hard · FRM Part 1 Valuation and Risk Models
An analyst computes the 99% 1-day Value at Risk (VaR) for a $100 million equity portfolio using two different methods. The Delta-Normal approach yields a VaR of $4.65 million based on a 2% daily volatility. However, the Historical Simulation (HS) approach using the last 500 days of data yields a VaR of $6.48 million.
Which of the following is the most likely reason for this discrepancy, and what does it imply about the underlying return distribution?
- The returns are positively skewed; the Delta-Normal method overstates risk by assuming the distribution is symmetric when the historical tail is actually shorter.
- 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.
- 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.
- 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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