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:

Average Return=12.39+(16.28)+21.62+20.034\text{Average Return} = \frac{12.39 + (-16.28) + 21.62 + 20.03}{4}

Calculating the sum:

12.3916.28+21.62+20.03=37.7612.39 - 16.28 + 21.62 + 20.03 = 37.76

Then, divide by 4:

Average Return=37.764=9.44%\text{Average Return} = \frac{37.76}{4} = 9.44\%

Answer: 9.44%

Do you want further details, or do you have any questions?


Here are 5 related questions for further exploration:

  1. What is the difference between the arithmetic average and the geometric average return?
  2. How would the calculation change if one year had a return of 0%?
  3. Why might an investor prefer to look at the geometric average return over the arithmetic average?
  4. How would this average return compare to a stock that had a constant return of 9.44% each year?
  5. 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