Explanation
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.

Explanation
If the current level of the S&P 500 is 2000, and a single day volatility is 1%, and the delta (ie change in portfolio value from a one point change) is $100, then the 1 day volatility for the portfolio in dollars is 2000 *
1% * $100 = $2,000.
At the 99% confidence level, the value of the inverse cumulative density function for the normal distribution is
2.33 (=NORMSINV(99%), in Excel). Therefore the 1 day VaR will be 2.33 * $2000 = $4,660. Extending it to
10 days using the square root of time rule, we get the 10 day VaR as equal to SQRT(10)*4660 = $14,736.
Since this method of calculating VaR relies upon a delta approximation of a risk factor (in this case the S&P500), it is the parametric approach to calculating VaR (the other methods being historical simulation, and Monte Carlo simulation).
The
2015 Handbook provides an excellent example of parametric (and other) VaR calculations in Chapter 3 of Volume III of Book 3. The spreadsheet used for the illustration can be downloaded from
http://www.prmia.org/prm-exam/handbook-resources.

Explanation
According to ISDA, a credit event is an event linked to the deteriorating credit worthiness of an underlying reference entity in a credit derivative. The occurrence of a credit event usually triggers full or partial termination of the transaction and a payment from protection seller to protection buyer. Credit events include
- bankruptcy,
- failure to pay,
- restructuring,
- obligation acceleration,
- obligation default and
- repudiation/moratorium.
A rating downgrade is not a credit event.

Explanation
Loss provisioning is intended to cover expected losses. Economic capital is expected to cover unexpected losses. No capital or provisions are set aside for losses in excess of unexpected losses, which will ultimately be borne by equity.
Choice 'd' is the correct answer.

Explanation
If the marginal probability of default of two securities A and B is P(A) and P(B), then the probability of both of them defaulting together is affected by the default correlation between them. Marginal probability of default means the probability of default of each security on a standalone basis, ie, the probability of default of one security without considering the other security.
The relationship that expresses the probability of joint default of the two is given by the following expression:

It is easy to see that in a situation where the Default Correlation of A & B = 0, ie, the defaults are independent, the combined probability of default is P(A)*P(B), exactly what we would intuitively expect. Also in the other extreme case where the default correlation is equal to 1 and P(A) = P(B) = p, ie the securities behave in an identical way, the expression resolves to just p, which is what we would expect.
From the above relationship, it is clear that the probability of joint default of A and B is the greatest when default correlation between the two is equal to 1, ie the securities behave in an identical way. Therefore Choice
'a' is the correct answer.