FRM Part I · FRM Exam Part I · Calculating and Applying VaR
A risk manager scales a one-day 99% parametric VaR of USD 2 million to a 10-day horizon, assuming i.i.d. normal returns with zero mean. What is the 10-day VaR?
The 10-day VaR is about USD 6.32 million. With i.i.d. normal returns and zero mean, VaR scales with the square root of time, so USD 2 million times the square root of 10 applies. Multiplying by 10 would wrongly overstate the risk.
- AUSD 6.32 millionCorrect
- BUSD 20.0 million
- CUSD 3.16 million
- DUSD 0.63 million
Explanation
Under the square-root-of-time rule, 10-day VaR = 2 million x sqrt(10) = 2 x 3.162 = USD 6.32 million. Multiplying by 10 gives USD 20 million, which wrongly assumes perfect serial correlation. USD 3.16 million is sqrt(10) x 1 and not based on the data.
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