A stock price is 20, 22, 19, 21, 24, and 24 on six successive Fridays. Which of the following is closest to the volatility per annum estimated from this data?
A. 50%
B. 60%
C. 70%
D. 80%
D
The price relative for the first week is 22/20 or 1.1 . The natural log of the price relative is ln(1.1) or 0.09531 . Similarly the ln of the price relatives for the other weeks are -0.1466, 0.1001, 0.1335, and 0 . The standard deviation of 0.09531, -0.1466, 0.1001, 0.1335, and 0 is 0.1138 . The volatility per week is therefore 11.38%. This corresponds to a volatility per year of 0.1138 multiplied by the square root of 52 or about 82%. The answer is therefore D.
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