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

A portfolio manager models daily portfolio P/L as normally distributed with a mean of USD 0 and a standard deviation of USD 2 million. Using the standard normal critical value of 1.645 for 95% confidence, what is the one-day 95% VaR?

The one-day 95% VaR is USD 3.29 million. Under a normal distribution with zero mean, VaR equals the critical value 1.645 multiplied by the standard deviation of USD 2 million, which gives 3.29 million.

  1. AUSD 1.645 million
  2. BUSD 3.29 millionCorrect
  3. CUSD 2.00 million
  4. DUSD 4.58 million

Explanation

With zero mean, VaR = z x sigma = 1.645 x 2 million = 3.29 million. Option 1.645 million forgets to multiply by sigma. Using 2.00 million treats sigma as the VaR. 4.58 million wrongly uses 2.326 (99%) instead of 1.645.

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