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Explanation:
A stress period typically includes extreme market events with higher volatility and significant tail risks. This increased variability in returns leads to wider confidence intervals for VaR estimates, as the uncertainty around the estimate is amplified due to the pronounced market movements.
A is incorrect: Longer periods generally include more data points, which reduce sampling variability and narrow confidence intervals. The effect of a longer historical period is opposite to that of a stress period, where fewer extreme events dominate the dataset.
B is incorrect: The stress period has higher volatility and tail risks, increasing the uncertainty and widening confidence intervals. Narrower confidence intervals are expected in periods with lower variability, not during stress periods.
D is incorrect: A longer historical period reduces sampling variability by including more data points, typically resulting in narrower confidence intervals. This distractor is plausible because candidates might mistakenly associate shorter periods with less uncertainty.
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Q.6469 A risk manager is evaluating the impact of different time periods on VaR confidence intervals. They are analyzing one-day 99% VaR estimates for the S&P 500 using historical simulation. They consider a recent one-year period, a longer historical period, and a one-year stress period. Which of the following describes the expected relationship between the time period used and the resulting confidence interval width?
A
The confidence intervals will be widest for the longer historical period.
B
The confidence intervals will be narrowest for the stress period.
C
The confidence intervals will be wider for the stress period compared to the recent one-year period.
D
The confidence intervals will be wider for the recent one-year period compared to the longer historical period.