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Normal mixtures address fat or heavy tails, not volatility clustering. Therefore statement I is not correct.

Statement II is not correct. Where VaR is calculated at low levels of confidence, VaR based on normal mixtures may be lower than that under a normal assumption. This is no different than for other fat tailed distributions.

Statement III is correct. In situations where multiple market scenarios can unfold with a given probability, and each scenario is normal, we can express the result with a normal mixture where the underlying normal distributions have the probabilities of the different scenarios.

Choice 'b' is the correct answer. All other answers are incorrect.

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.

Delta is non-linear with respect to prices for a number of securities such as bonds, options and other derivatives. It changes with changes in prices, and any hedge initially undertaken becomes quickly mismatched. Therefore delta hedges need to be managed quite actively and kept up-to-date. Therefore I is true.Primary risks comprise most of the risk in a position, and therefore portfolio managers are right to focus on them over secondary risks. Therefore II is true.The greater the hedge rebalance frequency, the lower is the hedge mismatch at any point in time, and therefore residual risks would be lower. However, rebalancing hedges requires rebalance trades to be done, and these involve transaction costs. Generally, a reasonable balance needs to be struck between the frequency of rebalances (a lower frequency increases residual risk, but this residual risk is not directionally biased) and the costs of rebalancing. III is correct.Vega risk is the risk arising due to changes in prices due to changes in volatility.  Options carry vega risk. Therefore any hedges against vega risks can only be obtained using other options positions.  (Vega risk may also be hedged using other volatility based products, eg an OTC volatility swap, or a VIX futures type product.)

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'.