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FRM Part II · FRM Exam Part II · Portfolio Risk: Analytical Methods

A portfolio worth USD 200 million has a daily volatility of 1.0%. A position of USD 50 million in Asset X has a beta of 1.2 with respect to the portfolio. Using a 95% confidence level (z = 1.645) under normality, what is the component VaR of Asset X?

Component VaR is about USD 0.99 million. Portfolio VaR is 1.645 times 1% times 200 million, or 3.29 million. Multiplying by the asset's weight of 25% and its beta of 1.2 to the portfolio gives roughly 0.99 million.

  1. AUSD 0.99 millionCorrect
  2. BUSD 0.82 million
  3. CUSD 1.23 million
  4. DUSD 3.29 million

Explanation

Portfolio VaR = 1.645 x 1.0% x 200 = 3.29 million. Component VaR = position weight x beta x portfolio VaR = (50/200) x 1.2 x 3.29 = 0.987, about 0.99 million. Omitting beta gives 0.82; using 1.2 x 1.0... without the weight gives 3.29 x 1.2 = 3.95 which is wrong; 1.23 comes from using the wrong base.

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