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Answer: The volatility of the annual returns is 15.6%
The correct answer is C, which states that the volatility of the annual returns is 15.6%. This is calculated by taking the square root of time, in this case, the square root of 12 months, and multiplying it by the historical volatility of the monthly returns, which is 4.5%. The calculation is as follows: \( \sqrt{12} \times 0.045 = 0.156 \). Option A and B are incorrect because implied volatility is derived from the market price of an option and is not directly related to historical volatilities. Implied volatility is a forward-looking measure of expected volatility and is used by traders and investors to price options. Option D is incorrect because it scales the volatility linearly with time instead of using the square root of time. The linear scaling would be \( 12 \times 0.045 = 0.54 \), which is not the correct method for annualizing monthly volatility. The question tests the understanding of the difference between historical volatility and implied volatility, as well as the correct method for annualizing monthly volatility by using the square root of time. This is an important concept in quantitative analysis for risk management and financial modeling.
Author: LeetQuiz Editorial Team
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A financial analyst is concerned about the market risk pertaining to a specific stock. After examining the stock's performance over the previous year, the analyst has determined that the historical volatility of its monthly returns is 4.5%. Based on this information, which of the following statements is most likely accurate?
A
The implied volatility of the annual returns is 15.6%.
B
The implied volatility of the annual returns is 54.0%.
C
The volatility of the annual returns is 15.6%
D
The volatility of the annual returns is 54.0%.
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