FRM Part I · FRM Exam Part I · Calculating and Applying VaR
A portfolio manager estimates a one-day 99% VaR of USD 2.0 million using a normal distribution. Assuming zero mean and independent daily returns, what is the approximate 10-day 99% VaR?
The 10-day VaR is about USD 6.32 million. With zero mean and independent returns, VaR scales with the square root of time, so 2.0 million multiplied by the square root of 10, about 3.162, gives 6.32 million. Multiplying by 10 would be wrong.
- AUSD 6.32 millionCorrect
- BUSD 20.0 million
- CUSD 4.47 million
- DUSD 2.00 million
Explanation
Under the square-root-of-time rule, 10-day VaR = 2.0 x sqrt(10) = 2.0 x 3.1623 = USD 6.32 million. Multiplying by 10 would ignore diversification across time and overstate VaR. Using sqrt(5) gives 4.47, which is the wrong time scaling.
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