Pass the PRMIA PRM Certification 8008 Questions and answers with CertsForce

Banks using the basic indicator approach must hold 15% of the average annual gross income for the past three years, excluding any year that had a negative gross income. Therefore Choice 'd' is the correct answer.

All the statements in this question are directly based on the principles for effective stress testing as laid down in the BCBS document on stress testing issued in May 2009. Statement 1 is correct and is an almost verbatim reproduction of principle 10 as laid down in that document. Statement II is incorrect as it is contrary to principle 11 laid down in the same document. Statement III is correct as discovering hidden vulnerabilities and inconsistencies in hedging strategies is one of the objectives of reverse stress tests. Similarly, even though reputational risk is not really covered under any risk category under Basel II (as it is not a part of either market, credit or operational risk), principle 14 of this paper requires the mitigation of spill-over effects on market confidence of reputational risk when thinking about stress tests.

Thus statements I, III and IV are correct and statement II is incorrect.

Recovery rates vary a great deal from year to year, and are difficult to predict. Therefore statement III is true. Similarly, any attempt to predict these is hamstrung by a high standard error, which can be as high as the historical mean itself. The error does not cancel itself out due to the effect of the business cycle making the error directionally biased. Thus statement IV is false.

Statement II is true as these are all factors that make forecasting recovery rates for any credit risk model rather difficult. Statement I is false because recovery rates are difficult to predict and assumptions are not easy to make.

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.

Normal mixtures have higher peaks, and therefore higher kurtosis than a normal distribution with an equivalent mean and variance. Therefore statement I is correct.

The term 'normal mixture' literally means that - the distribution is derived by summing two or more normal distributions. Statement II is correct. One interesting thing to note about normal mixtures is that their mean and variances are just the weighted averages of the means and variances of their underlying component normal distributions. But their kurtosis is higher than that of either of the components. They are more peaked, and have fatter tails, a property that makes them useful in finance.

Unfortunately there is no analytical formula for calculating VaR based on normal mixtures. However, we can back solve for VaR (using Excel's Solver, for example), given we know the density functions for the underlying normal distributions. Statement III is not correct.

Since the business units are uncorrelated, we can get the combined EC as equal to the square root of the sum of the squares of the individual EC estimates. Therefore Choice 'a' is the correct answer. [=SQRT(100^2+200^2+150^2)]

The probabilities of default of the two bonds are independent (as indicated by a zero default correlation). The various possible states of the portfolio are as follows:

First bond defaults, and the second does not: Probability * Loss = 0.03*0.92 * $50m = $1.38m

Second bond defaults, and the first does not: Probability * Loss = 0.97*0.08 * $50m = $3.88m

Both bonds default: Probability * Loss = 0.03*0.08 * $100m = $0.24m

Thus total expected loss on this portfolio = $5.5m. Since recovery rates are not provided, those should be assumed to be zero.

There is an easier way to solve this as well: default correlation does not affect expected losses, but their volatility. You can calculate the expected losses of the two bonds and add them up, ie, $50m*0.03 + $50m *0.08 = $5.5m

An observed fact that the KMV approach relies upon is that firms do not default when their liabilities exceed assets, but when asset values are somewhere between short term liabilities and the total liabilities. In fact, the 'default point' in the KMV methodology is defined as the short term debt plus half of the long term debt. The difference between expected value of the assets in one year and this 'default point', when expressed in terms of standard deviation of the asset values, is called the 'distance-to-default'.

Therefore Choice 'd' is the correct answer. The other choices are incorrect.

The persistence parameter, λ, is the coefficient of the prior day's variance in EWMA calculations. A higher value of the persistence parameter tends to 'persist' the prior value of variance for longer. Consider an extreme example - if the persistence parameter is equal to 1, the variance under EWMA will never change in response to returns.

1 - λ is the coefficient of recent market returns. As λ is lowered, 1 - λ increases, giving a greater weight to recent market returns or shocks. Therefore, as λ is lowered, the model will react faster to market shocks and give higher weights to recent returns, and at the same time reduce the weight on prior variance which will tend to persist for a shorter period.

Suppose during a historical event interest rates rose from 2% to 2.25%. This can be understood as a change of either 25 basis points, or a change of 12.5%. When applied to the current portfolio when interest rates are 0.50%, we may model this 'shock' as either a rise to 0.75%, or 0.5625% (ie a rise of 12.5% over existing levels). The former is called an absolute shock, and the latter a relative shock.

I is true as relative shocks can never change the sign of a risk factor. Yet interest rate changes are modeled as absolute changes as relative shocks can get artificially amplified or attenuated if the current level of interest rates is too different from those that existed during the crisis being modeled. Therefore II is true. III and IV are false as volatility is modeled as a relative shock and spreads are modeled as absolute shocks.