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FRM Part I · FRM Exam Part I · Measures of Financial Risk

Which change would most directly reduce the standard error of a historical-simulation 99% VaR estimate, holding the true return distribution fixed?

Increasing the number of independent observations lowers the standard error of the estimated quantile, because the error scales with one over the square root of n. Moving further into the tail reduces the density at the quantile and increases error, while smaller samples also worsen precision.

  1. AMoving from 99% to 99.9% confidence with the same sample
  2. BIncreasing the number of independent observations in the sampleCorrect
  3. CReplacing the 99% VaR with the 98% VaR and reporting it as 99%
  4. DUsing a sample window with fewer but more volatile observations

Explanation

The quantile standard error is sqrt(p(1-p)/n)/f(q), so it falls with larger n. Moving to 99.9% pushes into the tail where the density f(q) is smaller, which raises the error. Using fewer observations also raises it.

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