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

A risk manager has a one-day 95% VaR of USD 3.0 million for a portfolio with normally distributed returns and zero mean. Using z-values of 1.645 at 95% and 2.33 at 99%, and the square root of time rule, what is the approximate 10-day 99% VaR?

The 10-day 99% VaR is about USD 13.4 million. Converting the one-day 95% VaR to 99% gives roughly USD 4.25 million, and multiplying by the square root of 10 under the square root of time rule gives approximately USD 13.4 million.

  1. AUSD 13.4 millionCorrect
  2. BUSD 9.5 million
  3. CUSD 4.25 million
  4. DUSD 30.0 million

Explanation

Scale the confidence level: 3.0 x 2.33/1.645 = 4.25 million for one day at 99%. Then scale time: 4.25 x sqrt(10) = 4.25 x 3.162 = 13.4 million. USD 9.5 million only scales time (3.0 x 3.162) and ignores the confidence change.

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