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

A risk analyst bootstraps a sample of 500 daily portfolio losses to estimate 95% VaR. She draws 1,000 resamples (each of 500 observations, with replacement) and computes the 95% quantile of each, obtaining 1,000 VaR estimates with mean USD 2.40 million and standard deviation USD 0.30 million. Which statement is the most appropriate interpretation?

The standard deviation of the bootstrap VaR estimates, USD 0.30 million, approximates the standard error of the VaR estimate caused by sampling variation. It is not the loss volatility, and the mean of resamples does not reveal the true VaR, since the original sample's error persists.

  1. AThe USD 0.30 million is an estimate of the sampling variability (standard error) of the VaR estimateCorrect
  2. BThe USD 0.30 million is the daily volatility of portfolio losses
  3. CThe USD 2.40 million is the true population VaR, since 1,000 resamples remove all estimation error
  4. DThe USD 0.30 million is the model risk arising from choosing a wrong distribution

Explanation

The dispersion of the statistic across bootstrap resamples approximates its sampling error, so USD 0.30 million is the standard error of the VaR estimate. The bootstrap mean does not eliminate error from the original sample, and the method is non-parametric so it does not measure distributional model risk.

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