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

A portfolio worth USD 200 million has a 1-day 99% delta-normal VaR of USD 5.0 million. Asset A is USD 50 million of the portfolio and has beta of 1.2 relative to the portfolio (beta = cov(Ra,Rp)/var(Rp)). What is the component VaR of Asset A?

Component VaR of Asset A is USD 1.50 million. It equals the asset's portfolio weight of 25% multiplied by its beta of 1.2 to the portfolio and by total VaR of USD 5.0 million. Weight alone would give 1.25 million, ignoring its above-average contribution to portfolio risk.

  1. AUSD 1.25 million
  2. BUSD 1.50 millionCorrect
  3. CUSD 2.08 million
  4. DUSD 6.00 million

Explanation

Component VaR = w × beta × portfolio VaR = (50/200) × 1.2 × 5.0 = 1.5 million. Using weight alone ignores the beta (1.25). Beta times VaR without weight gives 6.0.

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