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[si2] ,

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.

http://www.bis.org/


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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

aAaB

aC

A B C

Industrial

goodsBasic 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).


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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%

Business

Basel II – Integrated Risk Capital