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

A portfolio has a one-day 99% VaR of USD 2.0 million, estimated under normality with zero mean. A risk manager wants the 10-day 99% VaR using the square-root-of-time rule. What is the result (to the nearest USD 0.01 million)?

The 10-day VaR is about USD 6.32 million. With zero-mean, independent normal returns, VaR grows with the square root of time, so the one-day figure of 2.0 million is multiplied by the square root of ten, roughly 3.162.

  1. AUSD 6.32 millionCorrect
  2. BUSD 20.00 million
  3. CUSD 2.00 million
  4. DUSD 3.16 million

Explanation

Under iid normal returns with zero mean, VaR scales with the square root of the horizon: 2.0 × √10 = 2.0 × 3.1623 = 6.32 million. Multiplying by 10 (20.00) wrongly scales linearly; 3.16 is just √10 without the base VaR.

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