hard · FRM Part 1 Valuation and Risk Models

Which of the following is the most likely reason for this discrepancy, and what does it imply about the underlying return distribution?

1. The returns are positively skewed; the Delta-Normal method overstates risk by assuming the distribution is symmetric when the historical tail is actually shorter.
2. The look-back window used for HS is too long; as the sample size increases, the HS VaR must mathematically converge to the parametric normal VaR by the Central Limit Theorem.
3. The portfolio contains deep out-of-the-money options; the Delta-Normal method uses full revaluation and captures the convexity that HS ignores through its linear approximation.
4. The returns exhibit positive excess kurtosis; the Delta-Normal method understates risk because it fails to account for the fatter tails present in the historical sample.

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