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Answer: Under the bootstrap procedure, the distribution of VaR is the sampling distribution, and the confidence interval can be calculated from the ordered VaR values.
## Explanation Let's analyze each option: **Option A**: Incorrect. While asymptotic standard error can be used to construct confidence intervals, it's not necessarily desirable to base confidence intervals on a single point estimate. This approach assumes normality and may not be robust for VaR estimation, especially in the tails of the distribution. **Option B**: Incorrect. This statement describes the process of ordering observations but doesn't actually explain how confidence intervals are computed using order statistics. The ordering is just the first step in the process. **Option C**: Incorrect. Both order statistics and bootstrap procedures typically assume independence of observations. The bootstrap procedure actually has the advantage of being able to handle some forms of dependence through block bootstrap methods, while standard order statistics approaches assume independence. **Option D**: Correct. Under the bootstrap procedure: - Multiple bootstrap samples are drawn from the original data - VaR is calculated for each bootstrap sample - The distribution of these VaR estimates forms the sampling distribution - Confidence intervals are constructed from the ordered VaR values (e.g., using percentiles) This approach is widely used in practice for constructing confidence intervals around VaR estimates because it doesn't rely on parametric assumptions about the underlying distribution.
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It is natural to ask about the accuracy of the VaR estimate. In order to evaluate this, we can compute the confidence intervals around the estimate whereby the true VaR should be within the interval a high percentage of the time. Which of the following statements correctly describes the approaches used to compute the confidence intervals?
A
It is desirable to base the confidence interval on the single point of the quantile estimate, and this view supports the use of asymptotic standard error of a quantile to construct the interval.
B
The use of order statistics starts with the pseudo history of portfolio value changes (denoted by ΔV), and reorders them from highest to lowest so that ΔV(1) ≥ ΔV(2) ≥ … ≥ ΔV(T).
C
The advantage of using order statistics over using bootstrap procedure is that the order statistics approach does not assume independence of the changes in portfolio value over time.
D
Under the bootstrap procedure, the distribution of VaR is the sampling distribution, and the confidence interval can be calculated from the ordered VaR values.