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FRM Part I · FRM Exam Part I · Simulation and Bootstrapping

A analyst wants to bootstrap the distribution of a 99% VaR estimate using 1,000 historical daily losses. Which statement best describes a limitation of the bootstrap in this application?

The bootstrap cannot generate a loss worse than the worst one in the original sample, because it only resamples observed values. This means extreme tail outcomes beyond the historical record are understated, which matters for high-confidence VaR. It does not require normality and can be applied to quantiles.

  1. AResampling with replacement can never produce a loss larger than the worst loss in the original sample, so the extreme tail is understatedCorrect
  2. BBootstrapping requires the losses to follow a normal distribution
  3. CBootstrapping always produces biased estimates of the sample mean
  4. DBootstrapping cannot be used for quantiles, only for means

Explanation

Bootstrap resamples contain only values observed in the original data, so no resampled loss can exceed the historical maximum. Tail risk beyond the observed history is therefore not captured. The bootstrap is nonparametric and does not require normality, and it can be applied to quantiles.

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