Pass the PRMIA PRM Certification 8008 Questions and answers with ExamsMirror

The correct answer is choice 'a'

Recall the following summary of the GARCH model. The long term variance in a GARCH model is given by ω/(1 - α - β). In this case, this works out to =SQRT(0.001/(1 - 0.05 - 0.93)) * SQRT(250) = 3.54%. Yesterday's volatility of 1% is irrelevant to the question.

Regardless of the approach being followed by a bank (ie, whether foundation IRB or advanced IRB), it must make its own estimates for the probability of default. Banks following the foundation IRB approach may use values set by the supervisor for the other three parameters, though those following the advanced IRB approach may use their own estimates for all four inputs. (This is also the difference between advanced IRB and the foundation IRB approaches.) Therefore Choice 'a' is the correct answer.

Also note the four difference elements that go as inputs to the internal ratings based approach in the choices provided.

This question emphasizes the difference between primary and secondary risks. Primary risks are the risks consciously undertaken, ie the risks whose premium the investor is trying to earn. Secondary risks are risks that accompany the primary risks that the investor will either hedge, or will ignore if they are small. It is important to watch out for secondary risks because they could become significant and offset the returns being sought even if the investor's market view is proved correct.

An investor in market index futures is betting that the index will rise. Index futures prices are largely driven by the spot value of the index, but are also affected by costs of carry. In particular, futures prices will be driven by interest rates, expected dividends, and any other factors that may cause the basis between spot and futures prices to diverge. These risks are secondary risks.

In this question, Choice 'd' represents the primary risk, and Choice 'a', Choice 'b' and Choice 'c' are all secondary risks. Therefore Choice 'd' is the correct answer.

The recovery rate, the default hazard rate (also called the average default intensity) and the spread on debt are linked by the equation Hazard Rate = Spread/(1 - Recovery Rate). Therefore, the recovery rate implicit in the given data is = 1 - 8%/10% = 20%.

Top down approaches do not consider event frequency and severity, on the other hand they focus on high level available data such as total capital, income volatility, peer group information on risk capital etc. Bottom up approaches focus on severity and frequency distributions for events. Statement I is therefore not correct.

Top down approaches do indeed rely upon high level aggregate data and tend to infer operational risk capital requirements from these. Bottom up approaches look at more detailed firm specific information. Statement II is correct.

Scenario analysis requires estimating losses from risk scenarios, and allows incorporating the judgment and views of managers in addition to any data that might be available from internal or external loss databases. Statement III is correct. Therefore Choice 'b' is the correct answer.

The change in the price of a security that follows a Weiner process is determined by its standard deviation and expected return. To get the price itself, we need to add this change in price to the current price. Therefore the future price in a Weiner process is determined by all three of current price, expected return and standard deviation.

Remember that VaR is merely a multiple of the portfolio's standard deviation. The multiple is determined by the confidence level, and for a 99% confidence level this multiple is 2.3264 (=-NORMSINV(1%) in Excel). Therefore one standard deviation at this level of confidence would be equal to VaR/2.3264.

In addition to the Z-value at 99% confidence, you should also remember what the Z value is for a 95% level of confidence, as PRM questions may expect you to know these. The standard Windows calculator allowed in the exam does not allow you to calculate these, so it is safer to just remember these values.

The easiest way to answer this question is to ignore the joint probability of default as that is irrelevant to expected losses. The joint probability of default impacts the volatility of the losses, but not the expected amount. One way to think about it is to think of asset portfolios, where diversification reduces risk (ie standard deviation) but the expected returns are nothing but the average of the expected returns in the portfolio. Just as the expected returns of the portfolio are not affected by the volatility or correlations (these affect standard deviation), in the same way the joint probability of default does not affect the expected losses. Therefore the expected losses for this portfolio are simply $1m x 10% + $1m x 15% = $250,000.

This can also be seen from the lens of a joint probability distribution as follows:

There are four possibilities for this portfolio:

- Only loan A defaults: loss of $1m: 9% probability

- Only loan B defaults: loss of $1m: 14% probability

- Both loan A and B default: loss of $2m: 1% probability

- Neither A nor B default: loss of $0m: 76% probability

Therefore the expected losses on the portfolio are ($1m x 9%) + ($1m x 14%) + ($2m x 1%) + ($0m x 76%) = $250,000.

(Notes: How is the above table calculated? The totals (10%, 90%, 15% and 85%) are filled in first. The top left cell (both A & B default) is given as 1%. We can now calculate the rest of the cells as the totals are known.)

The state of the economy, credit quality of individual borrowers and concentration risk are all factors that affect the credit risk facing a lender. Mark to market accounting does not change the credit risk, or the underlying economic reality facing the institution. Therefore Choice 'b' is the correct answer.

Choice 'a' 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.