Question 1

The probability of default of a security during the first year after issuance is 3%, that during the
second and third years is 4%, and during the fourth year is 5%. What is the probability that it would
not have defaulted at the end of four years from now?

Accepted Answer

D

Explanation: 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.

Question 2

The largest 10 losses over a 250 day observation period are as follows. Calculate the expected shortfall at a 98% confidence level: 20m 19m 19m 17m 16m 13m 11m 10m 9m 9m

Accepted Answer

C

Explanation: 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.

Question 3

If A and B be two debt securities, which of the following is true?

Accepted Answer

A

Explanation: 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: https://kxbjsyuhceggsyvxdkof.supabase.co/storage/v1/object/public/file-images/PRMIA_8010/page_81_img_1.jpg 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.

Question 4

The cumulative probability of default for a security for 4 years is 11.47%. The marginal probability of
default for the security for year 5 is 5% during year 5. What is the cumulative probability of default
for the security for 5 years?

Accepted Answer

C

Explanation: 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.

Question 5

For credit risk calculations, correlation between the asset values of two issuers is often proxied with:

Accepted Answer

C

Explanation: 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.

Question 6

Which of the following statements are true:

Accepted Answer

C

Explanation: 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.

Question 7

For a given mean, which distribution would you prefer for frequency modeling where operational
risk events are considered dependent, or in other words are seen as clustering together (as opposed
to being independent)?

Accepted Answer

C

Explanation: 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.

Question 8

Which of the following credit risk models relies upon the analysis of credit rating migrations to assess credit risk?

Accepted Answer

B

Explanation: 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).

Question 9

Credit exposure for derivatives is measured using

Accepted Answer

C

Explanation: 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.

Question 10

Which of the following distributions is generally not used for frequency modeling for operational risk

Accepted Answer

C

Explanation: 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.

Question 11

Which of the following best describes Altman's Z-score

Accepted Answer

C

Explanation: Choice 'c' correctly describes Altman's z-score. All other choices are incorrect.

Question 12

Once the frequency and severity distributions for loss events have been determined, which of the
following is an accurate description of the process to determine a full loss distribution for operational
risk?

Accepted Answer

B

Explanation: Once the frequency distribution has been determined (for example, using the binomial, Poisson or the negative binomial distributions) and the severity distribution has also been determined (for example, using the lognormal, gamma or other functions), the loss distribution can be produced by a Monte Carlo simulation using successive drawings from each of these two distributions. It is assumed that the severity and frequency are independent of each other. The resulting distribution gives a distribution showing the losses for operational risk, from which there Op Risk VaR can be determined using the appropriate percentile. Therefore Choice 'b' is the correct answer.

Question 13

According to the Basel II framework, subordinated term debt that was originally issued 4 years ago with a maturity of 6 years is considered a part of:

Accepted Answer

A

Explanation: According to the Basel II framework, Tier 1 capital, also called core capital or basic equity, includes equity capital and disclosed reserves. Tier 2 capital, also called supplementary capital, includes undisclosed reserves, revaluation reserves, general provisions/general loan-loss reserves, hybrid debt capital instruments and subordinated term debt issued originally for 5 years or longer. Tier 3 capital, or short term subordinated debt, is intended only to cover market risk but only at the discretion of their national authority. This only includes short term subordinated debt originally issued for 2 or more years. An interesting thing to note is the difference between 'subordinated term debt' under Tier 2 and the 'short term subordinated debt' under Tier 3. The distinction is based upon the years to maturity at the time the debt was issued. The remaining time to maturity is not relevant. For the subordinated term debt included under Tier 2, the amount that can be counted towards capital is reduced by 20% for every year when the debt is due within 5 years. This takes care of the time to maturity problem for Tier 2 subordinated debt. For Tier 3 short term subordinated debt, this is not an issue because debt will only qualify for Tier 3 if it has a lock-in clause stipulating that the debt is not required to be repaid if the effect of such repayment is to take the bank below minimum capital requirements.

Question 14

If E denotes the expected value of a loan portfolio at the end on one year and U the value of the
portfolio in the worst case scenario at the 99% confidence level, which of the following expressions
correctly describes economic capital required in respect of credit risk?

Accepted Answer

A

Explanation: Economic capital in respect of credit risk is intended to absorb unexpected losses. Unexpected losses are the losses above and beyond expected losses and up to the level of confidence that economic capital is being calculated for. The capital required to cover unexpected losses in this case is E - U, and therefore Choice 'a' is the correct answer. This question does raise an important point - are expected losses a part of economic capital, or are they not? Different text books say different things, and sometimes they say both the things. I have tried to take an approach that uses what I read in the PRMIA handbook. This writeup - http://www.riskprep.com/all-tutorials/37-exam-3/111-credit-var-an-intuitiveunderstanding - may help clarify things further.

Question 15

Loss provisioning is intended to cover:

Accepted Answer

D

Explanation: Loss provisioning is intended to cover expected losses. Economic capital is expected to cover unexpected losses. No capital or provisions are set aside for losses in excess of unexpected losses, which will ultimately be borne by equity. Choice 'd' is the correct answer.

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