Free PRMIA 8008 Practice Exam with Questions & Answers | Set: 4

When a derivative transaction is entered into, its value generally is close to zero. Over time, as the value of the underlying changes, the transaction acquires a positive or negative value. It is not possible to predict the future value of the transaction in advance, however distributional assumptions can be made and potential exposure can be measured in multiple ways. Of all the possible future exposures, it is generally positive exposures that are relevant to credit risk because that is the only situation where the bank may lose money from a default of the counterparty.

The maximum (generally a quantile eg, the 97.5th quantile) exposure possible over the time of the transaction is the 'Potential Future Exposure', or PFE.

The average of the distribution of positive exposures at a specified date before the longest trade in the portfolio is called 'Expected Exposure', or EE.

The expected positive exposure calculated as the weighted average of the future positive Expected Exposure across a time horize is called the EPE, or the 'Expected Positive Exposure'.

The price that would be received to sell an asset or paid to transfer a liability in an orderly transaction between market participants at the measurement date - is the 'fair value', as defined under FAS 157.

Therefore the corect answer is that EPE is the weighted average of the future positive expected exposure across a time horizon.

According to ISDA, a credit event is an event linked to the deteriorating credit worthiness of an underlying reference entity in a credit derivative. The occurrence of a credit event usually triggers full or partial termination of the transaction and a payment from protection seller to protection buyer. Credit events include

- bankruptcy,

- failure to pay,

- restructuring,

- obligation acceleration,

- obligation default and

- repudiation/moratorium.

A rating downgrade is not a credit event.

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).

Operational risk capital estimated using the implied capital model is merely the capital that is not attributable to market or credit risk. Therefore Choice 'b' is the correct answer. All other responses are incorrect.

Top down approaches rely upon available data such as total capital, income volatility, peer group information etc and attempt to imply the capital attributable to operational risk. They do not consider firm specific scenarios or causal factors. Bottom up approaches on the other hand attempt to determine operational risk capital based upon an identification and quantification of firm specific risks. Bottom up approaches help determine a traditional loss distribution from which capital requirements can be determined at a given level of confidence.

Therefore Choice 'd' is the correct answer.

All of the distributions referred to in the question can be used to model the loss severity distribution for op risk. Therefore Choice 'c' is the correct answer.

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-intuitive-understanding - may help clarify things further.

Exposure for derivative instruments can vary significantly over the lifetime of the instrument, depending upon how the market moves. The potential future exposure represents the extremes, not the most likely outcome. The expected exposure is the most suitable measure for pricing the credit risk. Over time, as multiple transactions are entered into, the expectation (or the mean) will be realized - though individual transactions may have more or less by way of exposure.

The notional amount may not be relevant, though for loans it may be the most important contributor to the expected exposure. Mark-to-market will represent the exposure at a given point in time, but cannot be predicted nor be used to price the credit risk.

The binomial, Poisson and the negative binomial distributions can all be used to model the loss event frequency distribution. The omega distribution is not used for this purpose, therefore Choice 'a' is the correct answer.

Also note that the negative binomial distribution provides the best model fit because it has more parameters than the binomial or the Poisson. However, in practice the Poisson distribution is most often used due to reasons of practicality and the fact that the key model risk in such situations does not arise from the choice of an incorrect underlying distribution.

A recap would be in order here: calculating operational risk capital is a multi-step process.

First, we fit curves to estimate the parameters to our chosen distribution types for frequency (eg, Poisson), and severity (eg, lognormal). Note that these curves are fitted at the UoM level - which is the lowest level of granularity at which modeling is carried out. Since there are many UoMs, there are are many frequency and severity distributions. However what we are interested in is the loss distribution for the entire bank from which the 99.9th percentile loss can be calculated. From the multiple frequency and severity distributions we have calculated, this becomes a two step process:

- Step 1: Calculate the aggregate loss distribution for each UoM. Each loss distribution is based upon and underlying frequency and severity distribution.

- Step 2: Combine the multiple loss distributions after considering the dependence between the different UoMs. The 'dependence' recognizes that the various UoMs are not completely independent, ie the loss distributions are not additive, and that there is a sort of diversification benefit in the sense that not all types of losses can occur at once and the joint probabilities of the different losses make the sum less than the sum of the parts.

Step 1 requires simulating a number, say n, of the number of losses that occur in a given year from a frequency distribution. Then n losses are picked from the severity distribution, and the total loss for the year is a summation of these losses. This becomes one data point. This process of simulating the number of losses and then identifying that number of losses is carried out a large number of times to get the aggregate loss distribution for a UoM.

Step 2 requires taking the different loss distributions from Step 1 and combining them considering the dependence between the events. The correlations between the losses are described by a 'copula', and combined together mathematically to get a single loss distribution for the entire bank. This allows the 99.9th percentile loss to be calculated.