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

A historical simulation uses a bootstrap of 10 days of returns to build a 10-day return path by sampling daily returns with replacement from a sample of 250 daily returns. Compared with using the actual 250 returns in time order, which limitation is most relevant to this approach?

The main limitation is that the iid bootstrap treats observations as independent draws, so it destroys serial dependence like volatility clustering in the original data. It does not require normality and does not systematically overstate tail risk, though it cannot create losses worse than observed.

  1. AIt destroys any serial dependence such as volatility clustering, because observations are treated as independent drawsCorrect
  2. BIt cannot produce any value not equal to a sample average
  3. CIt requires the returns to be normally distributed
  4. DIt always overstates tail risk because it uses sampling with replacement

Explanation

The iid bootstrap shuffles observations randomly, so any time dependence (autocorrelation, volatility clustering) in the original data is lost. It does not assume normality, and it does not systematically overstate tail risk; it simply cannot generate losses beyond those observed.

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