Module 23: Assessment of credit risk

Question 1

Credit risk may be decomposed into: (2)

Answer 1

• default risk - including, for example, the risk of loss due to a payment due being missed
• credit spread risk - the risk of changes in value due to changes in the credit spread (although this may be alternatively categorised as a component of market risk)

Question 2

Default risk in a portfolio can be assessed as 3 components

Answer 2

• the probability of default in respect of each counterparty
• the loss on default - a function of the exposure and the likely recoveries in the event of default, both of which could be uncertain
• the level and nature of interactions between the various credit exposures and other (non-credit) risks

Question 3

Information to assess credit risk may be sought from: (4)

Answer 3

• the credit issuer
• the counterparty
• publicly available data
• proprietary databases

Question 4

Assessment of credit risk is difficult due to: (4)

Answer 4

• lack of (publicly available) data
• skewness of loss distributions
• complex, and uncertain interdependencies
• model risk

Question 5

Qualitative credit models

Answer 5

Such models assess both default and credit spread risks using relevant factors, including:

• the nature of the borrower
• financial ratios
• economic indicators
• the nature and level of any security

The subjective nature of qualitative models are their main advantage and disadvantage.

Question 6

Quantitative credit models

Answer 6

Such models convert financial data into a credit measure, eg probability of default.

Examples include:

• credit-scoring
• structural (or firm-value)
• reduced-form
• credit-portfolio
• credit-exposure

Question 7

Merton model

Answer 7

Considers equity shares as a call option on the company’s assets.

The Black-Scholes option-pricing formula is used to value the shares. The model produces an estimate for the credit spread for a bond (even if it is unquoted) but the model makes a number of unrealistic assumptions.

Question 8

KMV model

Answer 8

Estimates the probability of default based upon empirical data on company defaults and how these defaults link to the distance to default (the gap between the current value of the company’s assets and the judged default threshold). It has some advantages over the Merton model, eg it can accommodate more realistic liability structures.

Question 9

Credit-migration models

Answer 9

Estimate how a credit rating might change over longer periods.

Historical data is used to determine rating-transition probabilities. Matrices of such probabilities are applied (repeatedly) to a company’s current rating to estimate the likelihood of each possible rating state in each future year.

The chance of default by a particular company in a future year is estimated as the assumed probability of default for companies with a particular rating in that year.

The general approach is to assume that the migration process follows a time-homogeneous Markov chain. The time-homogeneous assumption has been criticised using empirical evidence. It also assumes that the likelihood of default (“through the business cycle”) can be determined solely by the company’s credit rating.

Question 10

Key challenge when modelling the behaviour of a credit PORTFOLIO.

Answer 10

To understand the relationships between the various credit exposures, eg jointly-fat tails.

Question 11

5 Approaches to modelling credit PORTFOLIOS

Answer 11

• multivariate structural models
• multivariate credit-migration (or financial) models
• econometric or actuarial models
• common shock models
• time-until-default (or survival) models`

Question 12

multivariate structural models

Answer 12

eg multivariate KMV,

modelling asset values by using correlation matrices or copulas

Question 13

multivariate credit-migration (or financial) models

Answer 13

eg multivariate CreditMetrics,
which assumes that equity returns can be modelled using country-specific indices and (independent) firm-specific volatility.

Question 14

econometric or actuarial models

Answer 14

Do not model the asset value going forwards, but estimate the default rate of firms using external or empirical data.

Question 15

common shock models

Answer 15

determine the probability of no defaults by assuming that each bond defaults in line with a Poisson process, and considering shocks, each of which cause the default of one or more of the bonds in the portfolio

Question 16

time-until-default (or survival) models`

Answer 16

where survival CDFs (each based on a hazard rate determined from an implied probability of default) are linked by a suitable parameterised copula function, so as to estimate the aggregate default rate for the bond portfolio.

Question 17

How might recovery be measured?

Answer 17

Recovery might be measured as price after default or ultimate recovery. It is dependent upon many factors including: availability / marketability / liquidity of collateral, seniority of the debt and the rights of other creditors.

Estimated future recovery rates (or stochastic models) may be based upon historical recovery rates (and their volatility).

Question 18

Define

Hazard rate

Answer 18

In statistics, the hazard rate in respect of a defined event is:

The rate that the event occurs
… at a specified time
… on members of a defined group
… given that the event hasn’t yet occurred to members of that group.

Question 19

Define credit risk

Answer 19

The risk of loss due to
… contractual obligations not being met
… (in terms of quantity, quality or timing)
… either in part or in full, whether due to
- the inability of,
- or decision by,
the counterparty.

Question 20

Default could be defined to include some or all of the following events: (4)

Answer 20

• a payment due being missed
• a financial ratio falls above or below a certain level
• legal proceedings start against the credit issuer
• the present value of assets falls below that of liabilities due to economic factors.

Question 21

2 Key problems associated with the recovery process

Answer 21

• Recoveries can take a long time to obtain

- Usually require legal proceedings

Question 22

2 Methods of strengthening recoveries

Answer 22

• By requiring collateral from counterparties.

- By requiring third-party guarantees.

Question 23

Qualitative credit models:

6 Examples of factors upon which a subjective assessment of default and credit spread risk are based

Answer 23

1. The nature of the contractual obligation (eg for a loan, its seniority)
2. The level and nature of any security (eg parental guarantees, collateral)
3. The nature of the borrower (eg the company’s industry sector or individual’s employment status)
4. Economic indicators (eg inflation rates)
5. Financial ratios (eg a company’s gearing)
6. Face-to-face meetings with the credit issuer and/or counterparty.

The assessment should consider how the risk may change over time - perhaps over the life of the contractual obligation or over an economic cycle.

Question 24

Key advantage of qualitative credit models

Answer 24

A wide range of (subjective) factors can be incorporated into the assessment (beyond purely quantitative factors).

Question 25

5 Disadvantages of qualitative credit models

Answer 25

1. Excessive subjectivity
2. A lack of consistency between ratings (between sectors, between analysts, etc)
3. The meaning of subjective ratings may change over the economic cycle and/or as a result of changes in the economic environment.
4. Ratings may fail to respond to changes in the economic cycle or circumstances of the counterparty - in particular, there is often a reluctance to change a credit rating.

Question 26

Quantitative Credit Models:

Describe Credit-scoring models

Answer 26

Forecast the likelihood of a counterparty defaulting at a particular point in time given certain “fundamental” information about the counterparty.

Examples include

• empirical models (which analyse the incidence of default in the past for companies with a certain level of gearing, cashflow, profits, etc)
• expert models (which make use of the opinions of experts to assess the likelihood of default for a specified company)

Question 27

Quantitative Credit Models:

Describe Structural models

Answer 27

Estimate the likelihood of default using market information such as the company’s share price and the volatility of its share price (rather than use fundamental financial data).

Examples include the Merton and KMV models.

Question 28

Quantitative Credit Models:

Reduced-form Models

Answer 28

Do not model the mechanism leading to default, instead modelling it as a statistical process that typically depends upon economic variables.

Examples include credit-migration models which estimate how a counterparty’s credit rating might behave over time.

These credit ratings, in conjunction with default probabilities (perhaps determined using a structural model) enable the estimation of the overall likelihood of default in a particular future time period.

Question 29

Quantitative Credit Models:

Credit portfolio models

Answer 29

Used to estimate credit exposure across several counterparties, and may allow for the diversification effect of uncorrelated creditors.

Examples include multivariate structural, and multivariate credit migration models.

Question 30

State a key advantage of the Merton model

Answer 30

It allows us to estimate an appropriate credit spread for a bond, even when the bond is unquoted.

Question 31

State 6 disadvantages of the merton model

Answer 31

We assume:

• markets are frictionless (ie no transaction costs) with continuous trading
• the risk-free rate is deterministic
• Xt follows a log-normal random walk with fixed rate of growth and fixed volatility (ie independent of the company’s financial structure, eg level of gearing) - an unrealistic assumption
• Xt is an observable traded security - this assumption is rarely correct.
• The bond is a zero-coupon bond with only one default opportunity.
• Default results in liquidation - however, default can mean a variety of things other than liquidation.

Question 32

KMV model:

Define the distance to default

Answer 32

The number of standard deviations that the company’s assets have to fall in value before they breach the threshold ϐ.

DD₀ = ( X₀ - ϐ ) / ( σᵪ X₀ )

Using emprical data on company defaults and how these defaults link with DD, the model is used to estimate the likelihood of default for any given company over the coming year.

Question 33

3 Advantages of the KMV model over the Merton model

Answer 33

1. Coupon-paying bonds can be modelled.
2. More complex liability structures can be accommodated as the system uses the average coupon and the overall gearing level (rather than having to assume a single zero-coupon bond).
3. X₀ is not assumed to be observable, and is derived from the value of the company’s equity shares.

Question 34

2 Advantages of the credit migration approach

Answer 34

1. Volatile equity markets should not overly impact the results - empirically, this is often the case for the actual default probability of a particular firm.
2. The model does not rely on publicly-traded share information.

Question 35

The credit-migration approach relies on: (2)

Answer 35

• The credit migration process following a time-homogeneous Markov chain.
• There being a credit rating that reflects the company’s default likelihood “through the business cycle” (rather than reflecting the default change in the current economic environment).

Question 36

Disadvantages of the credit-migration approach

Answer 36

1. The time-homogeneity assumption has been criticised using empirical evidence and appears unintuitive (as a recently downgraded company is more likely to be downgraded again than a company that has been at that rating for a long time).
2. The approach assumes that default probabilities for each rating in each future year can be estimated.
3. The approach assumes that the likelihood of default can be determined solely by the company’s credit rating.
4. A low number of distinct credit ratings (compared to the number of rated organisations) results in a low level of granularity in the default estimates.
5. Rankings of organisations by the different credit rating agencies do not always coincide.
6. Not all organisations have obtained a (costly) credit rating.
7. Ratings are sometimes unavailable (withdrawn), eg if data required for rating has not been made available - although in such circumstances, the model might simply assume that the rating transitions in accordance with the adopted transition matrix.

Question 37

CreditMetrics

Answer 37

Estimates the value of a bond in one year’s time for each of its possible future ratings and deduces the bond’s expected future value.

Combining this information with the transition probabilities produces an estimate of the variance of the bond’s value in one year’s time.

Question 38

Econometric models

Answer 38

Estimate the default occurrence using combinations of macro-economic variables such as interest rates, inflation, etc.

Question 39

Actuarial models

Answer 39

(e.g. CreditRisk+)
Use average default rates and volatilities for the portfolio together with a broad brush estimate of future losses, which does not require Monte Carlo simulation.

Question 40

Common shock models:

Define what is meant by a “shock”

Answer 40

A shock is defined as an event that could occur that would knock out a particular subset of the bonds, due to default.

Question 41

Why is ultimate recovery often much larger than the price of debt after default

Answer 41

The market will tend to over-react to a company’s collapse while the receiver (insolvency practitioner) takes time to extract as much value as possible from the company’s residual assets.

Question 42

Explain how seniority affect the likely loss on default

Answer 42

The seniority of the debt affects how it ranks compared to other debt.

The more senior the debt,
… the higher call it has on any remaining assets
and hence
… a higher recovery rate.

Question 43

Explain how collateral affect the likely loss on default

Answer 43

If the lender holds some collateral against the debt, it may be able to take possession and sell that asset in the event of default.

The more liquid and marketable the collateral, the more value it has to the lender.