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FRM Part II · FRM Exam Part II · Non-parametric Approaches

A risk analyst has 500 daily P&L observations and wants a confidence interval around the 95% historical simulation VaR. She resamples the 500 observations with replacement many times, computes VaR from each resampled set, and uses the distribution of those VaRs. Which description best captures the key feature of this bootstrap procedure?

The bootstrap resamples the original observations with replacement to form datasets of the same size, so some observations repeat and others are left out. The VaR from each resample forms a distribution used for confidence intervals, without assuming any parametric distribution.

  1. AEach resampled dataset is drawn without replacement so that every observation appears exactly once
  2. BEach resampled dataset has the same size as the original and can contain some observations several times and others not at allCorrect
  3. CEach resampled dataset is generated from a fitted normal distribution using the sample mean and standard deviation
  4. DEach resampled dataset is built by applying declining weights to older observations

Explanation

The bootstrap draws with replacement from the original sample, producing samples of the same size in which observations may repeat or be omitted. Sampling without replacement would simply reproduce the original data and give no variation. The normal and age-weighted options describe parametric and weighted approaches instead.

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