Explanation:
The historical volatility is the annualized standard deviation of past stock price movements. To get it, we apply the square root of time rule on the monthly volatility:
Annual volatility = 1 − month volatility × √12
= 0.05 × √12
= 0.1732
A is incorrect. The annual volatility is incorrectly scaled by multiplying by 12 instead of the square root of time, giving 12 × 0.05 = 0.6.
C and D are incorrect. The implied volatility of a stock isn't based on historical pricing. Instead, it represents the market's stock price forecast based on price changes in an option contract on the stock.
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Q.79 A newly employed risk analyst has embarked on analyzing the market risk of a stock in the automobile industry. After scouring the stock's return data gathered over the past 24 months, the analyst estimates the historical volatility of the monthly returns at 5%. Which of the following is most likely correct?
A
The volatility of the annual returns is 60%.
B
The volatility of the annual returns is 17.3%.
C
The implied volatility of the annual returns is 17.3%.
D
The implied volatility of the annual returns is 60%.