a credit risk management framework.pdf

8/10/2019 A CREDIT RISK MANAGEMENT FRAMEWORK.pdf

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R ED ITRISK + CR ED ITRISK +CR ED ITRISK + CIT RISK +CR ED ITRISK + CR ED ITRISK +CR ED ITK+ CR ED ITRISK +CR ED ITRISK + CR ED ITRISKR ED ITRISK + CR ED ITRISK +CR ED ITRISK + CIT RISK +CR ED ITRISK + CR ED ITRISK +CR ED ITK+ CR ED ITRISK +CR ED ITRISK + CR ED ITRISKR ED ITRISK + CR ED ITRISK +CR ED ITRISK + CIT RISK +CR ED ITRISK + CR ED ITRISK +CR ED ITK+ CR ED ITRISK +CR ED ITRISK + CR ED ITRISKR ED ITRISK + CR ED ITRISK +CR ED ITRISK + CIT RISK +CR ED ITRISK + CR ED ITRISK +CR ED ITK+ CR ED ITRISK +CR ED ITRISK + CR ED ITRISKR ED ITRISK + CR ED ITRISK +CR ED ITRISK + CIT RISK +CR ED ITRISK + CR ED ITRISK +CR ED ITR egulated by S FA

CREDIT FIR STSUISSE B O S T O N

CR E D ITRIS K+

A C R E D IT R IS K M A N A G E M E N T FR A M E W O R K


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Copyright 1997 Credit Suisse First Boston International. All rights reserved.

CREDITRISK+ is a trademark of Credit Suisse First Boston International in countries of use.

CREDITRISK+ as described in this document (C REDITRISK+) is a method of credit risk management introduced by Credit Suisse Group.

No representation or warranty, express or implied, is made by Credit Suisse First Boston International or any other Credit Suisse Group

company as to the accuracy, completeness, or fitness for any particular purpose of C REDITRISK+. Under no circumstances shall

Credit Suisse First Boston International or any other Credit Suisse Group company have any liability to any other person or any entity

for (a) any loss, damage or other injury in whole or in part caused by, resulting from or relating to, any error (negligent or otherwise), of

Credit Suisse First Boston International or any other Credit Suisse Group company in connection with the compilation, analysis,

interpretation, communication, publication or delivery of C REDITRISK+, or (b) any direct, indirect, special, consequential, incidental orcompensatory damages whatsoever (including, without limitation, lost profits), in either case caused by reliance upon or otherwise resulting

from or relating to the use of (including the inability to use) C REDITRISK+.

Issued and approved by Credit Suisse First Boston International for the purpose of Section 57, Financial Services Act 198 6. Regulated by

the Securities and Futures Authority. The products and services referred to are not available to private customers.

is a leading global investment banking firm, providing comprehensive

financial advisory, capital raising, sales and trading, and financial

products for users and suppliers of capital around the world. It operates in over 60 offices across

more than 30 countries and six continents and has over 15,000 employees.

CREDIT FIR STSUISSE B O S T O N


3/72CR E D I TRIS K+ 1

Contents1. Introduction to C REDIT RISK+ 3

1.1 D evelopm ents in C redit R isk M anagem ent 3

1.2 C om ponents of C RE D ITRIS K + 31.3 The C R ED ITRIS K + M odel 4

1.4 Econom ic C apital 4

1.5 A pplications of C RE D ITRIS K + 5

1.6 Exam ple Spreadsheet Im plem entation 5

2. M odelling Credit Risk 62.1 R isk M odelling C oncepts 6

2.2 Types of C redit R isk 7

2.3 D efault R ate B ehaviour 8

2.4 M odelling A pproach 9

2.5 Tim e H orizon for C redit R isk M odelling 102.6 D ata Inputs to C redit R isk M odelling 11

2.7 C orrelation and Incorporating the Effects of B ackground Factors 14

2.8 M easuring C oncentration 16

3. The C REDIT R ISK+ M odel 173.1 S tages in the M odelling Process 17

3.2 Frequency of D efault Events 17

3.3 M oving from D efault Events to D efault Losses 18

3.4 C oncentration R isk and Sector A nalysis 20

3 .5 M ulti-Year Losses for a H old-to-M aturity Tim e H o rizon 21

3.6 Sum m ary of the C RE D ITRIS K + M odel 22

4. Economic Capital for Credit Risk 234.1 Introduction to Econom ic C apital 23

4.2 Econom ic C apital for C redit R isk 23

4.3 Scenario A nalysis 24

5. Applications of C REDIT RISK+ 265.1 Introduction 26

5.2 Provisioning for C redit R isk 26

5.3 R isk-B ased C redit Lim its 29

5.4 Portfolio M anagem ent 29


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AppendicesA . The C REDIT R ISK+ M odel 32

A 1 O verview of this A ppendix 32

A 2 D efault Events w ith Fixed D efault R ates 33A 3 D efault Losses w ith Fixed D efault R ates 35

A 4 Loss D istribution w ith Fixed D efault R ates 38

A 5 A pplication to M ulti-Year Losses 39

A 6 D efault R ate U ncertainty 41

A 7 Sector A nalysis 41

A 8 D efault Events w ith Variable D efault R ates 44

A 9 D efault Losses w ith Variable D efault R ates 46

A 10 Loss D istribution w ith Variable D efault R ates 47

A 11 C onvergence of Variable D efault R ate C ase to Fixed Default R ate C ase 49

A 12 G eneral Sector A nalysis 50

A 13 R isk C ontributions and Pairw ise C orrelation 52

B . Illustrative E xample 58B 1 Exam ple Spreadsheet-B ased Im plem entation 58

B 2 Exam ple Portfolio and S tatic D ata 58

B 3 Exam ple U se of the Spreadsheet Im plem entation 60

C . Contacts 66

D . Selected Bibliography 68

List of Tables

Table 1: R epresentations of the default rate process 9

Table 2: O ne-year default rates (% ) 12

Table 3: D efault rate standard deviations (% ) 13

Table 4: R ecovery rates by seniority and security (% ) 14

Table 5: M echanism s for controlling the risk of credit default losses 25

Table 6: P rovisioning for different business lines 28

Table 7: Exam ple of credit risk provisioning 28

Table 8: Exam ple portfolio 59

Table 9 : E xam ple m apping table of default rate inform ation 5 9

Table 10: E xam ple 1A - R isk contributions 64

Table 11: Exam ple 1B - R isk analysis of rem oved obligors 65Table 12: Exam ple 1B - Portfolio m ovem ent analysis 65

List of Figures

Figure 1: C om ponents of C RE D ITRIS K + 3

Figure 2: D efault rate as a continuous random variable 8

Figure 3: D efault rate as a discrete random variable 9

Figure 4: R ated corporate defaults by num ber of issuers 12

Figure 5: D efaulted bank loan price distribution 13

Figure 6: C R ED ITRIS K + M odel - D istribution of default events 18

Figure 7: C R ED ITRIS K + M odel - D istribution of default losses 19

Figure 8: Im pact of sectors on the loss distribution 21Figure 9: Econom ic capital for credit risk 24

Figure 10: P arts of the credit default loss distribution 25

Figure 11: C redit risk provisioning 27

Figure 12: U sing risk contributions 31

Figure 13: Flow chart description of A ppendix A 332 CREDIT FIRS TSUISSE B O S TO N



n roo CR1.1 Developments in Credit Risk Management

Since the beginning of the 1990s, C redit Suisse First B oston (C SFB ) has been developing and deploying

new risk m anagem ent m ethods. In 1 993, C redit Suisse G roup launched, in parallel, a m ajor project aim ed

at m odernising its credit risk m anagem ent and, using C SFB s expertise, at developing a m ore forw ard-

looking m anagem ent tool. In D ecem ber 1996, C redit Suisse G roup introduced C R ED ITRISK + - a C redit R isk

M anagem ent Fram ew ork.

C urrent areas of developm ent in credit risk m anagem ent include: m odelling credit risk on a portfolio basis;

credit risk provisioning; active portfolio m anagem ent; credit derivatives; and sophisticated approaches to capital

allocation that m ore closely reflect econom ic risk than the existing regulatory capital regim e. C R ED ITRISK +

addresses all of these areas and the relationships betw een them .

CR ED ITRISK + can be applied to credit exposures arising from all types of products including corporate and retail

loans, derivatives, and traded bonds.

1 .2 Components of CREDITRIS K+

The com ponents of C R ED ITRISK + and the interrelationships betw een them are show n in the follow ing diagram .

Figure 1 :

Components of CREDITRIS K+

CREDITRISK+ comprises threemain componentsa C REDITRISK+

Model that uses a portfolioapproach, a methodology forcalculating economic capital

for credit risk, and severalapplications of the technology.

Introduction to C REDIT RISK+ 1

CREDITRIS K+

Credit Risk Measurement

Credit DefaultLoss Distribution

Scenario Analysis

Provisioning

Limits

Portfolio Management

Econom ic Capital Applications

E xposures D efault R ates

CREDITRISK+ Model

R ecoveryR ates

D efault R ateVolatilities


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A m odern approach to credit risk m anagem ent should address all aspects of credit risk, from quantitative

m odelling to the developm ent of practical techniques for its m anagem ent. In addition to w ell-established credit

risk m anagem ent techniques, such as individual obligor (borrow er, counterparty or issuer) lim its and concentration

lim its, C R ED ITRISK + reflects the requirem ents of a m odern approach to m anaging credit risk and com prises three

m ain com ponents:

The C REDITRISK+ Model that uses a portfolio approach and analytical techniques applied w idely in theinsurance industry.

A methodology for calculating economic capital for credit risk.

Applications of the credit risk m odelling m ethodology including: (i) a methodology for establishing provisionson an anticipatory basis, and (ii) a means of measuring diversification and concentration to assist in

portfolio management.

1.3 The CREDITRIS K+ Model

CR ED ITRISK + is based on a portfolio approach to m odelling credit default risk that takes into account

inform ation relating to size and m aturity of an exposure and the credit quality and system atic risk of an obligor.

The C R ED ITRISK + M odel is a statistical m odel of credit default risk that m akes no assum ptions about the

causes of default. This approach is sim ilar to that taken in m arket risk m anagem ent, w here no attem pt is m ade

to m odel the causes of m arket price m ovem ents. The C RE D ITRISK + M odel considers default rates as continuous

random variables and incorporates the volatility of default rates in order to capture the uncertainty in the level

of default rates. O ften, background factors, such as the state of the econom y, m ay cause the incidence of

defaults to be correlated, even though there is no causal link betw een them . The effects of these background

factors are incorporated into the C R ED ITRISK + M odel through the use of default rate volatilities and sector

analysis rather than using default correlations as explicit inputs into the m odel.

M athem atical techniques applied w idely in the insurance industry are used to m odel the sudden event of an

obligor default. This approach contrasts w ith the m athem atical techniques typically used in finance. In financial

m odelling one is usually concerned w ith m odelling continuous price changes rather than sudden events.

A pplying insurance m odelling techniques, the analytic C R ED ITRIS K + M odel captures the essential

characteristics of credit default events and allow s explicit calculation of a full loss distribution for a portfolio of

credit exposures.

1.4 Economic Capita l

The output of the C R ED ITRISK + M odel can be used to determ ine the level of econom ic capital required to cover

the risk of unexpected credit default losses.

M easuring the uncertainty or variability of loss and the relative likelihood of the possible levels of unexpected

losses in a portfolio of credit exposures is fundam ental to the effective m anagem ent of credit risk. Econom ic

capital provides a m easure of the risk being taken by a firm and has several benefits: it is a m ore appropriate

risk m easure than that specified under the current regulatory reg im e; it m easures econom ic risk on a portfolio

basis and takes account of diversification and concentration; and, since econom ic capital reflects the changing

risk of a portfolio, it can be used for portfolio m anagem ent.

4 CREDIT FIRS TSUISSE B O S TO N



The C R ED ITRISK + M odel is supplem ented by scenario analysis in order to identify the financial im pact of low

probability but nevertheless plausible events that m ay not be captured by a statistically based m odel.

1.5 Applications of CREDITRIS K+

CRE D ITRISK + includes several applications of the credit risk m odelling m ethodology, including a forw ard-looking

provisioning m ethodology and quantitative portfolio m anagem ent techniques.

1.6 Example Spreadsheet Impleme ntation

In order to assist the reader of this docum ent, a spreadsheet-based im plem entation that illustrates the range

of possible outputs of the C R ED ITRISK + M odel can be dow nloaded from the Internet (http://w w w .csfb.com ).

1Introduction


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redi2.1 Risk Modelling Concepts

2.1.1 Types of U ncertainty Arising in the M odelling ProcessA statistically based m odel can describe m any business processes. H ow ever, any m odel is only a

representation of the real w orld. In the m odelling process, there are three types of uncertainty that m ust be

assessed: process risk, param eter uncertainty and m odel error.

Process RiskProcess risk arises because the actual observed results are subject to random fluctuations even w here the

m odel describing the loss process and the param eters used by the m odel are appropriate. Process risk is

usually addressed by expressing the m odel results to an appropriately high level of confidence.

Parameter UncertaintyParam eter uncertainty arises from the difficulties in obtaining estim ates of the param eters used in the m odel.

The only inform ation that can be obtained about the underlying process is obtained by observing the results

that it has generated in the past. It is possible to assess the im pact of param eter uncertainty by perform ingsensitivity analysis on the param eter inputs.

Model ErrorM odel error arises because the proposed m odel does not correctly reflect the actual process - alternative

m odels could produce different results. M odel error is usually the least tractable of the three types of

uncertainty.

2.1.2 Addressing Mode lling IssuesA s all of these types of uncertainty enter into the m odelling process, it is im portant to be aw are of them and

to consider how they can be addressed w hen developing a credit risk m odel. Indeed, a realistic assessm ent of

the potential effects of these errors should be m ade before any decisions are m ade based on the outputs of

the m odel.


M odelling Credit Risk 2



M odelling Credit Risk

The C REDITRISK+ Modelmakes no assumptionsabout the causes of default.

This approach is similar tothat taken in market riskmanagement, where noassumptions are madeabout the causes of marketprice movements.

All portfolios of exposuresexhibit credit default risk, asthe default of an obligorresults in a loss.

CR ED ITRISK + addresses these types of uncertainty in several w ays:

N o assum ptions are m ade about the causes of default. This approach is sim ilar to that taken in m arket riskm anagem ent, w here no assum ptions are m ade about the causes of m arket price m ovem ents. This not only

reduces the potential m odel error but also leads to the developm ent of an analytically tractable m odel.

The data requirem ents for the C R ED ITRISK + M odel have been kept as low as possible, w hich m inim ises theerror from param eter uncertainty. In the credit environm ent, em pirical data is sparse and difficult to obtain.

Even then, the data can be subject to large fluctuations year on year.

C oncerns about param eter uncertainty are addressed using scenario analysis, in w hich the effects of stresstesting each of the input param eters are quantified. For exam ple, increasing default rates or default rate

volatilities can be used to sim ulate dow nturns in the econom y.

2.2 Types of Credit Risk

There are tw o m ain types of credit risk:

Credit spread risk : C redit spread risk is exhibited by portfolios for w hich the credit spread is traded andm arked-to-m arket. C hanges in observed credit spreads im pact the value of these portfolios.

Credit default risk : A ll portfolios of exposures exhibit credit default risk, as the default of an obligor resultsin a loss.

2.2.1 Credit Spread RiskC redit spread is the excess return dem anded by the m arket for assum ing a certain credit exposure. C redit

spread risk is the risk of financial loss ow ing to changes in the level of credit spreads used in the m ark-to-

m arket of a product.

C redit spread risk fits m ore naturally w ithin a m arket risk m anagem ent fram ew ork. In order to m anage credit

spread risk, a firm s value-at-risk m odel should take account of value changes caused by the volatility of credit

spreads. Since the distribution of credit spreads m ay not be norm al, a standard variance-covariance approach

to m easuring credit spread risk m ay be inappropriate. H ow ever, the historical sim ulation approach, w hich does

not m ake any assum ptions about the underlying distribution, used in com bination w ith other techniques,

provides a suitable alternative.

C redit spread risk is only exhibited w hen a m ark-to-m arket accounting policy is applied, such as for portfolios

of bonds and credit derivatives. In practice, som e types of products, such as corporate or retail loans, are

typically accounted for on an accruals basis. A m ark-to-m arket accounting policy w ould have to be applied tothese products in order to recognise the credit spread risk.

2.2.2 Credit Default RiskC redit default risk is the risk that an obligor is unable to m eet its financial obligations. In the event of a default

of an obligor, a firm generally incurs a loss equal to the am ount ow ed by the obligor less a recovery am ount

w hich the firm recovers as a result of foreclosure, liquidation or restructuring of the defaulted obligor.

A ll portfolios of exposures exhibit credit default risk, as the default of an obligor results in a loss.

2


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C redit default risk is typically associated w ith exposures that are m ore likely to be held to m aturity, such as

corporate and retail loans and exposures arising from derivative portfolios. B ond m arkets are generally m ore

liquid than loan m arkets and therefore bond positions can be adjusted over a shorter tim e fram e. H ow ever,

w here the intention is to m aintain a bond portfolio over a longer tim e fram e, even though the individual

constituents of the portfolio m ay change, it is equally im portant to m easure the default risk that is taken byholding the portfolio.

CR ED ITRISK + focuses on m odelling and m anaging credit default risk.

2.3 Default Rate Behaviour

Equity and bond prices are forw ard-looking in nature and are form ed by investorsview s of the financial

prospects of a particular obligor. H ence, they incorporate both the credit quality and the potential credit quality

changes of that obligor.

Therefore, the default rate of a particular obligor, inferred from m arket prices, w ill vary on a continuous scale

and hence can be view ed as a continuous random variable. In m odelling credit risk, one is concerned w ith

determ ining the possible future outcom es over the chosen tim e horizon.

The process for the default rate can be represented in tw o different w ays:

Continuous variable : W hen treated as a continuous variable, the possible default rate over a given tim ehorizon is described by a distribution, w hich can be specified by a default rate and a volatility of the default

rate. The data requirem ents for m odelling credit default risk are analogous to the data requirem ents for

pricing stock options - a forw ard stock price and the stock price volatility are used to define the forw ard

stock price distribution. The follow ing figure illustrates the path that a default rate m ay take over tim e and

the distribution that it could have over that tim e.

Discrete variable : B y treating the default rate as a discrete variable, a sim plification of the continuousprocess described above is m ade. A convenient w ay of m aking default rates discrete is by assigning credit

ratings to obligors and m apping default rates to credit ratings. U sing this approach, additional inform ation

is required in order to m odel the possible future outcom es of the default rate. This can be achieved via a

rating transition m atrix that specifies the probability of keeping the sam e credit rating, and hence the sam e

value for the default rate, and the probabilities of m oving to different credit ratings and hence to different

values for the default rate. This is illustrated in the follow ing figure.


Possible path ofdefault rate

Frequency of defaultrate outcomes

Figure 2 :

Default rate as a

continuous random

variable

D e

f a u

l t r a

t e

Tim e ho rizon


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The discrete approach w ith rating m igrations and the continuous approach w ith a default rate volatility are

different representations of the behaviour of default rates. B oth approaches achieve the desired end result of

producing a distribution for the default rate.

The above tw o representations of default rate behaviour are sum m arised in the follow ing table:

Treatment of default rate Data requirements

C ontinuous variable D efault rates

Volatility of default rates

D iscrete variable C redit ratings

R ating transition m atrix

The C R ED ITRISK + M odel is a statistical m odel of credit default risk that m odels default rates as continuous

random variables and incorporates the volatility of the default rate in order to capture the uncertainty in the

level of the default rate. A m apping from credit ratings to a set of default rates provides a convenient approach

to setting the level of the default rate.

2.4 Modelling Approach

2.4.1 Risk MeasuresW hen m anaging credit risk, there are several m easures of risk that are of interest, including the follow ing:

Distribution of loss: The risk m anager is interested in obtaining distributions of loss that m ay arise from thecurrent portfolio. The risk m anager needs to answ er questions such as W hat is the size of loss for a given

confidence level?.

Identifying extreme outcomes: The risk m anager is also concerned w ith identifying extrem e or catastrophicoutcom es. These outcom es are usually difficult to m odel statistically but can be addressed through the use

of scenario analysis and concentration lim its.

Table 1:

Representations of the

default rate process

CR E D I TRIS K+ 9

M odelling Credit Risk

Figure 3 :

Default rate as a discrete

random variable

2Possible path ofdefault rate B

AAA

AA

BBB

BB

A

Default

Frequency of defaultrate outcomes

D e

f a u

l t

r a

t e

Tim e ho rizon

The C R ED ITRISK + M odel

treats default rates as

continuous random variables

and incorporates default

rate volatility to capture the

uncertainty in the level of

the default rate.


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2.4.2 A Portfolio Approach to Managing Credit RiskC redit risk can be m anaged through diversification because the num ber of individual risks in a portfolio of

exposures is usually large. C urrently, the prim ary technique for controlling credit risk is the use of lim it system s,

including individual obligor lim its to control the size of exposure, tenor lim its to control the m axim um m aturity

of exposures to obligors, rating exposure lim its to control the am ount of exposure to obligors of certain creditratings, and concentration lim its to control concentrations w ithin countries and industry sectors.

The portfolio risk of a particular exposure is determ ined by four factors: (i) the size of the exposure, (ii) the

m aturity of the exposure, (iii) the probability of default of the obligor, and (iv) the system atic or concentration

risk of the obligor. C redit lim its aim to control risk arising from each of these factors individually. The general

effect of this approach, w hen applied in a w ell-structured and consistent m anner, is to create reasonably w ell-

diversified portfolios. H ow ever, these lim its do not provide a m easure of the diversification and concentration

of a portfolio.

In order to m anage effectively a portfolio of exposures, a m eans of m easuring diversification and concentration

has to be developed. A n approach that incorporates size, m aturity, credit quality and system atic risk into a singleportfolio m easure is required. C R ED ITRISK + takes such an approach.

2.4.3 Modelling Techniques Used in the CREDITRIS K+ ModelThe econom ic risk of a portfolio of credit exposures is analogous to the econom ic risk of a portfolio of

insurance exposures. In both cases, losses can be suffered from a portfolio containing a large num ber of

individual risks, each w ith a low probability of occurring. The risk m anager is concerned w ith assessing the

frequency of the unexpected events as w ell as the severity of the losses.

In order to keep m odel error to a m inim um , no assum ptions are m ade about the causes of default.

M athem atical techniques applied w idely in the insurance industry are used to m odel the sudden event of anobligor default. In m odelling credit default losses one is concerned w ith sudden events rather than continuous

changes. The essential characteristics of credit default events are captured by applying these insurance

m odelling techniques. This has the additional benefit that it leads to a credit risk m odel that is analytically

tractable and hence not subject to the problem s of precision that can arise w hen using a sim ulation-based

approach. The analytic C R ED ITRISK + M odel allow s rapid and explicit calculation of a full loss distribution for a

portfolio of credit exposures.

2.5 Tim e H orizon for Credit Risk Modelling

A key decision that has to be m ade w hen m odelling credit risk is the choice of tim e horizon. G enerally, the tim e

horizon chosen should not be shorter than the tim e fram e over w hich risk-m itigating actions can be taken.

CR ED ITRISK + does not prescribe any one particular tim e horizon but suggests tw o possible tim e horizons that

can provide m anagem ent inform ation relevant for credit risk m anagem ent:

A constant tim e horizon, such as one year.

A hold-to-m aturity or run-off tim e horizon.

1 0 CREDIT FIRS TSUISSE B O S TO N

CREDITRISK+ is basedon a portfolio approach -summarising informationabout size, maturity, creditquality and systematic riskinto a single measure.



2.5.1 Constant Time H orizonA constant tim e horizon is relevant, as it allow s all exposures to be considered at the sam e future date.

For various reasons, one year is often taken as a suitable tim e horizon: credit risk m itigating actions can

norm ally be executed w ithin one year, new capital can be raised to replenish capital eroded by actual credit

losses during the period, and, furtherm ore, one year m atches the norm al accounting period. G iven thesefactors, C R ED ITRISK + suggests a tim e horizon of one year for credit risk econom ic capital.

2.5.2 Hold-to-Maturity Time HorizonA lternatively, a hold-to-m aturity tim e horizon allow s the full term structure of default rates over the lifetim e of the

exposures to be recognised. This view of the portfolio enables the risk m anager to com pare exposures of

different m aturity and credit quality and is an appropriate tool, in addition to the constant tim e horizon, for

portfolio m anagem ent. The role that the C R ED ITRISK + M odel plays in active portfolio m anagem ent is discussed

later in this docum ent.

A benchm ark tim e horizon of one year can be used for portfolios w here there is an intention to m aintain

exposures for longer than the term of the booked transactions (e.g. traded bond portfolios).

2.6 Data Inputs to Credit Risk Modelling

2.6.1 Data InputsA ny m odelling of credit risk is dependent on certain data requirem ents being m et. The quality of this data w ill

directly affect the accuracy of the m easurem ent of credit risk and therefore any decision to be m ade using the

results should be m ade only having fully assessed the potential error from uncertainties in the data used.

The inputs used by the C R ED ITRISK + M odel are:

C redit exposures

O bligor default rates

O bligor default rate volatilities and

R ecovery rates.

The C R ED ITRISK + M odel presented in this docum ent does not prescribe the use of any one particular data set

over another. O ne of the key lim itations in m odelling credit risk is the lack of com prehensive default data.

W here a firm has its ow n inform ation that is judged to be relevant to its portfolio, this can be used as the input

into the m odel. A lternatively, conservative assum ptions can be used w hile default data quality is being im proved.

2.6.2 Credit ExposuresThe exposures arising from separate transactions w ith an obligor should be aggregated according to the legal

corporate structure and taking into account any rights of set-off.

The C R ED ITRISK + M odel is capable of handling all types of instrum ents that give rise to credit exposure,

including bonds, loans, com m itm ents, financial letters of credit and derivative exposures. For som e of these

transaction types, it is necessary to m ake an assum ption about the level of exposure in the event of a default:

for exam ple, a financial letter of credit w ill usually be draw n dow n prior to default and therefore the exposure

at risk should be assum ed to be the full nom inal am ount.

In addition, if a m ulti-year tim e horizon is being used, it is im portant that the changing exposures over tim e areaccurately captured.

2M odelling Credit Risk


Exposures D efault R ates

CREDITRISK+ Model

R ecoveryRates



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Figure 4 :

Rated corporate de faults

by number of issuers

O ne-year default ratesshow significant fluctuations

from year to year.




CREDITRISK+ Model

Re coveryRates


Table 2:

One-year default rates (%)

2.6.3 Default RatesA default rate, w hich represents the likelihood of a default event occurring, should be assigned to each obligor.

This can be achieved in a num ber of ways, including:

O bserved credit spreads from traded instrum ents can be used to provide m arket-assessed probabilities ofdefault.

A lternatively, obligor credit ratings, together with a m apping of default rates to credit ratings, provide aconvenient w ay of assigning probabilities of default to obligors. The rating agencies publish historic default

statistics by rating category for the population of obligors that they have rated.

Credit rating O ne-year default rate

A aa 0.00

A a 0.03

A 0.01

B aa 0.12B a 1.36

B 7.27

Source: Carty & Lieberm an, 1997, M oodys Investors Service G lobal C redit R esearch

A credit rating is an opinion of an obligors overall financial capacity to m eet its financial obligations (i.e. its

creditw orthiness). This opinion focuses on the obligors capacity and w illingness to m eet its financial

com m itm ents as they fall due. A n assessm ent of the nature of a particular obligation, including its seniority in

bankruptcy or liquidation, should be perform ed w hen considering the recovery rate for an obligor.

It should be noted that one-year default rates show significant variation year on year, as can be seen in the

follow ing figure. D uring periods of econom ic recession, the num ber of defaults can be m any tim es the level

observed at other tim es.

Source: Standard & Poors R atings Perform ance 1996 (February 1997 )

A nother approach is to calculate default probabilities on a continuous scale, w hich can be used as asubstitute for the com bination of credit ratings and assigned default rates.

F r e q u e n c y

1981 1982 1983 1984 1985 198 6 1987 1988 1989 19 90 1 991 1992 1 993 199 4 1995 1 996

70

6 0

5 0

4 0

3 0

2 0

1 0

0



2M odelling Credit RiskCredit Risk Measurement


CREDITRISK+ Model

R ecoveryRa tes




CREDITRISK+ Model

R ecovery

Ra tes

D efault R ate

Volatilities

Table 3:

Default rate standard

deviations (% )

Figure 5 :

Defaulted bank loan

price distribution

F r e q u e n c y

2.6.4 De fault Rate VolatilitiesPublished default statistics include average default rates over m any years. A s show n previously, actual

observed default rates vary from these averages. The am ount of variation in default rates about these averages

can be described by the volatility (standard deviation) of default rates. A s can be seen in the follow ing table,

the standard deviation of default rates can be significant com pared to actual default rates, reflecting the highfluctuations observed during econom ic cycles.

One-year default rate (%)

Credit rating Average Standard deviation

A aa 0.00 0.0

A a 0.03 0.1

A 0.01 0.0

B aa 0.12 0.3

B a 1.36 1.3

B 7.27 5.1

Source: C arty & Lieberm an, 1996, M oodys Investors Service G lobal C redit R esearch

The default rate standard deviations in the above table w ere calculated over the period from 1970 to 1996

and therefore include the effect of econom ic cycles.

2.6.5 Recovery RatesIn the event of a default of an obligor, a firm generally incurs a loss equal to the am ount ow ed by the obligor

less a recovery am ount, w hich the firm recovers as a result of foreclosure, liquidation or restructuring of the

defaulted obligor or the sale of the claim . R ecovery rates should take account of the seniority of the obligationand any collateral or security held.

R ecovery rates are subject to significant variation. For exam ple, the figure below show s the price distribution

of defaulted bank loans and illustrates that there is a large degree of dispersion.

Source: D efaulted B ank Loan R ecoveries (Novem ber 1996) , M oodys Investors Service G lobal C redit R esearch

$ 0

- $ 1 0

$ 1 1

- $ 2 0

$ 2 1

- $ 3 0

$ 3 1

- $ 4 0

$ 4 1

- $ 5 0

$ 5 1

- $ 6 0

$ 6 1

- $ 7 0

$ 7 1

- $ 8 0

$ 8 1

- $ 9 0

$ 9 1

- $ 1 0 0

1 4

12

1 0

8

6

4

2

0


16/72

There is also considerable variation for obligations of differing seniority, as can be seen from the standard

deviation of the corporate bond and bank loan recovery rates in the table below .

Seniority and security Average Standard deviation

Senior secured bank loans 71.18 21.09

Senior secured public debt 63.45 26.21

Senior unsecured public debt 47.54 26.29

Senior subordinated public debt 38.28 24.74

Subordinated public debt 28.29 20.09

Junior subordinated public debt 14.66 8.67

Source: H istorical D efault R ates o f C orporate B ond Issuers, 1920-19 96 (January 1997 ) M oodys Investors Se rvice G lobal C redit R esearch

Publicly available recovery rate data indicates that there can be significant variation in the level of loss, given

the default of an obligor. Therefore, a careful assessm ent of recovery rate assum ptions is required. G iven thisuncertainty, stress testing should be perform ed on the recovery rates in order to calculate the potential loss

distributions under different scenarios.

2.7 Correlation and Incorporating the Effects of Background Factors

D efault correlation im pacts the variability of default losses from a portfolio of credit exposures. The C R ED ITRISK +

M odel incorporates the effects of default correlations by using default rate volatilities and sector analysis.

2.7.1 The Random N ature of D efaults and the Appearance of CorrelationC redit defaults occur as a sequence of events in such a w ay that it is not possible to forecast the exact tim e

of occurrence of any one default or the exact total num ber of defaults. Often, there are background factors

that may cause the incidence of default events to be correlated, even though there is no causal link between

them. For exam ple, if there is an unusually large num ber of defaults in one particular m onth, this m ight be due

to the econom y being in recession, w hich has increased the rates of default above their average level. In this

econom ic situation, it is quite likely that the num ber of defaults in the follow ing m onth w ill also be high.

C onversely, if there are few er defaults than on average in one m onth, because the econom y is grow ing, it is

also likely that there w ill be few er defaults than on average in the follow ing m onth. The defaults are correlated

but there is no causal link betw een them - the correlation effect observed is due to a background factor, the

state of the econom y, w hich changes the rates of default.

2.7.2 Impact of the Economy on Default RatesThere is general agreem ent that the state of the econom y in a country has a direct im pact on observed default

rates. A recent report by Standard and Poors stated that A healthy economy in 1996 contributed to a

significant decline in the total number of corporate defaults. Compared to 1995, defaults were reduced by

one-half .1 A nother report by M oodys Investors Service stated that The sources of [default rate volatility]

are many, but macroeconomic trends are certainly the most influential factors .2

A s the above quotations indicate and as can be seen in Figure 4 above, there is significant variation in the

num ber of defaults from year to year. Furtherm ore, for each year, different industry sectors w ill be affected to

different degrees by the state of the econom y. The m agnitude of the im pact w ill be dependent on how sensitive

an obligors earnings are to various econom ic factors, such as the grow th rate of the econom y and the level of

interest rates.


Table 4:

Recovery rates by

seniority and security (%)

Often, there arebackground factors thatmay cause the incidenceof defaults to be correlated,even though there is nocausal link between them.

1 Standard and PoorsRatings Performance1996, February 1997

2 Moodys Investors

Service, Corporate BondDefaults and DefaultRates, January 1996



Econom ic m odels that attem pt to capture the effect of changes in the econom y on default rates can be

developed in order to specify the default rates for subsequent use in a credit risk m odel. H ow ever, this

approach can have several w eaknesses, including the follow ing:

Since there are lim ited publicly available default rate statistics by country or by industry sector, it is difficultto verify the accuracy of an econom ic m odel used to derive default rates.

Even if a causal relationship could be established relating default rates to certain econom ic variables, it isquestionable w hether such relationships w ould be stable over several years.

Therefore, alternative approaches that attem pt to capture the observed variability of default rates have to be

sought.

2.7.3 Incorporating the Effects of Background FactorsIt is possible to incorporate the effects of background factors into the specification of default rates by allow ing

the default rate itself to have a probability distribution. This is accom plished by incorporating default rate

volatilities into the m odel.

The C R ED ITRISK + M odel m odels the effects of background factors by using default rate volatilities that result

in increased defaults rather than by using default correlations as a direct input. B oth approaches, the use of

default rate volatilities and default correlations, give rise to loss distributions w ith fat tails.

Section 3 of this docum ent describes in detail how the C R ED ITRISK + M odel uses default rate volatilities in the

m odelling of credit default risk.

The C RE D ITRISK + M odel does not attem pt to m odel correlations explicitly but captures the sam e concentration

effects through the use of default rate volatilities and sector analysis 3. There are various reasons w hy this

approach has been taken, including the follow ing:

Instability of default correlations : G enerally, correlations calculated from financial data show a high degreeof instability. In addition, a calculated correlation can be very dependent on the underlying tim e period of

the data. A sim ilar instability problem m ay arise w ith default rate volatilities: how ever, it is m uch easier to

perform scenario analysis on default rate volatilities, ow ing to the analytically tractable nature of a m odel

that uses volatilities rather than correlations.

Lack of empirical data : There is little em pirical data on default correlations. D efaults them selves areinfrequent events and so there is insufficient data on m ultiple defaults w ith w hich to calculate explicit

default correlations. Since default correlations are difficult to calculate directly, som e approaches use asset

price correlations to derive default correlations, but this can only be considered a proxy. This techniquerelies upon additional assum ptions about the relationship betw een asset prices and probabilities of default.

Furtherm ore, it is questionable how stable any relationship, that m ay be inferred or observed during a period

of norm al trading, w ould be in the event of default of a particular obligor. In addition, w here there is no asset

price for the obligor, for exam ple in a retail portfolio, there is no obvious w ay of deriving default correlations.

2M odelling Credit Risk

The C REDITRISK+ Modelcaptures concentration riskthrough the use of defaultrate volatilities and sectoranalysis.

3 Sector analysis isdiscussed in Sections2.8 and 3.4


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2.8 Measuring Concentrat ion

The above discussion has highlighted the fact that there are background factors that affect the level of default

rates. The state of the econom y of each different country w ill vary over tim e and, w ithin each country, different

industry sectors w ill be affected to differing degrees. A portfolio of exposures can have concentrations in

particular countries or industry sectors. Therefore, it is im portant to be able to capture the effect of

concentration risk in a credit risk m odel.

The C R ED ITRISK + M odel described in this docum ent allow s concentration risk to be captured using sector

analysis. A n exposure can be broken dow n into an obligor-specific elem ent, w hich is independent of all other

exposures, and non-specific or system atic elem ents that are sensitive to particular driving factors, such as

countries or industry sectors.




odeThe C REDIT RISK+ M odel 3



CREDITRISK+ Model

R ecoveryRa tes


3.1 Stages in the Modelling Process

The m odelling of credit risk is a tw o stage process, as show n in the follow ing diagram :

B y calculating the distribution of default events, the risk m anager is able to assess w hether the overall credit

quality of the portfolio is either im proving or deteriorating. The distribution of losses allow s the risk m anager to

assess the financial im pact of the potential losses as w ell as m easuring the am ount of diversification and

concentration w ithin the portfolio.

3.2 Frequency of Default Events

3.2.1 The Default ProcessThe C R ED ITRISK + M odel m akes no assum ption about the causes of default - credit defaults occur as a

sequence of events in such a w ay that it is neither possible to forecast the exact tim e of occurrence of any

one default nor the exact total num ber of defaults. There is exposure to default losses from a large num ber of

obligors and the probability of default by any particular obligor is sm all. This situation is w ell represented by the

Poisson distribution.

What is theFREQUENCYof defaults?

What is theSEVERITY

of the losses ?

Stage 1

Stage 2 Distribution ofdefault losses


20/72

W e consider first the distribution of the num ber of default events in a tim e period, such as one year, w ithin a

portfolio of obligors having a range of different annual probabilities of default. The annual probability of default

of each obligor can be conveniently determ ined by its credit rating and a m apping betw een default rates and

credit ratings. If w e do not incorporate the volatility of the default rate, the distribution of the num ber of default

events w ill be closely approxim ated by the Poisson distribution. This is regardless of the individual default ratefor a particular obligor.

H ow ever, default rates are not constant over tim e and, as w e have seen in the previous section, exhibit a high

degree of variation. H ence, default rate variability needs to be incorporated into the m odel.

3.2.2 Distribution of the Num ber of Default EventsThe C R ED ITRISK + M odel m odels the underlying default rates by specifying a default rate and a default rate

volatility. This aim s to take account of the variation in default rates in a pragm atic m anner, w ithout introducing

significant m odel error.

The effect of using default rate volatilities can be clearly seen in the follow ing figure, w hich show s thedistribution of the num ber of default events generated by the C R ED ITRISK + M odel w hen default rate volatility

is varied. A lthough the expected num ber of default events is the sam e, the distribution becom es significantly

skew ed to the right w hen default rate volatility is increased. This represents a significantly increased risk of an

extrem e num ber of default events.

3.3 Moving from Default Events to Default Losses

3.3.1 Distribution of Default Losses

G iven the num ber of default events, w e now consider the distribution of losses in the portfolio. The distributionof losses differs from the distribution of default events because the am ount lost in a given default depends on

the exposure to the individual obligors. U nlike the variation of default probability betw een obligors, w hich does

not influence the distribution of the total num ber of defaults, the variation in exposure m agnitude results in a

loss distribution that is not Poisson in general. M oreover, inform ation about the distribution of different

exposures is essential to the overall distribution. H ow ever, it is possible to describe the overall distribution of

losses because its probability generating function has a sim ple closed form am enable to com putation.


Including default rate volatility

Excluding default rate volatility

Figure 6:

CREDITRIS K+ Model -

Distribution of default

events

P r o

b a b

i l i t

y

N um ber of defaults



In the event of a default of an obligor, a firm generally incurs a loss equal to the am ount ow ed by the obligor

less a recovery am ount, w hich the firm obtains as a result of foreclosure, liquidation or restructuring of the

defaulted obligor. A recovery rate is used to quantify the am ount received from this process. R ecovery rates

should take account of the seniority of the obligation and any collateral or security held.

In order to reduce the am ount of data to be processed, tw o steps are first follow ed:

The exposures are adjusted by anticipated recovery rates in order to calculate the loss in a given default.

The exposures, net of the above recovery adjustm ent, are divided into bands of exposure w ith the level ofexposure in each band being approxim ated by a com m on average.

The C R ED ITRISK + M odel calculates the probability that a loss of a certain m ultiple of the chosen unit of

exposure w ill occur. This allow s a full loss distribution to be generated, as show n in the figure below .

3.3.2 Imp act of Incorporating De fault Rate VolatilitiesFigure 7 com pares the default loss distributions calculated w ithout default rate volatility and w ith default rate

volatility. The key features and differences are:

Same expected loss : B oth default loss distributions have the sam e level of expected losses.

Fatter tail : The key change is the level of losses at the higher percentiles; for exam ple, the 9 9th percentileis significantly higher w hen the im pact of the variability of default rates is m odelled. There is now

considerably m ore chance of experiencing extrem e losses.

S ince the tail of the distribution has becom e fatter, w hile the expected loss has rem ained unchanged, it can be

concluded that the variance of the default loss distribution has increased. This increase in the variance is due

to the pairwise default correlations between obligors. These pairwise default correlations are incorporated

into the C REDITRISK+ Model through the default rate volatilities and sector analysis. It should be noted that

w hen the default rate volatilities are set to zero, the default events are independent and hence the pairw ise

default correlations are also zero.

In A ppendix A , w e give an explicit form ula for the pairw ise default correlations im plied by the C R ED ITRISK +

M odel w hen default rate volatilities are incorporated into the m odel.

3CREDITRISK+ Model

Excluding default rate volatility

Including default rate volatility

Figure 7:

CREDITRIS K+ Model -

Distribution of defaultlosses

The C R ED ITRISK + M odel

allow s explicit calculation of

the loss distribution of a

portfolio of cred it exposures.

S ize o f loss

P r o

b a

b i l i t

y


22/72

3.4 Concentration Risk and S ector Analysis

The C R ED ITRISK + M odel m easures the benefit of portfolio diversification and the im pact of concentrations

through the use of sector analysis.

3.4.1 Concentration RiskD iversification arises naturally because the num ber of individual risks in a portfolio of exposures is usually large.

H ow ever, even in a portfolio containing a large num ber of exposures, there m ay be an opposing effect ow ing

to concentration risk. C oncentration risk results from having in the portfolio a num ber of obligors w hose

fortunes are affected by a com m on factor. In order to quantify concentration risk, the concepts of system atic

factors and specific factors are necessary.

Systema tic factorsSystem atic factors are background factors that affect the fortunes of a proportion of the obligors in the

portfolio, for exam ple all those obligors having their dom icile in a particular country. The fortunes of any one

obligor can be affected by a num ber of system atic factors.

Specific factorsIn general, the fortunes of an obligor are affected to som e extent by specific factors unique to the obligor.

System atic factors im pact the risk of extrem e losses from a portfolio of credit exposures, w hile diversification

largely elim inates the im pact of the specific factors.

C oncentration risk is dependent on the system atic factors affecting the portfolio. The technique for m easuring

concentration risk is sector analysis.

3.4.2 Se ctor Analysis - Allocating all Ob ligors to a Single Se ctorThe m ost straightforward application of the C R ED ITRISK + M odel is to allocate all obligors to a single sector.

This approach assum es that a single system atic factor affects the individual default rate volatility of each

obligor. Furtherm ore, this use of the m odel captures all of the concentration risk w ithin the portfolio and

excludes the diversification benefit of the fortunes of individual obligors being subject to a num ber of

independent system atic factors.

Therefore, the m ost straightforw ard application of the C R ED ITRISK + M odel, in w hich all obligors are allocated

to a single sector, generates a prudent estim ate of extrem e losses.

3.4.3 Sector Analysis - Allocating Obligors to one of Se veral Se ctors

In order to recognise som e of the diversification benefit of obligors w hose fortunes are affected by a num berof independent system atic factors, it can be assum ed that each obligor is subject to only one system atic factor,

w hich is responsible for all of the uncertainty of the obligors default rate. For exam ple, obligors could be

allocated to sectors according to their country of dom icile. O nce allocated to a sector, the obligors default rate

and default rate volatility are set individually. In this case, a sector can be thought of as a collection of obligors

having the com m on property that they are influenced by the sam e single system atic factor.

3.4.4 Sector Analysis - Apportioning Obligors across Several SectorsA m ore generalised approach is to assum e that the fortunes of an obligor are affected by a num ber of

system atic factors. The C R ED ITRISK + M odel handles this situation by apportioning an obligor across several

sectors rather than allocating an obligor to a single sector.


Concentration risk isdependent on the systematicfactors affecting the portfolio.The technique for measuringconcentration risk is sectoranalysis.


23/72

S o far it has been assum ed that all risk in the portfolio is system atic and allocable to one of the system atic

factors. In addition to the effects of system atic factors, it is likely that the fortunes of an obligor are affected

by factors specific to the obligor. Potentially specific risk requires an additional sector to m odel each obligor,

since the factor driving specific risk for a given obligor affects that obligor only. H ow ever, the C R ED ITRISK +

M odel handles specific risk w ithout recourse to a large num ber of sectors by apportioning all obligorsspecificrisk to a single Specific R isk Sector.

3.4.5 The Impa ct of Se ctors on the Loss DistributionA s stated above, the C R ED ITRISK + M odel allow s the portfolio of exposures to be allocated to sectors to reflect

the degree of diversification and concentration present. The m ost diversified portfolio is obtained w hen

each exposure is in its ow n sector and the m ost concentrated is obtained w hen the portfolio consists of a

single sector.

The figure below show s the im pact of sectors on the loss distribution. A s the num ber of sectors is increased,

the im pact of concentration risk is reduced. The graph illustrates this by plotting the ratio of the 99th percentile

of the credit default loss distribution for a given num ber of sectors to the 99th percentile of the credit default

loss distribution w hen the portfolio is considered to be a single sector.

3.5 Mu lti-Year Losses for a Hold-to-Ma turity Tim e Horizon

A s discussed in S ection 2 .5, the C R ED ITRISK + M odel allow s risk of the portfolio to be view ed on a hold-to-

m aturity tim e horizon in order to capture any default losses that could occur until m aturity of the credit

exposure.

A nalysing credit exposures on a m ulti-year basis enables the risk m anager to com pare exposures of differentsize, credit quality, and m aturity. The loss distribution produced provides, for any chosen level of confidence, an

indication of the possible cum ulative losses that could be suffered until all the exposures have m atured.

The benefits of looking at portfolio credit risk from this view point include the follow ing:

The full term structure of default probabilities is taken into account.

The full uncertainty of default losses over the life of the portfolio is also captured.

For exam ple, because the one-year average default rates for investm ent grade obligors are relatively sm all but

the corresponding exposures m ay be large, a one-year tim e horizon m ay not be the best m easure for active

portfolio m anagem ent. H ow ever, a m ulti-year view w ill reflect the fact that defaults follow a decline in credit

quality over m any years.

CR E D I TRIS K+ 21

3CREDITRISK+ Model

The C REDITRISK+ Modelallows the portfolio of exposures to be decomposedinto sectors to reflect thedegree of diversification andconcentration present.

Figure 8 :

Impact of se ctors on the

loss distribution

The C REDITRISK+ Modelallows the risk of the portfolioto be viewed on a hold-to-maturity time horizon in orderto capture any default lossesthat could occur until maturityof the credit exposure.

N um ber of sectors

9 9 t h

p e r c e n

t i l

e

r a

t i o

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

0 1 2 3 4 5 6 7 8 9


24/72

3.5.1 Using the CREDITRIS K+ Model to Calculate Multi-Year Loss DistributionsThe C R ED ITRISK + M odel can be used to calculate m ulti-year loss distributions by decom posing the exposure

profile over tim e into separate elem ents of discrete tim e, w ith the present value of the rem aining exposure in

each tim e period being assigned a m arginal default probability relevant to the m aturity and credit quality. These

decom posed exposure elem ents can then be used by the C R ED ITRISK + M odel to generate a loss distributionon a hold-to-m aturity basis.

3 .6 Summary o f the CREDITRIS K+ Model

The key features of the C R ED ITRISK + M odel are:

The C REDIT RISK+ Model captures the essential characteristics of credit default events. C redit defaultevents are rare and occur in a random m anner w ith observed default rates varying significantly from year

to year. The approach adopted reflects these characteristics by m aking no assum ptions about the tim ing

or causes of default events and by incorporating the default rate volatility. B y taking a portfolio approach,

the benefits of diversification that arise from a large num ber of individual risks are fully captured.C oncentration risk, resulting from groups of obligors that are affected by com m on factors, is m easured

using sector analysis.

The C REDIT RISK+ Model is scaleable and computationally efficient. The C R ED ITRISK + M odel is highlyscaleable and hence is capable of handling portfolios containing large num bers of exposures. The low data

requirem ents and m inim um of assum ptions m ake the C R ED ITRISK + M odel easy to im plem ent for a w ide

range of credit risk portfolios, regardless of the specific nature of the obligors. Furtherm ore, the efficiency

of the m odel allow s com prehensive sensitivity analysis to be perform ed on a continuing basis, w hich is a

key requirem ent for the ability to quantify the effects of param eter uncertainty.




4.1 Introduction to Economic Capital

4.1.1 The Role of Economic CapitalThe analysis of uncertainty is the essence of risk m anagem ent. Therefore, m easuring the uncertainty or

variability of loss and the related likelihood of the possible levels of unexpected losses in a portfolio of

exposures is fundam ental to the effective m anagem ent of credit risk. Sufficient earnings should be generated

through adequate pricing and provisioning to absorb any expected loss. The expected loss is one of the costs

of transacting business w hich gives rise to credit risk. H ow ever, economic capital is required as a cushion for

a firms risk of unexpected credit default losses , because the actual level of credit losses suffered in any one

period could be significantly higher than the expected level.

4.2 Economic Capital for Credit Risk

4.2.1 Credit Default Loss DistributionK now ledge of the credit default loss distribution arising from a portfolio of exposures provides a firm w ith

m anagem ent inform ation on the am ount of capital that the firm is putting at risk by holding the credit portfolio.

G iven that econom ic capital is necessary as a cushion for a firm s risk of unexpected credit default losses, a

percentile level provides a m eans of determ ining the level of econom ic capital for a required level of

confidence. In order to capture a significant proportion of the tail of the credit default loss distribution, the 99th

percentile unexpected loss level over a one-year tim e horizon is a suitable definition for credit risk econom ic

capital. This can be seen in the follow ing figure.

apitEconomic Capital for Credit Risk 4

Economic Capital


Scenario Analysis


26/72

4.2.2 Benefits and Features of Economic CapitalEconom ic capital as a m easure of risk being taken by a firm has several features and benefits including the

follow ing:

It is a m ore appropriate m easure of the econom ic risk than that specified under the current regulatory regim e.

It m easures econom ic risk on a portfolio basis and hence takes account of the benefits of diversification.

It is a m easure that objectively differentiates betw een portfolios by taking account of credit quality and sizeof exposure.

It is a dynam ic m easure, w hich reflects the changing risk of a portfolio and hence can be used as a toolfor portfolio optim isation.

4.3 Scenario Analysis4.3.1 The Role of Scenario AnalysisThe purpose of scenario analysis is to identify the financial im pact of low probability but nevertheless plausible

events that m ay not be captured by a statistically based m odel. Therefore, the use of a credit risk m odel should

be supplem ented by a program m e of stress testing of the assum ptions used.

There are two types of stress tests that should be perform ed: (i) scenario analysis w ithin the C R ED ITRISK +

M odel, and (ii) scenario analysis outside the C R ED ITRISK + M odel.

4.3.2 Scenario Analysis within the CREDITRIS K+ Model

The inputs into the C R ED ITRISK+

M odel can be stressed individually or in com bination. For exam ple, it ispossible to sim ulate dow nturns in the econom y by increasing default rates and default rate volatilities - sectors

of the portfolio can be stressed to varying degrees reflecting the fact that each sector could be affected to a

different extent. S im ilarly, the financial im pact of rating dow ngrades can be assessed by increasing the default

rate assigned to an obligor. For a derivatives portfolio, this can be extended to include the effects of m ovem ents

in m arket rates on credit exposures.

G iven the efficient m anner in w hich the default loss distribution can be calculated, it is possible to calculate

the im pact of changing param eter inputs used by the m odel across a w ide range of values.


Expected Loss

99th PercentileLoss Level

Economic Capital

Figure 9 :

Economic capital for

credit risk

Loss

P r o

b a

b i l i t

y

Economic Capital


Scenario Analysis


27/72

4.3.3 Scenario Analysis outside the CREDITRIS K+ ModelC ertain stress tests can be difficult to perform w ithin the C R ED ITRISK + M odel: for exam ple, the im pact of

political or financial uncertainty w ithin a country. For these types of scenarios, analysis that is conducted

w ithout reference to the outputs of the C R ED ITRISK + M odel, such as looking at the exposure at risk for a given

scenario, provides a realistic m eans of quantifying the financial im pact.

A firm should control the risk of catastrophic losses through the use of obligor and concentration lim its,

keeping any one of these lim its w ithin the loss for the percentile level used to determ ine the econom ic capital

given by the C R ED ITRISK + M odel.

The figure below illustrates the w ay in w hich the distribution of losses can be considered to be divided into

three parts.

It is possible to control the risk of losses that fall w ithin each of the three parts of the loss distribution in the

follow ing w ays:

Part of loss distribution Control mechanism

U p to Expected Loss A dequate pricing and provisioning

Expected Loss - 99th Percentile Loss Econom ic capital and/or provisioning

G reater than 99 th Percentile Loss Q uantified using scenario analysis andcontrolled w ith concentration lim its

Scenario analysis deals w ith quantifying and controlling the risk of extrem e losses. Losses up to a certain

confidence level, such as the 99th percentile level, are controlled by the use of adequate pricing, provisioning

and econom ic capital. Provisioning for credit risk is discussed in detail in Section 5.2.

CR E D I TRIS K+ 25

4Economic CapitalScenario analysis

provides a means of quantifying catastrophiclosses - potential lossescan be controlled throughconcentration limits.

Figure 10:

Parts of the credit default

loss distribution

Table 5:

Mechanisms for

controlling the risk of

credit default losses

Expected Loss

99th PercentileLoss Level

Economic Capital

Loss

P r o

b a

b i l i t

y

C overed bypricing andprovisioning

C overed by capitaland/or provisions

Q uantified using scenarioanalysis and controlledw ith concentration lim its


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R E D I5.1 Introduction

CR ED ITRISK + includes several applications of the credit risk m odelling technology in the areas of provisioning,

setting risk-based credit lim its, and portfolio m anagem ent.

5.2 Provisioning for Credit Risk

O ne application of C R ED ITRISK + is in defining an appropriate credit risk provisioning m ethodology that reflects

the credit losses of the portfolio over several years and hence that m ore accurately presents the true earnings

of the business by m atching incom e w ith losses.

5.2.1 The Nee d for Credit ProvisionsG enerally, current accounting and provisioning policies recognise credit incom e and credit losses at different

tim es, even though the tw o events are related. U sually, credit loss provisions are m ade only w hen exposures

have been identified as non-perform ing. These provisions are often supplem ented w ith other specific and

general credit provisions.

In relation to any portfolio of credit exposures, there is a statistical likelihood that credit default losses w ill occur,

even though the obligors are currently perform ing and it is not possible to identify specifically w hich obligors

w ill default. The level of expected loss reflects the continuing credit risk associated w ith the firm s existing

perform ing portfolio and is one of the costs of doing credit-related business. This level of expected loss should

be taken account of when executing any business that has a credit risk im pact.

W hen default losses are m odelled, it can be observed that the m ost frequent loss am ount w ill be m uch low er

than the average, because, occasionally, extrem ely large losses are suffered, w hich have the effect of increasing

the average loss. Therefore, a credit provision is required as a m eans of protecting against distributing excess

profits earned during the below average loss years.


Applications of C REDIT RISK+ 5

The C REDITRISK+ creditrisk provisioning methodologymore accurately reflects thetrue earnings of the businessby matching income withlosses.

Applications

Provisioning

Limits




5Applications

The Annual Credit Provisionreflects the continuing creditrisk associated with theportfolio and is one of the costsof doing business that createscredit risk.

Figure 11 :

Credit risk p rovisioning

The Increm ental C redit

R eserve protects against

unexpected credit losses

and is used to absorb losses

that are higher than the

expected level.

5.2.2 Annual Credit Provision (ACP)The starting point for provisioning is to separate the existing portfolio into a non-perform ing and a perform ing

portfolio. The non-perform ing portfolio should be fully provisioned to the expected recovery level available

through foreclosure, adm inistration or liquidation. O nce fully provisioned, the non-perform ing portfolio should

then be separated out and passed to a specialist team for ongoing m anagem ent.

A s for the perform ing portfolio, since no default has occurred, one needs a forw ard-looking provisioning

m ethodology. U nder C R ED ITRISK + , the A nnual C redit Provision (AC P) represents the future expected credit

loss on the perform ing portfolio, w hich is calculated as follow s:

ACP = Exposure x Default Rate x (100% - Recover Rate)

The AC P should be calculated frequently in order to reflect the changing credit quality of the portfolio. The A C P

is the first elem ent of the credit provisioning m ethodology.

5.2.3 Increme ntal Credit Reserve (ICR)The AC P represents only the expected or average level of credit losses. A s experience show s, actual losses

that occur in any one year m ay be higher or low er than this am ount, depending on the econom ic environm ent,

interest rates, etc. In fact, a better w ay of view ing the annual credit loss of the portfolio is as a distribution of

possible losses (outcom es), w hose average equals the AC P but has a sm all probability of m uch larger losses.

In order to absorb these variations in credit losses from year to year, a second elem ent of the provisioning

m ethodology, the Increm ental C redit R eserve (IC R ), can be established.

The C R ED ITRISK + M odel provides inform ation on the distribution of possible losses in the perform ing credit

portfolio. The IC R provides protection against unexpected credit losses (i.e. in excess of the A C P) and is

subject to a cap derived from the C R ED ITRISK + M odel (the IC R C ap). The IC R C ap represents an extrem e

case of possible credit losses (e.g. the 99th percentile loss level) on the perform ing portfolio.

ACP=Average level of credit losses

ICR Cap =99th Percentile Loss LevelTypical

ICR

Loss

P r o

b a

b i l i t

y


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5.2.4 Provisioning for Different Business LinesThe credit risk provisioning m ethodology described above relates to credit risk arising from a loans business

w here the incom e is accounted for on an accruals basis rather than by m arking-to-m arket.

A credit risk provision can also be established for other credit business lines, such as traded bond portfolios

and derivatives portfolios. In each case, the C R ED ITRISK + M odel provides the inform ation required in order to

establish the provision that ensures that the accounting principle of m atching incom e w ith losses is m aintained.

For exam ple, for a portfolio of bonds, part of the expected loss is incorporated w ithin the m arket price and

hence only the increm ental credit reserve is required. This is described in the follow ing table.

Portfolio type Accounting treatment Provision

Loan A ccrual AC P (1 year) charge to P& L each year

(C ounterparty risk) (credit neutral) IC R (1 year)

Derivatives M ark-to-m arket AC P (full m aturity) held as m ark-to-m arket adjustm ent

(C ounterparty risk) (credit neutral) IC R (1 year)

Bond M ark-to-m arket IC R (1 year) to support business and protect against

(Issuer risk) (credit inclusive) distribution of profits

5.2.5 Manag ing the Credit Risk ProvisionA s credit defaults occur, loans or exposures are m oved from the perform ing to the non-perform ing portfolio

and hence provisioned to the expected recovery level. This increase in provision is then charged first against

the AC P and then, to the extent necessary, against the IC R . To the extent that actual credit losses are less than

the AC P w ithin any given year, the balance is credited to the IC R up to the IC R C ap, beyond w hich the balance

is taken into P & L. This ensures that the IC R is replenished during low loss years follow ing a large unexpectedloss, but that the IC R never exceeds the IC R C ap.

A w orked exam ple can be seen in the table below :

Year 1 2 3 4 5

AssumptionsA ctual loan losses 500 600 300 300 650

AC P 500 525 550 610 625

IC R - Initial level 1,900 - - - -

IC R C ap 2,000 2,100 2,200 2,250 2,300

Income StatementO perating profit 2,100 2,100 2,205 2,315 2,430

Less: AC P (500) (525) (550) (610) (625)

A dd: excess unutilised provision over IC R C ap 0 0 0 135 0

Pre-tax profit 1,600 1,575 1,655 1,840 1,805

IC R (pre cap) 1,900 1,825 2,075 2,385 2,225

IC R C ap (as above) 2,000 2,100 2,200 2,250 2,300

Excess unutilised provision over IC R C ap 0 0 0 135 0

ICR (with cap applied) 1,900 1,825 2,075 2,250 2,225


Table 6:

Provisioning for different

business lines

Table 7:

Example of credit risk

provisioning



5.3 Risk-Based Credit Limits

A system of individual credit lim its is a w ell-established m eans of m anaging credit risk. M onitoring exposures

against lim its provides a trigger m echanism for identifying potentially unw anted exposures that require active

m anagem ent.

5.3.1 Standard Credit LimitsThe system of credit lim its m ay be view ed from a different perspective, if applying the m ethodologies described

w ithin this docum ent.

In particular, in order to equalise a firm s risk appetite betw een obligors as a m eans of diversifying its portfolio,

a credit lim it system could aim to have a large num ber of exposures w ith equal expected losses. The expected

loss for each obligor can be calculated as the default rate m ultiplied by the exposure am ount less the expected

recovery. This m eans that individual credit lim its should be set at levels that are inversely proportional to the

default rate corresponding to the obligor rating.

A s m ight be expected, this m ethodology gives larger lim its for better ratings and shorter m aturities, but has the

benefit of allow ing a firm to relate the size and tenor of lim its for different rating categories to each other.

This approach can be extended to base lim its on equalising the portfolio risk contribution for each obligor.

A discussion on risk contributions and their use in portfolio m anagem ent is provided later in this section.

5.3.2 Concentration LimitsA ny excess country or industry sector concentration can have a negative effect on portfolio diversification and

increase the riskiness of the portfolio. A s a result, a com prehensive set of country and industry sector lim its is

required to address concentration issues in the portfolio. C oncentration lim its have the effect of lim iting the loss

from identified scenarios and is a pow erful technique for m anaging tailrisk and controlling catastrophic losses.

5.4 Portfolio M anagement

The C R ED ITRISK + M odel m akes the process of controlling and m anaging credit risk m ore objective by

incorporating into a single m easure all of the factors that determ ine the am ount of risk.

5.4.1 IntroductionC urrently, the prim ary technique for controlling credit risk is through the use of lim it system s, including:

Individual obligor lim its to control the size of exposure

Tenor lim its to control the m axim um m aturity of transactions w ith obligors

R ating exposure lim its to control the am ount of exposure to obligors of certain credit ratings and

C oncentration lim its to control concentrations w ithin countries and industry sectors.

5Applications

A system of standardcredit limits can be supple-mented with portfolio levelrisk information to managecredit risk.

Applications

Provisioning

Limits



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5.4.2 Identifying Risky ExposuresThe risk of a particular exposure is determ ined by four factors: (i) the size of exposure, (ii) the m aturity of the

exposure, (iii) the probability of default, and (iv) the system atic or concentration risk of the obligor. C redit lim its

aim to control risk arising from each of these factors individually. H ow ever, for m anaging risks on a portfolio

basis, w ith the aim of creating a diversified portfolio, a different m easurem ent, w hich incorporates size, m aturity,credit quality and system atic risk into a single m easure, is required.

5.4.3 Me asuring DiversificationThe loss distribution and the level of econom ic capital required to support a portfolio are m easures of portfolio

diversification that take account of the size, m aturity, credit quality and system atic risk of each exposure.

If the portfolio w ere less diversified, the spread of the distribution curve w ould be w ider and a higher level of

econom ic capital w ould be required. C onversely, if the portfolio w ere m ore diversified, a low er level of econom ic

capital w ould be required. These m easures can be used in m anaging a portfolio of exposures.

5.4.4 Portfolio Managem ent using Risk ContributionsThe risk contribution of an exposure is defined as the increm ental effect on a chosen percentile level of the

loss distribution w hen the exposure is rem oved from the existing portfolio. If the percentile level chosen is the

sam e as that used for calculating econom ic capital, the risk contribution is the increm ental effect on the

am ount of econom ic capital required to support the portfolio.

R isk contributions have several features including the follow ing:

The total of the risk contributions for the individual obligors is approxim ately equal to the risk of the entireportfolio.

R isk contributions allow the effect of a potential change in the portfolio (e.g. the rem oval of an exposure)to be m easured.

In general, a portfolio can be effectively m anaged by focusing on a relatively few obligors that represent asignificant proportion of the risk but constitute a relatively sm all proportion of the absolute portfolio

exposures.

Therefore, risk contributions can be used in portfolio m anagem ent. B y ranking obligors in decreasing order of

risk contribution, the obligors that require the m ost econom ic capital can easily be identified.

This is illustrated in the follow ing exam ple. A portfolio w as created from w hich a sm all num ber of exposures

w ith the highest risk contributions w ere rem oved. The effect on the loss distribution and the levels for the

expected loss and the econom ic capital can be seen in the figure opposite.


For managing creditrisks on a portfolio basis,with the aim of creatinga diversified portfolio, adifferent measure thatincorporates the magnitudeof the exposure, maturity,credit quality and systematicrisk into a single measureis required.

In general, a portfoliocan be effectively managedby focusing on a relativelyfew obligors that representa significant proportion of the risk but constitute arelatively small proportionof the absolute portfolioexposures.

Applications

Provisioning

Limits



33/72

The reduction in the 99th percentile loss level is larger than the reduction in the expected loss level, w hich

leads to an overall reduction in the econom ic capital required to support the portfolio.

5.4.5 Techniques for Distributing Credit RiskO nce obligors representing a significant proportion of the risk have been identified, there are several

techniques for distributing credit risk that can be applied. These include the follow ing:

C ollateralisation: In the context of the C R ED ITRISK + M odel, taking collateral has the effect of reducing theseverity of the loss g iven that the obligor has defaulted.

A sset securitisations: A sset securitisations involve the packaging of assets into a bond, w hich is then soldto investors.

C redit derivatives: C redit derivatives are a m eans of transferring credit risk from one obligor to another,w hile allow ing client relationships to be m aintained.

CR E D I TRIS K+ 31

5Applications

Original 99th PercentileLoss Level

New 99th PercentileLoss Level

New Expected Loss

Original Expected Loss

Figure 12 :

Using risk contributions

Inform ation about risk

contributions can be used

to facilitate risk m anagem ent

and efficient use of econom ic

capital.

New Economic Capital

Original Economic Capital

Loss

P r o

b a

b i l i t

y


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A1 Overview of th is Append ix

This appendix presents an analytic technique for generating the full distribution of losses from a portfolio of

credit exposures. The technique is valid for any portfolio w here the default rate for each obligor is sm all and

generates both one-year and m ulti-year loss distributions.

The appendix applies the concepts discussed in Sections 2 and 3 of this docum ent. The key concepts are:

D efault rates are stochastic.

The level of default rates affects the incidence of default events but there is no causal relationship betw eenthe events.

In order to facilitate the explanation of the C R ED ITRISK + M odel, w e first consider the case in w hich the m ean

default rate for each obligor in the portfolio is fixed. W e then generalise the technique to the case in w hich the

m ean default rate is stochastic. The m odelling stages of the C R ED ITRISK + M odel and the relationships betw een

the different sections of this appendix are show n in the figure opposite.


odeAppendix A - The C REDIT RISK+ M odel A


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A2 Default Events with Fixed Default Rates

In S ections A 2 to A 5 w e develop the theory of the distribution of credit default losses under the assum ption

that the default rate is fixed for each obligor. G iven this assum ption and the fact that there is no causal

relationship between default events, w e interpret default events to be independent. In S ections A 6 onw ards,

the assum ption of fixed default rates is relaxed, w hich introduces dependence betw een default events.

In Section A 13 this dependence is quantified by calculating the correlation betw een default events im pli

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