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FRM Part II · FRM Exam Part II · VaR and Risk Budgeting in Investment Management

A fund has a portfolio value of USD 200 million and a 1-day 99% VaR of USD 4.0 million. Position A is USD 80 million and has a beta to the portfolio of 1.25 (beta = cov(R_A, R_P)/var(R_P)). Using the parametric approach, what is the component VaR of Position A?

The component VaR of Position A is USD 2.0 million. It equals the weight (40%) times its beta to the portfolio (1.25) times the total VaR of USD 4.0 million. Ignoring beta would give USD 1.6 million, understating its risk contribution.

  1. AUSD 2.0 millionCorrect
  2. BUSD 1.6 million
  3. CUSD 4.0 million
  4. DUSD 2.5 million

Explanation

Component VaR = w_A x beta_A x VaR = (80/200) x 1.25 x 4.0 = 0.4 x 1.25 x 4.0 = USD 2.0 million. Using 0.4 x 4.0 = 1.6 ignores beta (the weight-only error). Check: a beta of 1.25 means the position contributes more than its weight share of risk, so 50% of VaR is plausible.

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