PRMIA 8008 - PRM Certification - Exam III: Risk Management Frameworks, Operational Risk, Credit Risk, Counterparty Risk, Market Risk, ALM, FTP - 2015 Edition

Choice 'c' is the correct answer. Refer to the detailed loss event type classification under Basel II (see Annex 9 of the accord). You should know the exact names of all loss event types, and examples of each.

The z value at the 95% confidence level is 1.64. Since the variance is 0.16, the annual volatility is 40%. Therefore the daily volatility is 40% x √10/250 = 8%. The VaR therefore is 8% x 1.64 x $240m = $31,488,000

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.

The number of futures contracts to sell are equal to $10m x 1.1/$50,000 = 220. Liquidating his portfolio would reduce the beta to zero, but would also get rid of the bets he wants to play on. Therefore Choice 'c' is the correct answer.

(Note that futures and spot prices generally move together allowing futures positions to be used for hedging the risk against movement in spot prices. However there is a basis risk between spot and futures, therefore the a perfect hedge is never possible with futures. If interest rates move a great deal, spot and futures prices may diverge. Of course, this risk is generally quite low but may become amplified with large leveraged portfolios. Just something to be aware of.)

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.

Tier 3 capital, or short term subordinated debt, is intended only to cover market risk but only at the discretion of their national authority.

The credit risk horizon for credit VaR is generally one year. Therefore Choice 'b' is the correct answer.

When we do a Monte Carlo simulation, the statistic we obtain (eg, the expected price) is an estimate of the real variable. The difference between the real value (which would be what we would get if we had access to the entire population) and that estimated by the Monte Carlo simulation is measured by the 'standard error', which is the standard deviation of the difference between the 'real' value and the simulated value (ie, the 'error').

As we increase the number of draws in a Monte Carlo simulation, the closer our estimate will be to the true value of the variable we are trying to estimate. But increasing the sample size does not reduce the error in a linear way, ie doubling the sample size does not halve the error, but reduces it by the inverse of the square root of the sample size. So if we have a sample size of 1000, going up to a sample size of 100,000 will reduce the standard error by a factor of 10 (and not 100), ie, SQRT(1/100) = 1/10. In other words, standard error is proportional to 1/√N, where N is the sample size.

Therefore Choice 'c' is correct and the others are incorrect.

I, III and IV represent situations where Monte Carlo simulations can be employed. I is not a situation where Monte Carlo can be used, as there is no basis available to simulate the returns. When no distribution assumption is possible, it may be advisable to use historical simulations. Therefore Choice 'd' is the correct answer, and the others are incorrect.

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.

The capital adequacy ratio, also called the minimum capital requirement for credit risk per Basel II is 8% of risk weighted assets. The other choices are incorrect.