Which of the following statements is true in relation to a normal mixture distribution:I.

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.