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

An analyst bootstraps a 95% VaR for a portfolio and finds that the standard error of the bootstrapped VaR is large relative to the VaR itself. Which action would most directly reduce this estimation uncertainty in the underlying historical simulation?

Collecting more historical observations is the most direct way to cut estimation uncertainty, because the quantile is then estimated from more data. More bootstrap resamples only smooth the bootstrap distribution, and a higher confidence level makes tail estimates less precise.

  1. AIncreasing the number of bootstrap resamples from 1,000 to 100,000 only
  2. BLowering the confidence level from 95% to 99%
  3. CIncreasing the number of historical observations in the original sampleCorrect
  4. DReplacing P&L observations with their absolute values

Explanation

Sampling error in the VaR quantile falls as the original sample grows, as more data supports the tail estimate. More resamples only make the bootstrap distribution smoother and do not add information. Moving to 99% puts the quantile further into the sparse tail and raises error. Using absolute values distorts the loss distribution.

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