FRM Part II · FRM Exam Part II · VaR and Risk Budgeting in Investment Management
A fund has an annual tracking error of 4.0% against its benchmark and a portfolio value of USD 500 million. Assuming normally distributed active returns with zero mean, what is the approximate 95% (z = 1.645) one-year relative VaR?
Relative VaR equals the z-score times tracking error times portfolio value: 1.645 × 4% × USD 500 million, which is about USD 32.9 million. Tracking error is the standard deviation of active returns, so it is scaled by the confidence multiplier.
- AUSD 20.0 million
- BUSD 32.9 millionCorrect
- CUSD 8.2 million
- DUSD 3.3 million
Explanation
Relative VaR = 1.645 × 4.0% × USD 500 million = 1.645 × 20 million = USD 32.9 million. USD 20.0 million omits the z multiplier. USD 8.2 million wrongly divides by 4 (as if scaling by a time factor).
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