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

A portfolio manager decomposes the 95% one-day VaR of a three-desk portfolio into component VaRs. Which statement about component VaR is correct?

Component VaRs sum exactly to total portfolio VaR because VaR is homogeneous of degree one, so marginal VaR times position size allocates the total. Stand-alone VaR ignores diversification, and incremental VaR generally does not add up. Hedges can show negative components.

  1. AComponent VaRs of all positions sum to the total portfolio VaRCorrect
  2. BComponent VaR equals the VaR of each position computed on a stand-alone basis
  3. CComponent VaR is the difference between portfolio VaR with and without the position, and these differences sum to total VaR
  4. DComponent VaR is always positive for every position in a diversified portfolio

Explanation

Component VaR is marginal VaR times position size, and by Euler's theorem for a homogeneous degree-one risk measure the components add up to total VaR. Stand-alone VaR ignores diversification and does not sum to total. The with-and-without difference is incremental VaR, which generally does not sum to total. Hedging positions can have negative component VaR.

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