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

An analyst estimates the 99% one-day VaR of a portfolio using the bootstrap, resampling with replacement from 250 historical daily returns that include no market crash. Which limitation is most directly illustrated?

The bootstrap can only reproduce values already in the historical sample, so it cannot generate losses worse than any observed. A sample without a crash will therefore understate tail risk and VaR. It does not need normality, and replications are not limited to the sample size.

  1. ABootstrap samples can contain only values that appear in the original data, so losses worse than any observed cannot be generatedCorrect
  2. BBootstrap requires the returns to follow a normal distribution
  3. CBootstrap cannot be repeated more than 250 times
  4. DBootstrap always overstates tail risk because of replacement

Explanation

The bootstrap draws only from the observed sample, so its simulated outcomes cannot exceed the worst observed loss. If the history has no crash, the tail risk will be understated. It is non-parametric, so normality is not required, and the number of replications is not limited by sample size.

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