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

A risk analyst at a bank has 500 daily P&L observations and wants a confidence interval around the 99% historical simulation VaR. She resamples the 500 observations with replacement many times, forming a new sample of 500 each time and computing the 99% VaR for each. What does the bootstrap procedure primarily provide?

The bootstrap generates many resampled datasets drawn with replacement from the original observations and computes VaR for each. The resulting distribution of VaR estimates yields a standard error and confidence interval, so it measures estimation precision without assuming any parametric return distribution.

  1. AA distribution of VaR estimates from which a standard error and confidence interval can be derivedCorrect
  2. BA VaR estimate that gives more weight to recent observations
  3. CA VaR estimate that assumes returns are normally distributed
  4. DA VaR estimate adjusted for current volatility using a GARCH model

Explanation

Bootstrapping resamples the original data with replacement, producing many VaR estimates. The spread of these estimates gives a standard error and confidence interval. Age weighting and volatility adjustment are different refinements, and the bootstrap is non-parametric so it makes no normality assumption.

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