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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 95% VaR of USD 1.5 million under a normal, zero-mean, i.i.d. assumption (z at 95% = 1.645). Using the square-root-of-time rule, what is the approximate 10-day VaR at the 99% confidence level (z at 99% = 2.326)?

The 10-day 99% VaR is about USD 6.71 million. Back out daily volatility of about 0.912 million from the 95% VaR, multiply by 2.326 to get a 99% one-day VaR of 2.12 million, then scale by the square root of 10.

  1. AUSD 6.71 millionCorrect
  2. BUSD 4.74 million
  3. CUSD 2.12 million
  4. DUSD 15.0 million

Explanation

Daily sigma = 1.5/1.645 = 0.9119 million. The 1-day 99% VaR = 2.326 x 0.9119 = 2.121 million. The 10-day VaR = 2.121 x sqrt(10) = 2.121 x 3.162 = 6.71 million. The 4.74 figure results from scaling by sqrt(5) instead; 2.12 omits the horizon scaling.

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