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

A trader holds a position whose daily P/L is normally distributed with mean USD 0.5 million and standard deviation USD 4 million. Using z = 2.326 for 99% confidence, what is the one-day 99% VaR, defined as the loss relative to zero P/L?

The 99% VaR is about USD 8.80 million. A positive expected profit reduces the loss quantile, so VaR equals 2.326 times 4 million, which is 9.304 million, minus the mean of 0.5 million.

  1. AUSD 9.30 million
  2. BUSD 8.80 millionCorrect
  3. CUSD 9.80 million
  4. DUSD 2.33 million

Explanation

VaR = -mu + z x sigma = -0.5 + 2.326 x 4 = -0.5 + 9.304 = 8.80 million (rounded). Adding the mean gives 9.80, a sign error. Ignoring the mean gives 9.30. 2.33 omits sigma scaling.

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