FRM Part II · FRM Exam Part II · Portfolio Risk: Analytical Methods
A portfolio manager reports a one-day 99% parametric VaR of USD 2.0 million for a portfolio with normally distributed returns and zero mean. Using the square-root-of-time rule, what is the approximate 10-day 99% VaR?
The 10-day VaR is about USD 6.32 million, because with zero-mean, independent, normal returns VaR scales with the square root of time: 2.0 million times the square root of 10. Multiplying by 10 would overstate risk.
- AUSD 6.32 millionCorrect
- BUSD 20.0 million
- CUSD 2.0 million
- DUSD 3.16 million
Explanation
Under iid normal returns with zero mean, VaR scales with the square root of time. 2.0 x sqrt(10) = 2.0 x 3.1623 = 6.32 million. Multiplying by 10 would wrongly assume perfect serial correlation, and 3.16 is sqrt(10) without the 2.0 scaling.
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