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Answer: Repeated sampling with replacement.
## Explanation When using **historical simulation with bootstrapping** to estimate VaR: - **Option A (Filter outliers)**: This is not typically part of bootstrapping. Bootstrapping uses the original data distribution, including outliers, to preserve the empirical distribution characteristics. - **Option B (Repeated sampling with replacement)**: ✅ **CORRECT** - This is the fundamental step in bootstrapping. It involves creating multiple resamples from the original dataset by drawing observations with replacement, which allows for estimating the sampling distribution of VaR. - **Option C (Identify tail region from reordering)**: This describes standard historical simulation without bootstrapping, where you sort returns and take the appropriate percentile. - **Option D (Apply weighting procedure)**: This describes filtered historical simulation or other weighted approaches, not basic bootstrapping. **Key Insight**: Bootstrapping specifically involves repeated sampling with replacement from the original dataset to create multiple simulated datasets, from which VaR can be estimated with better statistical properties than simple historical simulation.
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Johanna Roberto has collected a data set of 1,000 daily observations on equity returns. She is concerned about the appropriateness of using parametric techniques as the data appears skewed. Ultimately, she decides to use historical simulation and bootstrapping to estimate the 5% VaR. Which of the following steps is most likely to be part of the estimation procedure?
A
Filter the data to remove the obvious outliers.
B
Repeated sampling with replacement.
C
Identify the tail region from reordering the original data.
D
Apply a weighting procedure to reduce the impact of older data.
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