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

An analyst computes a VaR from a large sample using the order-statistic approach. The estimated VaR is USD 4.00 million and its standard error is USD 0.25 million. Assuming the estimator is approximately normal, what is the approximate 95% confidence interval for the true VaR (use 1.96 as the critical value)?

The approximate 95% confidence interval is USD 3.51 million to USD 4.49 million. It is the estimate plus or minus 1.96 times the standard error: 4.00 ± 1.96 × 0.25 = 4.00 ± 0.49. Using one standard error or the one-tailed 1.645 value would give intervals that are too narrow.

  1. AUSD 3.51 million to USD 4.49 millionCorrect
  2. BUSD 3.75 million to USD 4.25 million
  3. CUSD 3.18 million to USD 4.82 million
  4. DUSD 3.59 million to USD 4.41 million

Explanation

Interval = estimate ± 1.96 × SE = 4.00 ± 1.96×0.25 = 4.00 ± 0.49, giving 3.51 to 4.49. Option B uses one standard error (about 68%). Option C uses 3.29 SE (wrong multiplier). Option D uses 1.645 × SE, the one-tailed value.

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