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

A risk manager runs a bootstrap on 1,000 historical losses to estimate 95% VaR. She generates 200 bootstrap samples, each of size 1,000, and computes the 95% VaR for each. She wants a single best point estimate of VaR from the bootstrap. Which approach is consistent with the standard bootstrap method?

Use the average of the 200 bootstrap VaR estimates. The bootstrap point estimate is the mean across resamples, which reduces sampling noise compared with a single sample, whereas picking the maximum or one sample introduces bias or discards information.

  1. ATake the average of the 200 bootstrap VaR estimatesCorrect
  2. BTake the largest of the 200 bootstrap VaR estimates as the conservative estimate
  3. CTake the VaR from the first bootstrap sample only
  4. DTake the sum of the 200 VaR estimates divided by 1,000

Explanation

The bootstrap estimate of the quantile is the mean of the VaRs from the resampled datasets, which is typically more precise than a single sample estimate. Using the maximum biases the estimate upward. Using one sample wastes the information, and dividing by 1,000 is meaningless.

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