8010 Practice Questions

The probability that the security would not default in the next 4 years is equal to the probability of

survival at the end of the four years. In other words, =(1 - 3%)*(1 - 4%)*(1 - 4%)*(1 - 5%) = 84.93%.

Choice 'd' is the correct answer.

For a dataset with 250 observations, the top 2% of the losses will be the top 5 observations. Expected

shortfall is the average of the losses beyond the VaR threshold. Therefore the correct answer is (20 +

19 + 19 + 17 + 16)/5 = 18.2m .

Note that Expected Shortfall is also called conditional VaR (cVaR), Expected Tail Loss and Tail average.

If the marginal probability of default of two securities A and B is P(A) and P(B), then the probability of

both of them defaulting together is affected by the default correlation between them. Marginal

probability of default means the probability of default of each security on a standalone basis, ie, the

probability of default of one security without considering the other security.

The relationship that expresses the probability of joint default of the two is given by the following

expression:

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It is easy to see that in a situation where the Default Correlation of A & B = 0, ie, the defaults are

independent, the combined probability of default is P(A)*P(B), exactly what we would intuitively

expect. Also in the other extreme case where the default correlation is equal to 1 and P(A) = P(B) = p,

ie the securities behave in an identical way, the expression resolves to just p, which is what we would

expect.

From the above relationship, it is clear that the probability of joint default of A and B is the greatest

when default correlation between the two is equal to 1, ie the securities behave in an identical way.

Therefore Choice 'a' is the correct answer.

The cumulative probability of default for the security for the 5 years is [1 - (1 - probability of default

upto year 4)*(1 - probability of default in year 5)]. An easier way to think about this is that the

Probability of survival till year 5 = (Probability of survival till year 4 * Probability of survival during

year 5). Using the relationship that probability of default = 1 - probability of survival, we can calculate

the required probability in all cases.

In this case, the cumulative probability of default for the security for 5 years = 1 - (1 - 11.47%)*(1 -

5%) = 15.8695%, therefore Choice 'c' is the correct answer.

Asset returns are relevant for credit risk models where a default is related to the value of the assets

of the firm falling below the default threshold. When assessing credit risk for portfolios with multiple

credit assets, it becomes necessary to know the asset correlations of the different firms. Since this

data is rarely available, it is very common to approximate asset correlations using equity prices.

Equity correlations are used as proxies for asset correlation, therefore Choice 'c' is the correct

answer.

Credit risk is the risk from a borrower defaulting on moneys lent. Counterparty risk, on the other

hand, is the risk that a counterparty to a derivative transaction will be unable to pay at the time the

transaction is in-the-money.

Credit risk therefore relates more to the banking book, counterparty risk relates more to the trading

book. Credit risk and counterparty risk differ in that for counterparty risk, the amount at risk

fluctuates for counterparty risk depending upon the value of the underlying derivative. Counterparty

risk generally starts at zero, for most swaps and other derivatives are near zero value at inception.

Over time, as the prices of the underlying instruments move, one party ends up owing money to the

other. A deterioration in the financial situation of the party owing moneys may lead to a loss to the

other party, resulting in counterparty risk. Counterparty risk can also arise from stock lending

operations and repo trades.

Credit risk on the other hand is the traditional risk of default by a borrower, or a bank's customer

who has taken a loan or has an overdraft or other credit facility.

Statement I is therefore incorrect as credit risk and counterparty risks are different.

Statement II is correct as counterparty risk is 'contingent' in the sense it arises only if the transaction

with the counterparty ends up being in-the-money, and the counterparty defaults.

Statement III is incorrect. The statement describes credit risk.

Statement IV is incorrect, as the exposure is known for moneys lent. Derivative exposures for the

future are difficult to estimate, they can even turn from moneys owed to moneys due as the value of

the underlying changes.

An interesting property that distinguishes the three most used distributions for modeling event

frequency is that for a given mean, their variances differ. The ratio of variance to mean (the variance-

mean ratio, calculated as variance/mean) can then be used to decide the kind of distribution to use.

Both the variance and the mean can be estimated from available data points from the internal or

external loss databases, or the scenario exercise.

The variance-mean ratio reflects how dispersed a distribution is. (In the PRMIA handbook, the

variance to mean ratio has been described as the "Q-Factor".)

The Poisson distribution has its mean equal to its variance, and therefore the variance to mean ratio

is 1. For the negative binomial distribution, this ratio is always greater than 1, which means there is

greater dispersion compared to the mean - or more intervals with low counts as well as more

intervals with high counts. For the binomial distribution, the variance to mean ratio is less than one,

which means it is less dispersed than the Poisson distribution with values closer to the mean.

In a situation where operational risk events are seen as clustering together, or dependent, the

variance will be higher and it would be more appropriate to use the negative binomial distribution.

The correct answer is Choice 'b'. The following is a brief description of the major approaches

available to model credit risk, and the analysis that underlies them:

1. CreditMetrics: based on the credit migration framework. Considers the probability of migration to

other credit ratings and the impact of such migrations on portfolio value.

2. CreditPortfolio View: similar to CreditMetrics, but adds the impact of the business cycle to the

evaluation.

3. The contingent claims approach: uses option theory by considering a debt as a put option on the

assets of the firm.

4. KMV's EDF (expected default frequency) based approach: relies on EDFs and distance to default as

a measure of credit risk.

5. CreditRisk+: Also called the 'actuarial approach', considers default as a binary event that either

happens or does not happen. This approach does not consider the loss of value from deterioration in

credit quality (unless the deterioration implies default).

Current replacement values are a very poor measure of the credit exposure from a derivative

contract, because the future value of these instruments is unpredictable, ie is stochastic, and the

range of values it can take increases the further ahead in the future we look. Therefore it is common

for credit exposures for derivatives to be measured using forward looking exposure profiles, which

are distributions of the expected value of the derivative at the time horizon for which credit risk is

being measured. To be conservative, a high enough quintile of this distribution is taken as the 'loan

equivalent value' of the derivative as the exposure. Choice 'c' is the correct answer.

The notional value of derivative contracts generally tends to be quite high and unrelated to their

economic value or the counterparty exposure. Therefore notional value is irrelevant.

Frequency modeling is performed using discrete distributions that have a positive integer as a

resultant - this allows for the number of events per period of time to be modeled. Of the

distributions listed above, Poisson, negative binomial and binomial can be used for modeling

frequency distributions. The Poisson and negative binomial distributions are encountered the most in

practice.

The gamma distribution is a continuous distribution and cannot be used for frequency modeling.