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

A risk team estimates the 95% VaR of a portfolio and obtains USD 10.0 million. They then compute a 90% confidence interval of USD 8.5 million to USD 11.5 million. The team's head then asks for a 99% confidence interval for the same VaR, using the same sample and normal approximation (critical values 1.645 for 90% and 2.576 for 99%). What is the approximate 99% interval?

The approximate 99% interval is USD 7.65 million to USD 12.35 million. The 90% half-width of 1.5 implies a standard error of about 0.912, and multiplying by 2.576 gives a half-width of about 2.35 around the USD 10.0 million estimate. Using the 95% multiplier would understate the width.

  1. AUSD 7.65 million to USD 12.35 millionCorrect
  2. BUSD 8.01 million to USD 11.99 million
  3. CUSD 7.07 million to USD 12.93 million
  4. DUSD 6.50 million to USD 13.50 million

Explanation

The 90% half-width is 1.5 = 1.645 × SE, so SE ≈ 0.912. The 99% half-width = 2.576 × 0.912 ≈ 2.349, but equivalently 1.5 × 2.576/1.645 = 2.349. Hmm: this gives 10 ± 2.35 = 7.65 to 12.35. Option B scales by 1.96/1.645 (95% instead of 99%). Option C uses a multiplier of 3.29/1.645 (wrong ratio of about 2.0). Option D adds a flat 1.0 million.

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