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.

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.

Choice ' d ' represents a risk concentration due to excessive exposure to a single country, even though spread across different industries as the risk factors (economy, exchange rate, interest rate, political risk etc) are the same for all companies in the country.

Choice ' a ' represents a risk concentration because even though the risk factors are different, they are highly correlated and therefore effectively behave as one. These undetected correlations proved to be fatal to many financial institutions during the credit crisis.

Choice ' b ' represents a risk concentration as was borne out by the recent credit crisis. Large banks had to take over the obligations of SIVs they had created, even though the SIVs were separate legal entities with no legally enforceable recourse to the originating bank. This had to be done for moral and reputational reasons, and banks had to absorb the losses of these supposedly separate vehicles.

Choice ' c ' does not represent a risk concentration, in fact it is not a risk at all because it refers to collateral held, even though the collateral may have been provided by the same counterparty. In this case the risk is to the party providing the collateral (in case the party holding the collateral rehypothecates or sells the collateral and is unable to return it).

Therefore Choice ' c ' is the correct answer.

The BCBS document on stress testing provides a very nice articulation of risk concentration, and the relevant text from that document is produced verbatim here: [Risk concentration] may arise along different dimensions: single name concentrations; concentrations in regions or industries; concentrations in single risk factors; concentrations that are based on correlated risk factors that reflect subtler or more situation-specific factors, such as previously undetected correlations between market and credit risks, as well as between those risks and liquidity risk; concentrations in indirect exposures via posted collateral or hedge positions; concentrations in off-balance sheet exposure, contingent exposure, non-contractual obligations due to reputational reasons.

The ' middle office ' is a term used for the risk management function, therefore Choice ' d ' is the correct answers. The other functions describe what the ' back office ' does (IT, accounting). The ' front office ' includes the traders.

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.

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%.

The difference between the yields on corporate bonds and the risk free rate is called the corporate bond spread. Widening of the spread means that corporate bonds yield more, and their yield curve shifts upwards, driving down bond prices. The increase in the spread is a consequence of the market risk from holding these interest rate instruments, which is a part of market risk. If the reduction in the value of the portfolio were to be caused by a change in the credit rating of the bonds held, it would have been a loss arising due to credit risk. Counterparty risk and liquidity risk are not relevant for this question. Therefore Choice ' c ' is the correct answer.

If the daily standard deviation is 2%, the 10-day standard deviation will be 2%* √10 = 0.063245. The value of Z at the 95% confidence level is 1.64485. Therefore the VaR value is 1.64485 * 0.063245 = 10.4%. The other choices are incorrect.

This is easy to calculate as follows: At the 99% confidence level, the VaR=2.326 * Std Deviation (remember the z values at the 95% and 99% levels, the PRMIA exam may not give you these values). Thus the 1-day standard deviation is $250m/2.326, and the 250-day standard deviation is √250 * ($250m/2.326) = $1,699.4m.

Remember: if you know the VaR, you know the standard deviation. Once you know the standard deviation for any period of time, you can convert it into standard deviation for another period using the square root of time rule. You can also calculate the VaR at a different confidence level too.

The exact formula for VaR is = -(Zα σ + μ), where Z α is the z-multiple for the desired confidence level, and μ is the mean return. Now Zα is always a negative number, or at least will certainly be provided the desired confidence level is greater than 50%, and μ is often assumed to be zero because generally for the short time periods for which market risk VaR is calculated, its value is very close to zero.

Therefore in practice the formula for VaR just becomes -Zασ, and since Z is always negative, we normally just multiply the Z factor without the negative sign with the standard deviation to get the VaR.

For this question, there are two ways to get the answer. If we use the formula, we know that -Zασ= 250,000 (as μ=0), and therefore -Zασ - μ = 250,000 - 10,000 = $240,000.

The other, easier way to think about this is that if the mean changes, then the distribution ' s shape stays exactly the same, and the entire distribution shifts to the right by $10,000 as the mean moves up by $10,000. Therefore the VaR cutoff, which was previously at -250,000 on the graph also moves up by 10k to -240,000, and therefore $240,000 is the correct answer.

The other choices are intended to confuse by multiplying the z-factor for the 99% confidence level with 10,000 etc.