Math Problem Statement
What are the arithmetic and geometric average returns for a stock with annual returns of 4 percent, 9 percent, −5 percent, and 17 percent?
Multiple Choice
6.25%; 5.95%
8.63%; 5.95%
5.95%; 6.25%
6.25%; 8.63%
8.63%; 6.25%
Solution
To solve for the arithmetic and geometric average returns, let’s go through each one:
Arithmetic Average Return
The arithmetic average return is simply the sum of the returns divided by the number of periods.
Given returns:
Geometric Average Return
The geometric average return is calculated as the -th root of the product of values, minus 1, where is each annual return and is the number of periods.
Calculating this step-by-step:
Now, multiplying them:
Taking the fourth root:
Subtracting 1:
Answer
The correct answer is:
6.25%; 5.95%
Would you like further details or have any questions?
Related Questions:
- How do you interpret the difference between arithmetic and geometric average returns?
- Why might an investor prefer the geometric mean over the arithmetic mean?
- How would the averages change if there was a negative return greater than 17%?
- What would the effect of compounding be on these averages over more years?
- How do arithmetic and geometric returns differ in interpreting stock volatility?
Tip: Arithmetic returns are useful for estimating average short-term performance, while geometric returns are better for understanding compounded growth over time.
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Math Problem Analysis
Mathematical Concepts
Arithmetic Average
Geometric Average
Stock Returns
Formulas
Arithmetic Average = (Sum of returns) / (Number of periods)
Geometric Average = (Product of (1 + each return))^(1/Number of periods) - 1
Theorems
Arithmetic Mean
Geometric Mean
Suitable Grade Level
Undergraduate Finance or Business Studies
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