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FRM Part I · FRM Exam Part I · Calculating and Applying VaR

A risk manager computes a one-day 95% VaR for a portfolio worth USD 50 million with a daily return standard deviation of 2% and zero mean, assuming normality (z = 1.645). The manager then increases the confidence level to 99% (z = 2.33) with the same data. By how much does VaR increase, to the nearest USD 0.01 million?

VaR rises by about USD 0.69 million. The 95% VaR is 1.645 × 2% × 50 million = 1.645 million, while the 99% VaR is 2.33 × 2% × 50 million = 2.33 million, and the difference is roughly 0.685 million.

  1. AUSD 0.69 millionCorrect
  2. BUSD 1.65 million
  3. CUSD 2.33 million
  4. DUSD 0.34 million

Explanation

95% VaR = 1.645 × 2% × 50m = USD 1.645m. 99% VaR = 2.33 × 2% × 50m = USD 2.33m. The increase is 2.33 − 1.645 = USD 0.685m, about 0.69m. USD 1.65m and 2.33m are the individual VaR figures, not the difference.

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