FRM Part I · FRM Exam Part I · The Black-Scholes-Merton Model
A trader computes historical volatility from daily continuously compounded returns of a stock. The sample standard deviation of daily log returns is 1.5%. Assuming 252 trading days per year, what is the annualized volatility closest to?
The annualized volatility is about 23.8%. Variance scales linearly with time, so daily volatility is multiplied by the square root of 252 (about 15.875), giving 1.5% x 15.875 = 23.8%. Multiplying by 252 would incorrectly scale volatility linearly.
- A23.8%Correct
- B1.5%
- C18.9%
- D378.0%
Explanation
Annualized volatility = daily standard deviation x sqrt(252) = 1.5% x 15.875 = 23.8%. Multiplying by 252 instead of its square root gives 378%, which wrongly scales volatility linearly with time. Using sqrt(252) is correct because variance grows linearly in time.
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