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

A risk analyst bootstraps the mean of a sample of 40 returns using 1,000 resamples. The bootstrap means have an average of 0.80% and a standard deviation of 0.25%. Which statement about a bootstrap estimate of the standard error of the sample mean is correct?

The bootstrap standard error of the sample mean is the standard deviation of the bootstrapped means, which is 0.25%. No further division by the square root of the number of resamples or observations is needed, because the replications already reflect sampling variability.

  1. AThe standard error estimate is 0.25%Correct
  2. BThe standard error estimate is 0.25% / sqrt(1,000) = 0.0079%
  3. CThe standard error estimate is 0.80% / sqrt(40) = 0.126%
  4. DThe standard error estimate is 0.25% / sqrt(40) = 0.040%

Explanation

The standard deviation of the bootstrap replications of the statistic is itself the bootstrap estimate of the standard error. Dividing by sqrt(1,000) or sqrt(40) wrongly applies a further scaling, and the 0.80% is the mean, not a dispersion measure.

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