FRM Part I · FRM Exam Part I · Simulation and Bootstrapping
An analyst has a sample of 50 independent daily returns and wants to estimate the standard error of the sample median using the bootstrap. Which procedure is correct?
The bootstrap draws many same-sized resamples with replacement from the observed data, computes the median for each, and uses the standard deviation of those medians as the standard error estimate. Without replacement, full-size draws would reproduce the original sample and show no variability.
- ADraw many samples of 50 returns with replacement from the original sample, compute the median of each, and take the standard deviation of these mediansCorrect
- BDraw many samples of 50 returns without replacement from the original sample, compute the median of each, and take the standard deviation of these medians
- CDraw many samples of 50 values from a normal distribution fitted to the sample mean only, and average their medians
- DDraw one resample of 50 returns with replacement and divide its standard deviation by the square root of 50
Explanation
The bootstrap resamples with replacement from the observed data, same size as the original, repeats many times, and computes the statistic each time. The standard deviation of the bootstrap statistics estimates its standard error. Sampling without replacement at full size would just reproduce the original sample every time, giving zero variation.
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