FRM Part I · FRM Exam Part I · Measuring and Monitoring Volatility
A stock priced at $100 has an annualized volatility of 20%. Assuming 256 trading days per year and i.i.d. returns, what is the approximate one-standard-deviation daily price move in dollars?
Daily volatility equals annual volatility divided by the square root of the number of trading days: 20% divided by 16 is 1.25%. On a $100 stock this is a one-standard-deviation move of about $1.25. Dividing by 256 directly or using variance gives wrong figures.
- A$0.08
- B$1.25Correct
- C$1.56
- D$5.00
Explanation
Daily volatility = 20% / √256 = 20% / 16 = 1.25%, which on a $100 price is $1.25. Dividing by 256 instead of its square root gives 0.08%, or $0.08. Dividing the variance (400) by 256 gives 1.5625, which is a mixed-up variance figure. Dividing by 4 gives $5.00, which is wrong.
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