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

Which statement about estimating VaR and expected shortfall (ES) from a finite sample is most accurate?

ES is usually more sensitive to sampling error than VaR at the same confidence level because it relies on the few extreme tail observations, which are sparse and volatile. Precision of quantile estimates worsens, not improves, at higher confidence levels because the tail density is lower.

  1. AES estimated from the tail is typically more sensitive to sampling error than VaR at the same confidence level because it depends on extreme observationsCorrect
  2. BES is always estimated with lower standard error than VaR because it averages many values
  3. CVaR estimates become more precise as the confidence level is raised toward 100% for a fixed sample size
  4. DThe standard error of a quantile estimate does not depend on the density at the quantile

Explanation

ES averages tail losses, which are sparse and highly variable, so its estimate is typically noisier than the VaR quantile at the same level. Quantile error rises as confidence increases because density falls, and it depends directly on the density at the quantile.

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