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

A risk analyst computes a one-day 99% normal VaR of USD 2.33 million for a portfolio with zero mean. The analyst needs a 10-day 99% VaR, assuming i.i.d. normal returns and zero mean. Approximately what is the 10-day VaR?

Under i.i.d. normal returns with zero mean, VaR grows with the square root of the horizon. Multiplying USD 2.33 million by the square root of 10 (about 3.162) gives roughly USD 7.37 million. Linear scaling by 10 would overstate risk.

  1. AUSD 7.37 millionCorrect
  2. BUSD 23.3 million
  3. CUSD 5.43 million
  4. DUSD 2.56 million

Explanation

With zero mean and i.i.d. returns, VaR scales with the square root of time: 2.33 * sqrt(10) = 2.33 * 3.162 = 7.37 million. Multiplying by 10 gives 23.3 million, which wrongly scales linearly. 5.43 is 2.33 squared, and 2.56 is not a valid scaling.

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