Math Problem Statement
You own a stock that had returns of 12.39 percent, −16.28 percent, 21.62 percent, and 20.03 percent over the past four years. What was the arithmetic average return for this stock?
Multiple Choice
10.23%
9.82%
8.26%
9.44%
8.85%
Solution
To find the arithmetic average return, we add up all the yearly returns and divide by the number of years. Here are the returns:
- Year 1: 12.39%
- Year 2: -16.28%
- Year 3: 21.62%
- Year 4: 20.03%
The arithmetic average return is calculated as:
Calculating the sum:
Then, divide by 4:
Answer: 9.44%
Do you want further details, or do you have any questions?
Here are 5 related questions for further exploration:
- What is the difference between the arithmetic average and the geometric average return?
- How would the calculation change if one year had a return of 0%?
- Why might an investor prefer to look at the geometric average return over the arithmetic average?
- How would this average return compare to a stock that had a constant return of 9.44% each year?
- What does a negative return in a year imply about the stock’s performance that year?
Tip: The arithmetic average is useful for understanding average performance over time but does not account for compounding effects like the geometric average does.
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Math Problem Analysis
Mathematical Concepts
Statistics
Arithmetic Average
Percentages
Formulas
Arithmetic Average Return = (Sum of Returns) / Number of Years
Theorems
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Suitable Grade Level
Grades 9-12
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