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

An analyst uses the standard (iid) bootstrap to estimate the 99% one-day VaR of a trading book from 500 historical daily P&L observations. Which limitation is most directly inherent to this method?

The bootstrap draws only from observed outcomes, so it cannot generate losses worse than the worst one in the sample. This limits its ability to capture extreme tail events, making tail-risk estimates such as 99% VaR dependent on whether the sample includes severe episodes.

  1. AIt can only produce losses at least as large as the worst loss observed in the sample, so tail estimates cannot extrapolate beyond the dataCorrect
  2. BIt requires the analyst to assume that returns are normally distributed
  3. CIt cannot be used when the sample size is smaller than the number of simulations
  4. DIt always overstates VaR because resampling with replacement duplicates large losses

Explanation

Bootstrapping resamples only from observed data, so no simulated value can exceed the worst observed loss. Extreme tail events not in the sample are therefore unrepresented. It does not need normality, and the number of replications can exceed the sample size without issue. Duplication does not systematically bias VaR upward.

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