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

A desk's estimated one-day 99% VaR is 3.00% of portfolio value, with an estimated standard error of 0.20%. Assuming the estimator is approximately normally distributed, which is the 95% confidence interval for the true VaR?

The interval is roughly 2.61% to 3.39%. For a two-sided 95% confidence interval under approximate normality, add and subtract 1.96 standard errors, which is 1.96 x 0.20% = 0.392%, around the 3.00% estimate.

  1. A2.61% to 3.39%Correct
  2. B2.67% to 3.33%
  3. C2.80% to 3.20%
  4. D2.40% to 3.60%

Explanation

A 95% two-sided interval uses 1.96 standard errors: 1.96 x 0.20% = 0.392%. The interval is 3.00% ± 0.392%, or 2.61% to 3.39%. The 2.67%-3.33% option wrongly uses 1.645, the one-sided 95% value, and 2.40%-3.60% uses 3 standard errors.

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