Math Problem Statement
Sharif's portfolio generated returns of 10 percent, 9 percent, −2 percent, and 6 percent over four years. What was his average return over this period?
Solution
To calculate Sharif's average return over the four-year period, you need to find the arithmetic mean of the four annual returns.
The formula for the average return is:
Given the returns:
Let's calculate the sum of these returns:
Now, divide the sum by the number of years (4 years):
So, Sharif's average return over the four-year period was 5.75%.
Would you like more details on this calculation, or do you have any other questions?
Here are 5 related questions you might find useful:
- How does the arithmetic mean differ from the geometric mean in calculating average returns?
- What would Sharif's average return be if one of the returns were negative?
- How would the average return change if we added a fifth year with a 15% return?
- What is the importance of considering average returns over multiple years?
- How does variance in returns affect the risk profile of a portfolio?
Tip: When calculating average returns for investments, it's important to distinguish between arithmetic and geometric means, especially for volatile returns. The geometric mean is generally more accurate for understanding compounded growth rates over time.
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Math Problem Analysis
Mathematical Concepts
Arithmetic Mean
Percentage Calculations
Formulas
Arithmetic Mean Formula
Theorems
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Suitable Grade Level
Grades 9-12
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