ERM Chapter 23

Question 1

What are the two components of credit risk? Describe what is meant by them.

Answer 1

1. Default risk - not well defined, could be defined to include some or all of the following events:
   - payment due is missed
   - financial ratio falls above or below a certain level
   - legal proceedings start against the credit issuer
   - present value of assets fall below that of liabilities due to economic factors

These events can be caused by default of counterparty’s own trading partners or by national trading controls imposed by governments.

2. Credit spread - measure of the difference between the yield on a risky and risk-free security, typically a corporate bond and a government bond respectively. Credit spread risk is the risk of change in value of an asset due to changes in the credit spread.

Question 2

What are the two components of default risk in respect of a single counterparty?

Answer 2

1. probability of default

2. loss on default

Question 3

What three component must be considered when assessing default risk in a credit portfolio?

Answer 3

1. probability of default of each counterparty
2. loss on default (function of the exposure and the likely recoveries in the event of default)
3. level and nature of interactions between the various credit exposures and other risks in the portfolio

Question 4

Outline two examples where market risk and credit risk are interrelated.

Answer 4

1. Pension schemes are exposed to market risks which are not independent of the credit risk of the sponsor.
2. Credit risks associated with long-term loans are not independent of changes in the yield curve.

Question 5

Describe four sources of information used to assess credit risk.

Answer 5

1. Credit issuer - credit rating agencies will carry out in-depth interviews with the institutions they rate.
2. Counterparty - banks will have standardised questionnaires for new borrowers.
3. Publicly available data - information disclosed under Basel disclosure rules or stock exchange listing rules.
4. Proprietary databases - companies such as Experian hold vast amounts of data on individuals’ credit histories, which are used to support banks’ lending decisions.

Question 6

Describe six factors upon which assessments of default and credit spread risk are based.

Answer 6

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

Question 7

What are the advantages and disadvantages of using qualitative factors in assessing creditworthiness.

Answer 7

A:
- a wide range of subjective factors can be incorporated into the assessment

D:

• excessive subjectivity
• a lack of consistency between ratings (between sectors, between analysts etc.)
• the meaning of subjective ratings may change over the economic cycle and/or as a result of changes in the economic environment
• ratings may fail to respond to changes in the economic cycle or circumstances of the counterparty

Question 8

List and outline the different types of quantitative models used to assess credit risk.

Answer 8

Credit-scoring models:

• forecast the likelihood of a counterparty defaulting at a particular point in time given certain ‘fundamental’ information about the counterparty
• examples include empirical models that consider the incidence of default based on level of gearing, cashflow profits etc., and expert models that make use of the opinions of experts to assess the likelihood of default for a specific company.

Structural models:

• estimate the likelihood of default using market information such as the company’s share price and the volatility of its share price
• examples include the Merton and KMV models.

Reduced-form models:

• 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 enable estimation of overall likelihood of default in a particular future time period.

Credit portfolio models:

• 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
• in many cases the exposure that an institution has to a counterparty is straightforward to calculate, in others it is not.

Credit exposure models:

• employed in more complex circumstances, in order to estimate credit exposure
• example includes a Monte Carlo approach estimating the expected and maximum credit exposures

Question 9

List three difficulties encountered with all of the quantitative modelling approaches.

Answer 9

1. the lack of publicly available data on default experience
2. the skewness of the distribution of credit losses
3. the correlation of defaults between different counterparties

Question 10

Outline the Merton model.

Answer 10

• equity shares are considered as a call option on the company’s total assets. If the total assets in the company rise in value and exceed the nominal value of debt by the time the debt has to be repaid then equity shareholders repay the debt and own the company’s residual assets. If assets fail to perform and are worth less than the nominal debt then they receive nothing.
• the value of debt is equal to the value of a risk-free bond less the value of a put option on the company’s total assets.

S0 = X0 x O(d1) - B x e ^(-rT) x O(d2)
St = value of shares at time t
Xt = value of company's assets at time t
T = time to redemption
r = continuously compunded rfr
B = nominal value of debt
d1 = [ln(X0/B) + (r+o^2/2)T]/[ox x sqrt(T)]
d2 = d1 - ox x sqrt(T)
ox = volatility of company's total assets

A:
- allows us to estimate an appropriate credit spread for a bond, even when the bond is unquoted

D:
Assumptions include
- market is frictionless
- rfr is deterministic
- Xt follows a log-normal random walk with fixed rate of growth and fixed volatility
- Xt is an observable traded security
- the bond is a zero-coupon bond with only one default opportunity
- default results in liquidation

Question 11

Outline the KMV model.

Answer 11

• used the concept introduced by Merton that a company will default at first instance that Xt falls below B
• uses the concept of distance to default, which is the number of SD’s the company’s assets have to fall in value before they breach the threshold B:
  DD = [X0 - B]/[ox x X0]

A:

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
3. X0 is not observable, and is derived from the value of the company’s equity shares

Question 12

Outline credit migration models.

Answer 12

• used for longer-term exposure to counterparties, estimating how credit rating may change over time
• Modelling process has three steps:
  1. historical data is used to determine the probability that a company rated X at the beginning of the year will transition to be rated Y at the end of the year. These probabilities are recorded in rating transition probability matrices.
  2. These matrices are applied to a counterparty’s current rating to estimate the likelihood of each possible rating in each future year.
  3. Using the probability of default for a company of a given rating, the model estimates the chance of default in each future year.

A:

• volatile equity markets should not overly impact the results
• the model does not rely on publicly-traded share information

D:

• time-homogeneity assumption has been criticised using empirical evidence and appears unintuitive
• approach assumes that default probabilities for each rating in each future year can be estimated
• approach assumes that the likelihood of default can be determined solely by a company’s credit rating
• low number of distinct credit ratings results in a low level of granularity in the default estimates
• rankings of organisations by the different credit rating agencies do not always coincide
• not all organisations have obtained a credit rating
• ratings are sometimes unavailable

Question 13

Outline the different types of credit portfolio models.

Answer 13

Multivariate structural models:

• multivariate versions of the Merton or KMV models can be constructed to model asset values of organisations associated with the credit portfolio.
• multivariate normal or t-distribution might be used to model the log of these values, whilst an explicit copula might be used to model the relationship between these values.

Multivariate credit-migration models:

• by extending credit-migration models to cope with portfolios of organisations, we can model the number of organisations that default each year.
• by combining the exposure to each organisation, and proportion of exposure that is lost upon default, we can derive a distribution for the portfolio via simulation.

CreditMetrics:
- assumes that equity returns can be modelled using country-specific indices and firm-specific volatility
- monte-carlo simulations can be used to derive potential:
> movements in equity values
> corresponding changes in the overall value of each organisation’s assets
> associated changes in rating
> implied changes in the values of bonds in the portfolio
- assumptions include:
> each credit rating has an associated probability of default
> a change in rating is a function of a change in the value of an organisation’s assets and the volatility of the value of those assets
> the value of assets of each organisations in the portfolio behaves log-normally
> correlation between the asset values can be estimated from the correlation between the corresponding equity values
> equity returns can be modelled using country-specific indices and firm-specific volatility

Econometric and Actuarial models:

• econometric models estimate the default occurrence using combinations of macro-economic variables such as interest rates, inflation etc.
• actuarial models use average default rates and volatilities of the portfolio together with broad-brush estimates of future losses, which does not require Monte-Carlo simulation
• different as they do not model asset value going forwards, rather estimating default rates of firms using external or empirical data

Common shock models:
- for a portfolio of bonds, the probability of no defaults can be modelled using copulas

Time-until-default or survival models:
- aim to model the incidence of defaults by using copulas to describe the relationship between the times of default of bonds in a portfolio