FRM Part I · FRM Exam Part I · Simulation and Bootstrapping
A bank bootstraps a sample of 40 annual returns of a thinly traded emerging-market index to estimate the 95% confidence interval for mean return. A colleague argues the method is reliable because the bootstrap can generate thousands of replications. Which statement best assesses this claim?
Increasing replications only reduces the noise from resampling; it does not fix a small or unrepresentative original sample. The bootstrap can only reflect the 40 observations available, so its accuracy remains limited by the sample, not by the number of replications.
- ACorrect: with enough replications the bootstrap eliminates sampling error in the original sample
- BIncorrect: more replications reduce simulation noise only, but the bootstrap remains limited by how well the 40 observations represent the true distributionCorrect
- CCorrect: replications above 1,000 guarantee convergence to the true population distribution
- DIncorrect: the bootstrap requires at least 250 original observations to give any result
Explanation
Replications reduce Monte Carlo error in the bootstrap approximation, but the resampled distribution is still anchored to the 40 observed points. If they are unrepresentative, the bias persists regardless of replications. No guarantee or fixed minimum of 250 observations exists in the method.
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