FRM Part I · FRM Exam Part I · Measuring and Monitoring Volatility
The daily log returns of a portfolio are assumed i.i.d. with a standard deviation of 1.2% per day. Using the square-root-of-time rule with 252 trading days per year, what is the approximate annualized volatility?
Under i.i.d. returns, variance scales linearly with time, so volatility scales with the square root of time. Annualized volatility is 1.2% times the square root of 252, about 15.875, giving roughly 19.05%. Multiplying by 252 directly would wrongly scale the standard deviation linearly.
- A19.05%Correct
- B302.4%
- C14.40%
- D1.20%
Explanation
Annual volatility = 1.2% × sqrt(252) = 1.2% × 15.875 = 19.05%. Multiplying by 252 gives 302.4%, which scales volatility linearly instead of by the square root. 14.40% uses 12 as the multiplier, which would be a monthly count, and is wrong.
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