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FRM Part II · FRM Exam Part II · Non-parametric Approaches

A bank's 99% one-day historical simulation VaR uses 400 observations. A risk analyst bootstraps this sample 1,000 times and finds the bootstrap VaR distribution is strongly right-skewed (in loss terms), with a long tail of high VaR values. Which interpretation and action is most appropriate?

Percentile-based bootstrap intervals are preferable. A strongly skewed bootstrap VaR distribution means a symmetric interval built from the mean and standard error would misstate the uncertainty, whereas taking the actual percentiles of the bootstrap estimates captures the asymmetry in tail risk.

  1. AA symmetric normal-based interval around the mean is likely misleading, so percentile-based bootstrap intervals should be preferredCorrect
  2. BThe skew proves the original sample contains data errors that must be deleted before any VaR is computed
  3. CThe skew implies the VaR estimator is unbiased, so the standard error alone is sufficient
  4. DThe skew means the number of resamples must be reduced to below the sample size

Explanation

A skewed bootstrap distribution reflects that a few extreme tail losses sometimes appear multiple times in a resample, producing high VaR. A symmetric mean plus-or-minus z x SE interval then misrepresents the uncertainty, so using percentiles of the bootstrap distribution is better. Skew does not prove data errors or unbiasedness, and the number of resamples is unrelated.

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