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

A risk analyst has a sample of 250 daily returns on a portfolio and wants to estimate the sampling variability of the 95% historical-simulation VaR without assuming a distribution for returns. Which description best matches the standard bootstrap procedure?

The standard bootstrap draws observations from the original sample with replacement to form many same-sized resamples, calculates the statistic (here VaR) on each, and studies the resulting distribution. This gives sampling variability without a distributional assumption, unlike parametric Monte Carlo simulation.

  1. ADraw 250 returns from the sample with replacement, compute the VaR on each resampled data set, and repeat many times to obtain a distribution of VaR estimatesCorrect
  2. BDraw 250 returns from the sample without replacement, compute VaR once, and use the sample standard deviation as its standard error
  3. CFit a normal distribution to the sample, then draw new returns from it using random numbers to compute VaR once
  4. DRemove the 5% worst returns from the sample and compute the average of the remaining returns as the VaR

Explanation

The bootstrap resamples the observed data with replacement to create many pseudo-samples of the same size, computes the statistic on each, and uses the resulting distribution to measure sampling error. Sampling without replacement at full size just reproduces the original sample every time. Fitting a normal distribution is a parametric Monte Carlo approach, not a bootstrap.

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