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

A risk manager compares standard historical simulation with bootstrap historical simulation for a 99% VaR on a portfolio with a short 250-day window. Which statement about the bootstrap is most accurate?

Bootstrap historical simulation only reshuffles observations already in the sample, so if the 250-day window lacks stress events the bootstrapped VaR will still understate tail risk. It improves the assessment of sampling error but cannot create new, more extreme losses or fix an unrepresentative window.

  1. AIt removes the dependence on historical data and so eliminates the problem of an unrepresentative sample
  2. BIt can create observations more extreme than any in the original sample, improving tail coverage
  3. CIt still relies on the original sample, so if the window omits stress events the bootstrap VaR will also understate tail riskCorrect
  4. DIt is guaranteed to produce a higher VaR than the original estimate

Explanation

Resampling only reuses the observed data, so it cannot add losses worse than those observed or reflect regimes absent from the window. It improves estimate of sampling precision, not representativeness. The bootstrap mean can be above or below the original VaR, so no guarantee holds.

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