FRM Part I · FRM Exam Part I · Simulation and Bootstrapping
A bank uses a bootstrap with historical returns to estimate the standard error of a 99% VaR estimate. Which statement about the effect of the sample design on sampling error is most accurate?
More bootstrap resamples reduce only the simulation noise of the bootstrap calculation; the sampling error from the finite original dataset stays, because every resample is drawn from that same sample. The bootstrap also does not need normally distributed data.
- AIncreasing the number of bootstrap resamples from the same historical sample eliminates the sampling error from the limited original data.
- BIncreasing the number of bootstrap resamples reduces only the simulation error of the bootstrap estimate, while the error due to the finite original sample remains.Correct
- CBootstrap standard errors are invalid unless the original returns are normally distributed.
- DSampling error in a bootstrap depends only on the number of resamples, not on the size of the original sample.
Explanation
Bootstrap resamples are drawn from the one observed sample. More resamples reduce the Monte Carlo noise in the bootstrap estimate, but the information content is bounded by the original sample size, so its sampling error persists. The bootstrap does not require normality, which rules out the third option.
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