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

A sponsor has a total fund of $2 billion. Its policy benchmark VaR is determined by the policy mix, while managers add active risk. At the 95% confidence level (z = 1.645), the sponsor estimates an active (relative) annual tracking error of 2.0% of the fund. What is the relative (active) VaR in dollars, assuming normal returns and zero expected active return?

The relative VaR is about $65.8 million. It equals 1.645 times the 2% tracking error times the $2 billion fund. Using only the tracking error gives $40 million, which omits the confidence-level multiplier needed for a 95% VaR.

  1. A$65.8 millionCorrect
  2. B$40.0 million
  3. C$32.9 million
  4. D$131.6 million

Explanation

Relative VaR = 1.645 × 2.0% × $2,000m = $65.8m. $40m omits the z multiplier (2% × 2bn). $32.9m uses a 1% tracking error instead of 2%, and $131.6m doubles the result by mistake.

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