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FRM Part II · FRM Exam Part II · Estimating Market Risk Measures: An Introduction and Overview

Two risk managers estimate VaR for the same portfolio from the same 1,000 daily returns. Manager A uses the 95% confidence level and Manager B uses the 99% level. Both use the same nonparametric quantile-standard-error method. Which statement is most accurate regarding the standard errors of their estimates?

The 99% VaR estimate has the larger standard error. Few observations lie near an extreme quantile, so the density at that point is low and the estimate is less precise. Using the same sample or the same order-statistic method does not equalize precision across confidence levels.

  1. AB's standard error is generally larger, because fewer observations lie near the 99% quantileCorrect
  2. BA's standard error is generally larger, because the 95% quantile is closer to the mean
  3. CThe standard errors are equal because the sample is the same
  4. DThe standard errors are identical because both quantiles are estimated by order statistics

Explanation

The standard error of a quantile depends on p(1-p)/n and on the density at the quantile. Deep in the tail the density is low, so fewer observations inform the estimate and the standard error is larger, despite the smaller p(1-p) term. The same sample does not imply the same precision.

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