Explanation
Choice 'd' is correct because VaR is sub-additive in cases where correlation is less than one.
Specific VaR refers to the risk in the portfolio from security selection, ie the risk from holding the specific equities in the portfolio, while systematic risk refers to the market risk. Definitionally, specific risk and systematic risk are uncorrelated, ie their correlation is zero. Since their correlation is zero, combining them will produce a VaR number lower than their stand alone aggregate. Total risk includes both specific risk and systematic risk, and can be calculated taking into account the specific and systematic VaRs and their correlation.
All other answers are therefore incorrect.

Explanation
Marginal probabilities of default are the probabilities for default for a given period, conditional on survival till the end of the previous period. Cumulative probabilities of default are probabilities of default by a point in time, regardless of when the default occurs. If the marginal probabilities of default for periods 1, 2... n are p1, p2...pn, then cumulative probability of default can be calculated as Cn = 1 - (1 - p1)(1-p2)...(1-pn). For this question, we can calculate the probability of default for year 3 as =1 - (1-2%)*(1-3%)*(1-4%) = 8.74%

Explanation
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.
Therefore any losses from poor strategic planning will not be a part of operational risk. Choice 'd' is the correct answer.
Note that floods, earthquakes and the like are covered under the definition of operational risk as losses arising from loss or damage to physical assets from natural disaster or other events.

Explanation
Statement I is true, the quantiles of the averaged models are equal to the geometric average of the quantiles of the original models.
Statement II is correct, the number of data points from which model parameters are estimated must be greater than the number of parameters. So if a distribution, say Poisson, has one parameter, we need at least two data points to estimate the parameter. Other complex distributions may have multiple parameters for shape, scale and other things, and the minimum number of observations required will be greater than the number of parameters.
Statement III is true, if the ILD data and scenarios cover the same risk, they are essentially different perspectives on the same risk, and therefore should be combined as weighted averages.
But if they cover completely different risks, the models will need to be added together, not averaged - which is why Statement IV is true.

Explanation
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.)