Explanation
All four data sources are expected to be utilized as inputs as appropriate for operational risk calculations under the advanced measurement approach. Of these, the last one, BEICF, is slightly different from the rest as it does not yield data points that become the basis of curve fitting or other statistical computions underlying capital calculations. It includes items such as KRIs, risk assessments etc and allow the risk manager to assess the qualitative aspects of loss data.

Explanation
The probability of default would make the future cash flows from both the bonds identical. If p be the probability of default, the cash flows from the risky corporate bond would be
= (cash flows in the event of default x probability of default) + (cash flows without default x (1 - probability of default))
=> p*0 + (1 - p)*(1 + 8.5%) = (1 - p)*1.085.
The cash flows from the treasury bond would be 1.04. These two should be equal, ie,
1.04 = (1- p)*1.085, implying p = 4.15%.
(Note: The above is a simplification intended for the exam. In reality investors would demand a 'credit risk premium' for the corporate bond over and above the expected default loss rate. They are unlikely to be happy with just being compensated with exactly the expected default loss rate plus the risk-fre rate because the expected default loss rate itself is uncertain. They would demand some premium over and above what the default rate alone might mathematically imply above the risk free rate. In this question, this credit risk premium is ignored.)

Explanation
Stress tests can cover known events, but since the future is unknown, and new events may be entirely different from what has happened in the past, they provide no assurance that an institution's worst case losses would be covered. Hence II is false.
Stress testing is required to be performed as part of Basel II, and therefore III is false.
Historical events do not have sharply defined start and end dates. Often, even after a crises ends, its after effects may continue to affect the markets for a long time. In such cases, it may be difficult to define the start and end of the crises. In many cases, the crises may persist for months or even years, making it difficult for the risk manager to identify a time period that covers the essence of the crises, and yet is focused enough to constitute a plausible scenario. Therefore IV is false too. Only I is true, and the correct answer is Choice 'b'.

Explanation
Operational risk as defined in Basel II specifically excludes strategic and reputational risk. Therefore Choice
'd' is the correct answer.
Note that Basel II defines operational risk as follows:
Operational risk is defined as the risk of loss resulting from inadequate or failed internal processes, people and systems or from external events. This definition includes legal risk, but excludes strategic and reputational risk.

Explanation
This question requires the calculation of the credit VaR of the bonds - note that in the real exam the question may not refer to 'credit' VaR, but that can be inferred from the context, ie because the probability of default is provided, it can only be asking for the credit VaR. (Note the difference from the market risk VaR which is driven by interest rate changes affecting the value of the bonds - there are other questions addressing that calculation).
Credit VaR = Expected Value - Worst case portfolio value at the selected percentile (ie the confidence level) Thus if we know the distribution of the portfolio value in the future, we can find out the value at the required percentile (in this case 99%), and the VaR will be the difference between this value and the expected value of the portfolio.
An important piece of information provided is that the defaults are independent, ie they are not correlated. This means joint probabilities of default or survival can be easily found by multiplying the relevant probabilities.
The following outcomes are possible:
1. Both bonds default: Probability = 1% * 1% = 0.01%. Portfolio value = $0 (because both bonds have defaulted & there is zero recovery)
2. One bond defaults and the other survives: Probability = 2 * 1% * 99% = 1.98%. Portfolio value = $1m (because one bond survives with a value of $1m and the defaulted bond has a value of $0). (Note that because there are two ways in which this can happen, ie bond 1 defaults, bond 2 survives; and bond 1 survives, bond 2 defaults, we need to multiply the probability by 2).
3. Both bonds survive: Probability = 99% * 99% = 98.01%. Portfolio value = $2m.
Expected value is therefore $1.98m (which is equal to 2 * $1m * (1 - 1%), or alternatively can also be obtained by multiplying the probabilities in the above three outcomes with the value associated with each).
The future distribution of the value of the portfolio can be constructed from the three outcomes outlined above:
a. Upto the 98.01th percentile the value of the portfolio is $2m, and the VaR is zero (being greater than the expected value, so there is nothing to lose) b. From the 98.01th percentile to the 99.99th percentile (98.01+ the next 1.98%), the value of the portfolio is
$1m. VaR in this range is $0.98m (=$1.98m - $1m)
c. From the 99.99th to the 100th percentile the value of the portfolio is $0, and the VaR is $1.98m.
Since the question is asking for VaR at the 99% confidence level, it lies in the range in 'b' above, and therefore the VaR is $0.98m.
Therefore Choice 'c' is the correct answer and the rest are incorrect.