Pass the PRMIA PRM Certification 8008 Questions and answers with ExamsMirror

According to Basel II, where marking-to-market is not possible, banks may mark-to-model, where this can be demonstrated to be prudent. Marking-to-model is defined as any valuation which has to be benchmarked, extrapolated or otherwise calculated from a market input. When marking to model, an extra degree of conservatism is appropriate. Supervisory authorities will consider the following in assessing whether a mark-to-model valuation is prudent:

• Senior management should be aware of the elements of the trading book which are subject to mark to model and should understand the materiality of the uncertainty this creates in the reporting of the risk/performance of the business.

• Market inputs should be sourced, to the extent possible, in line with market prices. The appropriateness of the market inputs for the particular position being valued should be reviewed regularly.

• Where available, generally accepted valuation methodologies for particular products should be used as far as possible.

• Where the model is developed by the institution itself, it should be based on appropriate assumptions, which have been assessed and challenged by suitably qualified parties independent of the development process. The model should be developed or approved independently of the front office. It should be independently tested. This includes validating the mathematics, the assumptions and the software implementation.

• There should be formal change control procedures in place and a secure copy of the model should be held and periodically used to check valuations.

• Risk management should be aware of the weaknesses of the models used and how best to reflect those in the valuation output.

• The model should be subject to periodic review to determine the accuracy of its performance (e.g. assessing continued appropriateness of the assumptions, analysis of P&L versus risk factors, comparison of actual close out values to model outputs).

• Valuation adjustments should be made as appropriate, for example, to cover the uncertainty of the model valuation.

The model should be created independent of the front office, and not by it. Therefore statement III does not represent an appropriate choice. Choice 'a' is the correct answer.

The question is asking for the probability of default over a 6 month period when the probability of annual default is known. If we let the 6 month probability of defaut be 'd', then the probability of survival at the end of 1 year would be (1 - d)^2. This we know is equal to 1 - 3% = 0.97. Therefore we can calculate 'd' to be equal to 1.51%. Choice 'c' is the correct answer, the others are incorrect.

Note that an exam question may ask for probability of the security having survived after 6 months, in which case the answer might be 1 - 1.51%. Also note that such questions will always require you to use the probability of survival (1 - probability of default) for doing the calculations. That is because the probabilities of survival can be multiplied over periods of time, but not probabilities of default as the first default in any period is the 'game-over' event after which neither survival nor defaults mean anything. Therefore you generally always have to get the probability of survival till a point in time, and use that for any other calculations.

Statement I is incorrect. A transition matrix expresses the probabilities of moving to a given set of ratings at the end of a period (usually one year) conditional upon a given rating at the beginning of the period. It does not make a reference to an individual security and certainly not to the probability of migrating to other ratings during its entire lifetime.

Statement II is correct. Marginal default probabilities are the probability of default in a given year, conditional upon survival at the beginning of that year.

Statement III is incorrect. Cumulative probabilities of default will always be greater than the marginal probabilities of default - except in year 1 when they will be equal.

Statement IV is correct. LGD = 1 - Recovery Rate, therefore a low recovery rate implies higher LGD.

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.

Bank B's exposure is measured by the price it paid for the bonds, which in this case is $7m ($10m x 70/100). Hence Choice 'c' represents the correct answer.

(Note that the question is asking for 'exposure' and not the legal claim in the event of default. The legal claim in the event of default would be the full notional of $10m. )

The initial issue price and issue size are irrelevant.

Be wary of questions asking you to calculate VaR where the mean or expected returns are different from zero. The VaR formula of z-value times standard deviation needs to have an adjustment for the expected return [ie use VaR = z-value times standard deviation minus expected return]. In this case, the standard deviation for 1 day for the portfolio is =SQRT(1/250)*20%*$10m = $126,491. The VaR is therefore (2.326 * $126,491) - ($10,000,000 * 10% * 1/250) = $290,218.

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.

All the above listed reasons are valid explanations as to why an institution level stress test cannot be estimated by merely summing up the results of the stress tests of the individual desks.

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.

Choice 'd' is the correct answer. Settlement risk, as the name suggests, arises upon settlement when one of the parties delivers its obligation under the transaction and the other does not. Consider a EUR/USD FX forward contract maturing in a month. At maturity, one of the parties will deliver EURs and the other USDs. If one party fails to deliver, then it constitutes a very large risk to the other party. This risk is much larger than pre-settlement risk, because the amount at risk is the entire notional and not just the replacement value. Of course, settlement risk exists for a very short period of time, no more than a number or hours or a day.

There is no such thing as 'replacement risk', and credit risk is a larger category of which settlement risks is one component. Settlement risk is the most appropriate answer.