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Answer :
The arithmetic average return is 6.25 percent and the geometric average return is 5.89 percent
What is the arithmetic and geometric average return?
The arithmetic average return can be determined by adding the stock returns together and dividing it by the total annual returns that is provided.
Arithmetic average return = sum of returns / total number of returns
(4 + 9 - 6 + 18) / 4
= 25 / 4 = 6.25 percent
The geometric average return is used to determine the compound growth rate.
Geometric average return= [(1 + return) x (1 + return) x (1 + return) + (1 + return)]^(1/n) -
Where:
n = number of returns provided
[(1.04) x (1.09) x (0.94) x (1.18)]^(1/4) - 1 = 0.0589 = 5.89%
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Final answer:
The arithmetic average return for the stock is 6.25%, and the geometric average return is 5.89%.
Explanation:
To calculate the arithmetic average return, we simply take the sum of the individual yearly returns and divide by the number of years.
Arithmetic average return = (4% + 9% - 6% + 18%) / 4 = 25% / 4 = 6.25%.
To calculate the geometric average return, we multiply the returns, represented as decimal numbers, and then take the fourth root (since there are four years of returns), subtract one and then convert it back to a percentage.
Geometric average return = [(1.04) × (1.09) × (0.94) × (1.18)]^(1/4) - 1 = 1.0589 - 1 = 0.0589, or 5.89%.
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