
Institutions should have adequate arrangements in place for actively monitoring,
managing and mitigating concentration risk against agreed policies and limits, thresholds
or similar concepts.
Monitoring should be incorporated into the institution's usual risk management and reporting
systems and be undertaken sufficiently frequently to reflect the nature of the business(es) and at
a sufficiently senior level within the institution.
Given that concentration risk, by its nature, tends to relate to aggregation of risk it is essential
that appropriate oversight is exercised by the management body ultimately at a strategic level.
If issues of concern are identified by the monitoring activity, an institution's management
should consider those issues and the appropriate response. Management responses might, for
example, include but are not limited to:
4
Gini coefficients can be used to measure any form of uneven distribution. It is a number between 0 and 1, where
0 corresponds with complete risk homogeneity (where every exposure has the same risk) and 1 corresponds with
absolute concentration (where one exposure carries all the risks, and the other exposures have zero risks).

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 Proceeding to a more detailed review of the risk environment in the particular
sector(s),
 Applying additional stress tests and scenario analyses,
 Reviewing with greater intensity the economic performance of existing borrowers,
 Reviewing approval levels for new business, or
 Regularly reviewing risk mitigation techniques, their value and their legal
enforceability.
Having assessed an issue, an institutions management may conclude that it is appropriate to
take mitigating action. For example, one or more of the following might be considered
appropriate:
 Reducing limits or thresholds on risk concentrations,
 Adjusting new business acquisition to address undue concentrations,
 Transferring credit risk to other parties, buying protection from other parties
(examples include credit derivatives, collateral, guarantees, sub-participation,
assignment) or selling down either directly or as part of securitization transactions,
or
 Allocating additional internal capital (see Concentration 5 below).
Concentration 5
Institutions should assess the amount of internal capital which they consider to be
adequate to hold against the level of concentration risk in their portfolio.
Institutions should undertake this assessment as part of their ICAAP, in a transparent way. In
doing so, they should take account of a range of relevant factors, including the quality of their
risk management and other internal systems and controls, ability to take effective management
action to adjust levels of concentration risk and the implications of stress-testing and scenario
analysis.
While the role of capital therefore needs to be assessed within this broader context, and keeping
in mind that the weight attached to the different factors will vary from institution to institution,
the expectation is that the higher the levels of concentration, the greater the onus will be on
institutions to demonstrate how they have assessed the implications in terms of internal capital.

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C Appendix: Credit Portfolio Approach
This appendix illustrates, also by mean of an example, the main concepts and ideas behind the
one factor/ multifactor models used in this analysis.
Consider the following hypothetical portfolio of obligors:
Obligor Rating Sector (Factor)
A 4 Industrial goods
B 2 Industrial goods
C 4 Basic materials
In a one factor model, the asset value return Zi of obligor i (i = A, B, C) is defined as a
combination of a single systematic factor E, which represents the state of the economy affecting
all obligors “in the same way”, and an idiosyncratic factor Xi:
Zi = ai ∙ E + bi ∙ Xi
In a multifactor model, the asset (value) return Zi of an obligator i (i = A, B, C) is defined as a
combination of a systematic factor Esector(i), which represents the state of the economy of the
industry sector to which obligor i belongs, and an idiosyncratic factor Xi:
Zi = ai ∙ Esector(i) + bi ∙ Xi
The “weights” ai and bi are related to ρi, the asset return correlation of obligor i:
ai = sqrt(ρi)
bi = sqrt(1-ρi)
Asset return correlation ρi is the specific contribution of i’s asset to the systematic risk of the
portfolio. It is, in other words, an indicator of the sensitivity of exposures to systematic risk.
In a (Basel II IRB) one factor model, asset return correlation for obligor i depend (exclusively)
on the rating of i itself:
ρi = F(ORR(i)).

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In a multifactor model, instead, asset return correlations depend, usually, on the industry
sector:
ρi = F(sector(i)).
Moreover, in a multifactor model, asset return correlations between each industry sector pair
(the factors) have to be specified. We will indicate, for example, the asset return correlations
between the sector to which obligor i belongs and the sector to which j belongs as
R(sector(i), sector(j)).
Note that if i and j belongs to the same sector (like A and B do), then R(sector(i), sector(j)) will
obviously be 100%.
The following image visualizes the different approaches that the two models use with respect to
the asset return correlation structure.
(Basel II IRB) One factor model Multi factor model
A B C
Economy
aA
aB
aC
A B C
Industrial
goods
Basic materials
aA aB aC
R
The “direct” correlation between the asset value returns of two obligors i and j can be derived
as:
r(i, j) = ai ∙ R(sector(i),sector(j)) ∙ aj
Note that in the one factor model case, R(sector(i),sector(j)) is obviously 100% for any pair of
obligors, so that the formula reduces to:
r(i, j) = ai ∙ aj

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= sqrt(ρi) ∙ sqrt(ρj)
= sqrt(F(ORR(i)) ∙ F(ORR(j)))
In a multifactor model, if i and j belongs to the same sector (like A and B do), then, in a
multifactor model, the formula reduces to:
r(i, j) = ai ∙ R(sector(i),sector(j)) ∙ aj
= ai ∙ aj
= sqrt(ρi) ∙ sqrt(ρj)
= F(sector(i)) ∙ F(sector(j))
= F(sector(i)) ∙ F(sector(i))
= sqrt(ρi) ∙ sqrt(ρi)
= ρi (= ρj)
Using the parameters that we will use in this analysis, we would observe, according to the two
models, the following two different asset correlations between these hypothetical obligors:
Obligor pair
(i, j)
Asset return correlation r(i,j)
One factor model Multifactor model
A, B 19% 26%
A, C 17% 12%
B, C 19% 12%
It can be noted that in a multifactor model, direct correlations between obligors in the same
sector, like A and B, are (by “construction”) higher than direct correlations between obligors of
different sectors (A and C, for example).

Page 21 of 24
D Appendix: Parameters
This appendix summarizes the parameters used in the models.
Common parameters (one factor and multifactor model)
 PDs
ORR 1 2 3 4 5 6 7
PD 0.40% 0.63% 1.04% 1.82% 3.37% 6.60% 21.91%
These have been estimated using internal ABN AMRO data and the following assumed
mapping between ORR and international rating scales:
Rating BBB- BB+ BB BB- B+ B B-/C
ORR 1 2 3 4 5 6 7
 EAD is calculated as (current) utilization + 75% of the remaining credit:
EAD = Util. + 75% (Limit – Util.) = 25% Util. + 75% Limit
 LGD has been set to 55%.
One-Factor model parameters
 Asset correlation is supposed (following Basel approach) to be linked to the ORR (in
particular, to the PD) in the following way:
0.12 * (1 – EXP(-50 * PD)) / (1 – EXP(-50))
+ 0.24 * (1 – (1 – EXP(-50 * PD)) / (1 – EXP(-50)))
Therefore, we get:
ORR 1 2 3 4 5 6 7
ρ 22% 21% 19% 17% 14% 12% 12%

Page 22 of 24
Multi-Factor model parameters
 We identify the following six industry segments:
o Basic Materials
o Consumer goods
o ICT
o Industrial goods
o Services
o Financial sector
The 14 industries found among the provided large corporate portfolio have therefore
been mapped to such six industry segments according to the following table:
Industry Factor
(Petro)chemicals Basic Materials
Agribusiness Consumer goods
Automotives Consumer goods
Building materials Basic Materials
Communications ICT
Contracting Industrial goods
Cotton trade Consumer goods
Durable Goods Consumer goods
Financial services Financial sector
IT ICT
Petroleum & gas Basic Materials
Power Supply Basic Materials
Tourism Services
Transportation Services
 To each segment correspond a factor, i.e. we use a 6-factor model. The correlation (R)
between any two (different) industry factors is set to 50%:
R
Basic
Materials
Consumer
Goods
ICT
Industrial
Goods
Services
Financial
Sector
Basic Materials 100% 50% 50% 50% 50% 50%

Page 23 of 24
Consumer goods 50% 100% 50% 50% 50% 50%
ICT 50% 50% 100% 50% 50% 50%
Industrial goods 50% 50% 50% 100% 50% 50%
Services 50% 50% 50% 50% 100% 50%
Financial sector 50% 50% 50% 50% 50% 100%
 Obligor asset return correlations are set to λ∙ρ, where ρ has been estimated by expert
judgment as
Sector
Basic
Materials
Consumer
goods
ICT
Industrial
goods
Services
Financial
sector
ρ 17% 14% 17% 17% 14% 20%
and λ chosen in such a way that applying the 99.9% IRB Basel analytical formula with
λ∙ρ as asset correlations would yield the same capital requirement given by the 99.9%
IRB Basel capital analytical formula with the Basel PD dependent asset correlations. In
particular, the λ used was:
Portfolio λ
Top-20 0.927025
Extended 0.905750

Page 24 of 24
E Appendix: Sensitivity Analysis
Results presented substantially rely on a number of parameters. As an example, we here show
the effects of changes in some of the parameters, in particular, correlation and the use of a
different confidence level.
Top-20 Portfolio:
99.9% Case
Correlation between industry factors (R)
All 0%
Base case
(All 50%)
All 100%
(One Factor)
Intra
corr.
(ρ)
Low (all λ∙12%) +82% +92% +100%
Base case (λ∙17% to λ∙20%) +84% +96% +111%
High (all λ∙24%) +88% +103% +133%
Extended Portfolio:
99.9% Case
Correlation between industry factors (R)
All 0%
Base case
(All 50%)
All 100%
(One Factor)
Intra
corr.
(ρ)
Low (all λ∙12%) +16% +26% +36%
Base case (λ∙17% to λ∙20%) +19% +30% +46%
High (all λ∙24%) +23% +43% +68%

Basel II – Integrated Risk Capital

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