FRM Part I · FRM Exam Part I · Measuring Return, Volatility, and Correlation
A risk analyst estimates that a stock's daily log-return volatility is 1.50%. Assuming returns are i.i.d. and there are 252 trading days in a year, what is the annualized volatility, to the nearest 0.01%?
Annualized volatility is about 23.81%. Under i.i.d. returns, variance scales linearly with time, so volatility scales with the square root of time. Multiplying the 1.50% daily figure by the square root of 252, about 15.8745, gives 23.81%.
- A23.81%Correct
- B18.90%
- C378.00%
- D5.67%
Explanation
Annual volatility = daily volatility x sqrt(252). sqrt(252) = 15.8745, so 1.50% x 15.8745 = 23.81%. Multiplying by 252 instead of its square root gives 378%, which wrongly scales volatility linearly rather than variance.
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