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

A risk manager compares a standard historical simulation VaR with the bootstrapped VaR (the average of VaR estimates across resamples) at the 99% level using only 250 observations. Which statement best describes the expected relationship and reason?

The bootstrapped VaR is usually more stable because averaging across resamples smooths the dependence on the few extreme observations that set the 99% cut-off in a small sample. It does not add genuinely new information or scenarios, and is not systematically larger.

  1. AThe bootstrapped estimate is typically more stable because averaging smooths the sensitivity to which single observation is the cut-off quantileCorrect
  2. BThe bootstrapped estimate must be identical because resampling adds no new information
  3. CThe bootstrapped estimate will always be larger because resampling with replacement duplicates losses
  4. DThe bootstrapped estimate removes the need for a long sample because it creates new market scenarios not seen in the data

Explanation

With 250 points, the 99% VaR depends on the 2nd or 3rd worst loss, which is noisy. Averaging across resamples smooths this, so the estimate is usually more precise. It is not identical in general, not always larger, and it cannot generate scenarios beyond those observed in the sample.

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