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

A risk manager estimates 95% VaR by historical simulation from n independent observations. Which change would be expected to reduce the standard error of the VaR quantile estimate, holding the underlying distribution fixed?

Increasing the sample size reduces the standard error of the VaR quantile estimate. The error is proportional to the square root of p(1-p)/n divided by the density at the quantile, so more data shrinks it, while going further into the tail or using fewer observations enlarges it.

  1. AIncreasing the sample size nCorrect
  2. BMoving the confidence level from 95% to 99.9%
  3. CUsing a bin width of zero when estimating density at the quantile
  4. DReducing the sample size to focus on recent data only

Explanation

The standard error of a quantile estimate is sqrt(p(1-p)/n)/f(q), so it falls as n rises. Moving deeper into the tail lowers the density f(q) and raises the error. Fewer observations also raises the error.

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