1

TK 6413 / TK 5413 : ISLAMIC RISK MANAGEMENT

TOPIC 3: THE MEASUREMENT OF CREDIT RISK

2

(I) INTRODUCTION

• Traditionally, majority of financial analyst used their subjective analysis or judgmental approach to assess credit risk. They used information from different obligor characteristics and the result was the subjective opinion of an expert to approve or not a loan.

• Now, credit institutions are not so much based on the relationship with their customers, but are basically using the technology and are developing sophisticated models to upgrade their credit risk management system.

3

a) Credit Ratings

• Rating agencies such as Moody’s and S&P are in the business of providing ratings describing the creditworthiness of corporate bonds.

• Moody’s for instance used the Aaa, Aa, Baa, Ba, B and Caa where bonds with ratings Baa or above are considered to be investment grade.

• S&P on the other hand used the AAA, AA, A, BBB, BB, B and CCC ratings;

4

• A credit rating is designed to provide information about the default probabilities; as such one might expect frequent changes in a company’s credit rating as positive and negative information reaches the market; in fact, ratings change relatively infrequently; when rating agencies assign ratings, one of their objectives is ratings stability.

• Rating agencies also try to “rate through the cycle”;

5

b) Internal Credit Ratings

• Most banks have procedures for rating the creditworthiness of their corporate and retail clients. Using the internal ratings based (IRB) approach in Basel II allows banks to use their internal ratings in determining:• The probability of default(PD);• The loss given default (LGD);• The exposure at default (EAD);• The maturity (M);

• Internal ratings based approaches for PD typically involve profitability ratios, such as return on assets, and balance-sheet ratios such as the current-ratio and the debt-to-equity ratio.

6

c) Altman’s Z-score

• Edward Altman has pioneered the use of accounting ratios to predict defaults.

• The Z-score was calculated as:Z = 1.2X1 + 1.4X2 + 3.3X3 + 0.6X4 + 0.999X5

where, X1 = Working capital / Total assetsX2 = Retained earnings / Total assetsX3 = earnings before interest and taxes / Total assetsX4 = Market value of equity / Book value of total liabilities;X5 = Sales / Total assets

7

• If the Z-score is

• Greater than 3.0, the company is unlikely to default;

• Between 2.7 and 3.0, the company should be ‘on alert’;

• Between 1.8 and 2.7, there is a good chance for the company to default;

• Less than 1.8, probability of a financial embarrassment is very high;

8

d) Historical Default Probabilities

• From the data given below for investment-grade bonds, the probability of default in a year tends to be an increasing function of time:

Rating Terms (Years) 1 2 3 4 5 7 10 15 20

Aaa 0.00 0.00 0.00 0.04 0.12 0.29 0.62 1.21 1.55 Aa 0.02 0.03 0.06 0.15 0.24 0.43 0.68 1.51 2.70 A 0.02 0.09 0.23 0.38 0.54 0.91 1.59 2.94 5.24

Baa 0.20 0.57 1.03 1.62 2.16 3.24 5.10 9.12 12.59 Ba 1.26 3.48 6.00 8.59 11.17 15.44 21.01 30.88 38.56 B 6.21 13.76 20.65 26.66 31.99 40.79 50.02 59.21 60.73

Caa 23.65 37.20 48.02 55.56 60.83 69.36 77.91 80.23 80.23

Average Cumulative Default Rates (%), 1970 - 2003

9

(II) CREDIT RISK ASSESSMENT MODELS

• Credit risk can be assessed using;• Qualitative methods,• Quantitative methods; and• Hybrid models;

• Qualitative methods are defined systems based on the judgment of experts who are involved in the credit-approval process;

10

• Quantitative methods on the other hand are based either on statistical models or on causal models; the statistical models can be in the form of:

• Univariate analysis;• Discriminant analysis;• Logistic regression models;

Causal models derived credit ratings using a theoretical business-based model and use only a few input parameters without explicitly taking qualitative data into account;

11

• The hybrid forms of credit-assessment models are combinations of empirical (or expert) models and one of the other two model types-statistical and causal; three types of hybrid model types;

• Horizontal linking of model types;• Overrides;• Knock-out criteria;

12

a) Qualitative Methods

• The expert systems developed combine the analysis of the credit worthiness of the obligor with the practical experience and observations of the experts who apply the analysis;

13

• The credit risk assessment based on qualitative criteria involves the following steps:

• The experts are rating the obligor based on predefined qualitative credit worthiness characteristics together with some additional factors that may influence the client’s behavior.

• The links for the ratings are defined in a qualitative manner that is determined by the experts.

• The qualitative base risk grade drives the level of risks.

• The individual grades are aggregated to generate an overall assessment.

14

Model Layout of the expert systemQ

ualit

ative

Ch

arac

teris

tics

Asse

ssm

ent

RATINGS RISK VALUES GRADES

Very Good

Good

Satisfactory

Sufficient

Insufficient

Low

BelowAverage

Average

Above Average

High

1

2

3

4

5

15

• In the case of the Murabaha contract the ‘experts’ are facing the challenge of how to identify the criteria that will evaluate whether the client will comply with the agreed payment obligations that are set as installments on fixed time buckets.

• In Ijarah contracts, the lessee (financial institution) should define rules and criteria that are related to future behavior of the lessor that may expose the institutions to credit risk; and its dependency on the external factors (market, business and operational)

• In the Mudarabah and Musharakah contracts, the qualitative criteria that financial institutions may define and apply to assess the credit risk exposure are more subjective and more complex. The default on expected cash flows is mostly related to the actual resulting business profit, where the financial institution may be directly or indirectly responsible.

16

b) Quantitative Methods

• These methods are based either on statistical models or on causal models. Each model is built under several assumptions. So, it is only logical to say there is a level of uncertainty that can influence,

i. The model result;ii. For the factors that might not be predicted;iii. The correctness of the estimation of

parameters;iv. How close the model to reality.

17

1) Statistical Models:

• In the construction of the quantitative models, risk analyst should follow process with certain steps namely;

i. Identifying the availability and accessibility of historical data, data clearance, unification and selection to be used for credit financial risk analysis.

ii. Simulating data used for the credit financial risk analysis.

iii. Determination of model methodology.iv. Assessment of the parameters of the model.v. Qualitative and quantitative validation.vi. Conclusions.

18

• Univariate Analysis:

• Univariate analysis looks at the central tendency of the values as well as at the dispersion. The analysis includes tests that compare samples from different groups; it evaluates one variable of interest and then compare it with another group it terms of its means, variance and the like.

• It uses t-test if data is approximately normal; the Mann-Whitney U-test for non-parametric tests and other tests to compare two samples such is the Chi-Square test or the Kolmogorov-Smirnov test;

19

• Discriminant Analysis:

• In its basic form, discriminant analysis seeks for a linear function of variables that best distinguishes between two or more predefined groups of obligors. If the two groups are predefined – good and bad debtors – then we seek the function of financial ratios that best distinguishes between solvent and distressed obligors.

20

• Logistic Regression Model:

• In these models, the Binomial Logistic Regression or Multinominal Logistic Regressions are applied to credit-assessment procedures; the objective is to use certain credit-worthiness Characteristics (independent variables) to determine whether borrowers are classified as solvent or distressed (dependent binary variable). Accordingly, the probability P that a borrower is classified solvent or distressed is measured according to the following formula:

where n is the number of criteria included in the scoring function and ai, I = 1, 2, ….. n are the coefficient of the indicators.

1 1 + exp – [(a0 + a1x1 + a2x2 + …… + anxn)]

P =

21

2) Causal Models:

• Causal models derive credit ratings using a theoretical business-based model and use only a few (exclusively quantitative) input parameters without explicitly taking qualitative data into account. The most prevailing class of causal models is option-pricing models as proposed by Merton and Black & Scholes.

• The equity value of the firm E, can be treated as a call option written on the value of assets, A, where the strike price, B, is given by all the short-term liabilities, Bs, plus half of the long-term ones, BL. Therefore, the distance to default DD can be determined as a multiple of asset volatility as =

A

Ls BBADD

]2

1[

22

3) Hybrid Models:

• The hybrid forms of credit-assessment models are combinations of empirical (or expert) models and one of the other two model types-statistical and causal. Three different types of hybrid forms one usually met:

i. Horizontal linking of model types;ii. Overrides;iii. Knock-out criteria;

23

(i) Horizontal Linking of model types

Quantitative Data

Qualitative Data

Credit Rating

24

(ii) Overrides

Quantitative andQualitative Data

Proposed Rating

OVERRIDE

Final Credit Rating

25

(iii) Knock-out criteria

Knock-outCriteria

Quantitative And

Qualitative Data

Credit Rating

26

(III) CREDIT RISK EVALUATION

• The main parameters that should be considered in the valuation of credit risks are the expected and unexpected losses. The calculation of the expected and unexpected losses require the calculation of the probability of default (PD), the loss given default (LGD), and the exposure at default (EAD).

27

a) Defaults:

• In general, default occurs when there is a loss that is initiated from the counterparty’s inability to comply with its obligations. Specifically, for the typical Islamic financial contracts the probability of defaults occurs in the following circumstances:

i. For Murabaha contracts, it is likelihood that the buyer of the goods (counterparty) will be unable to repay the installments that he/she is obligated to.

ii. For the Ijarah contracts, it is the probability that the lessee (counterparty) will be unable to repay at installment points or at the end of the contracts. Moreover, it could be the probability of an early leave, from the lessee side, before the contracts maturity date.

28

iii. For the Salam contracts, it is the probability from the seller’s (counterparty) side to default on delivering the commodity at the delivery date. On the other hand, it is also the default probability from the buyer to buy the commodity at the agreed price.

iv. Similarly, for the istisna contracts, from the manufacturers and/or constructors side, it is the likelihood of default on delivering the commodity or constructed asset at the delivery date. Moreover, for the financial institution, it is the probability of not receiving the agreed selling price from the buyer or user.

29

v. In the Permanent Musharakah contracts of partnership where the business partners has the role of the counterparty, it is the likelihood for the business to default in providing the expected cash. However, in the Diminishing Musharakah contracts, it is the probability that the partners default on buying the equities at the agreed prefixed price using the installment basis.

vi. In the Mudarabah contracts of partnership agreement and during the investment period, it is the probability that the business venture defaults in carrying on the business development and/or the project’s implementation. Moreover, during the profit and loss period it is the likelihood that the business venture defaults in providing the expected profit.

30

• The estimation of the PD for the Islamic financial products is one of the most challenging issues for financial institutions. The main steps that are commonly used for this purpose are:

i. Analyzing the credit risk aspects of the counterparty;

ii. Mapping the counterparty to an internal risk grade which has an associated PD; and

iii. Calculate the PD.

31

(b) Estimating the Probability of Default

PDt = DCt x 100TC

where: PDt is the annual percentage probability of default, DCt is the number of defaulted contracts during the period t under examination, and TC is the total number of contracts of the examined class.

• For the different types of financial Islamic contracts, and their underlying assets, the definition of their defaults on, for example, payment, delivery, expected profit, is based on criteria that are delivered either from the financial institutions or from the regulators.

32

• The ‘materiality’ is another point that must be clarified in order to provide a concrete definition of the probability of default. The ‘materiality’ notion coincides with the meaning of ‘substantiality. The most common implied definition that banks consider as ‘material’ is the fact that the debtor is unable or unwilling to pay the installments to buy or to deliver the assets as agreed for more than μ consecutive months (usually μ is set as 3 or 6 months). This is the level after which the ‘road’ to default is irreversible for a certain confidence level.

33

• Based on the schedule payments, repayments, or deliveries, the estimations of PD for μ number of past due months can be defined by replacing the DCt above with above with . Thus the probability of default is

found as in the following equation:

Where, n = number of loansdi = 0, if loan is activedi = 1, if loan is defaulted

TPDAI = total past due amount of installmentsCAI = contractual amount of installmentsM = number of months for the period tAIF = frequency of installments within the period t

ii

idi

n

ii

t AIF

Mx

CAI

TPDAIx

TC

dPD ,11001

n

iid

1

34

Period for measuring

defaults

Sum of the examined loan

class

No. of defaulted loans

Probability of default

31 Dec -2005 – 1 Jan 2007

8,600 60 0.69%

31 Dec 2006 – 1 Jan 2008

9,300 80 0.86%

31 Dec 2007 – 1 Jan 2008

10,500 90 0.91%

Case study

Different cases for estimating the probability of default based on quantitative criteria.

35

c) Exposure at Default ( EAD )

• EAD is the estimation of the institution’s exposure in the event of, and at the time of, counterparty, defaults. Based on Basel Credit Risk Model, the potential exposure, in currency, is measured for the period of 1 year or until the maturity date, whichever comes first. Under Basel II, a bank must provide an estimate of the exposure at Default (EAD), in a banks internal system. All these loss estimates should seek to fully capture the risks of an underlying exposure

d) Loss Given Default ( LGD )

• LGD is a weighting of the loss when a default occurs. The LGD is derived within a credit risk model by taking into account any collateral or security that covers the corresponding loss due to the default.

36

• The LGD is usually defined as the ratio of losses to exposure at default ( EAD ). There are broadly three ways of measuring LGD:

i. Market LGD, which is based on the observed prices from the

market soon after the time where the actual default event occurs. This is the market price of the goods in Murabaha Contract, the market rental is the Ijarah contract, the commodity or asset price is the Salam and Istisna contracts

ii. Workout LGD, which is based on the estimated cash flows, result from the contracts that default considering the timing of event. This is the expected cash flow from the payment in the Murabaha contracts, from the renter in the Ijarah contract, from the sales of the commodities or assets in the Salam and Istisna contracts and from the profits in the Musharakah and Mudarabah contracts.

iii. Implied LGD, which is an entirely different approach to obtain on estimate of LGD. It considers the “ Credit Spreads “ of the non-defaulted, but however risky, cases in Islamic Contracts that may result in defaulted events.

37

An important parameter to estimated in the identification and assessment analysis of the LGD is the estimation of the recovery rate ( RR ). When EAD is expressed in absolute term, i.e. in its nominal value at the time of the default, the recovery rate is expressed in percentage terms as shown below, Where,

= variable attributed to the recovered part of the asset paid in cash by the obligor at the time i,

= represents the recovered part of the potential collateral related to the asset at time i,

= represents all administrative costs realized,= the variation of the market value in percentage.

The LGD is related to the recovery rate where,LGD = 1-RR

10011

x

EAD

RR iiiT

i

i

i

i

38

• The estimation of the LGD is difficult due to:

i. The availability, of quality data for defining the default, assessing the recovery from the collaterals, and estimating the cost resulting from the defaults;

ii. The different priorities of payments in relation to other payments the obligor is past due;

iii. The legal regime declares itself bankrupt may differ from country to country;

iv. The legal regime for collections before or after the obligor declares itself bankrupt may differ from time to time throughout the collection period;

v. The uncertainty of the duration of cash payments made by the obligor;

vi. The continuous changes in the market values of the assets.

39

e) Credit value-at-risk (VaR) on expected and unexpected losses:

• The estimation of the credit VaR is based on the distribution of the actual losses observed in a credit portfolio considering also certain confidence level and pre-specified loss holding period. Under the credit risk portfolios, the assumption that usually underlies the distribution of the portfolios is that of lognormal.

• There are two types of losses, notably expected and unexpected, that are considered in the estimation of credit VaR.

40

UCL ECL

ConfidenceLevel

Losses

Probability

ECL = Expected Credit LossUCL = Unexpected Credit Loss

41

•The Expected Credit Loss (ECL) is calculated on the PD, LGD and EAD,

ECL = PD X LGD X EAD

however, if EAD is assumed to be one unit currency then,

ECL = PD X LGD

•On the other hand, the Unexpected Credit Loss (UCL) is given by,

UCL = σ credit x m

Where m is the appropriate quantile of the credit loss distribution, in order for the model to reach the credit VaR confidence level where,

m = VaRcredit – EL = UL

σ credit σ credit

(…)

42

Where VaR ( ) is the measure of Credit VaR and is the volatility

of the individual asset expressed in terms of the volatility of PD and LGD where,

Using the figure shown above involving ECL and UCL, VaR ( ) = ECL – UCL

As such,

UCL = ECL – VaR ( )

• The credit VaR refers to the unitary one that is the VaR used to quatify the risk of a unique credit element; in reality, however, these are multiple assets in a credit portfolio; the analysis of correlations between the portfolio’s assets is particularly useful for the estimation of the LGD of a credit portfolio.

creditσ credit

credit

credit

222 .. PDLGDcredit LGDPD

43

Incorporating the elements of ‘assets correlation’ and ‘default correlation’, the standard deviation of the portfolio credit becomes,

Where ij is the correlation coefficient for assets i and j

And

Therefore, the corresponding UCL of the credit portfolio is,

σ credit

jiij

n

j

n

icreditp ULUL

11

,

jjii

jijiij

PDPDPDPD

PDPDDDP

1.1.

..

mUCL creditpp .,

i

a

i

UCLUCL

1

44

f) Economic capital and credit VaR

• The credit VaR estimation should be viewed as the economic capital to be held as a buffer against the UCL. Thus, in credit risk, economic capital is required as a cushion for an institution’s 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.

• In economic capital estimation, there is no common agreement on the definitions referring to key parameters such as confidence level and time horizon that should be well defined and set.

45

g) Loss data and Credit VaR estimations

• The suitability of the methodologies used for producing efficient estimations of the Credit VaR is related to the loss data distribution and thus should be assess within the context of the corresponding availability of historical loss data. Therefore, the quality of the estimation will depends on,

i. When there is fully available historical loss data;ii. When there is partly available historical loss

data;iii. Lack of historical data