FRM Part I · FRM Exam Part I · The Black-Scholes-Merton Model
An analyst computes daily continuously compounded returns for a stock and finds a sample standard deviation of 1.5% per day. Assuming 252 trading days per year and independent returns, what is the estimated annualized volatility?
The annualized volatility is about 23.81%. Under independent returns, variance scales with time, so daily volatility is multiplied by the square root of 252 trading days: 1.5% times 15.8745 equals 23.81%.
- A23.81%Correct
- B18.90%
- C1.50%
- D37.80%
Explanation
Annualized volatility = daily standard deviation x sqrt(252) = 1.5% x 15.8745 = 23.81%. Using 252 instead of its square root (multiplying by 252) would give 378%, and dividing is wrong. Option 37.80% results from multiplying by 25.2, a scaling error.
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