Question

An investment produced annual rates of return of 5%, 12%, 8%, and 11% respectively over the past four years. What is the standard deviation of these returns? (Hint: Find the average return, then calculate its standard deviation. You can use the Excel function to solve it too.)

A) Approximately 2.26%
B) Approximately 2.84%
C) Approximately 2.71%
D) Approximately 2.05%

Answer 1

To find the standard deviation of the returns, calculate the average return, subtract each return from the average, square the result, calculate the average of the squared differences, and take the square root of this average. The standard deviation of these returns is approximately 2.74%.

Step-by-step explanation:

To find the standard deviation of a set of returns, we need to first calculate the average return. Then, we subtract each return from the average, square the result, and calculate the average of the squared differences. Finally, we take the square root of this average to get the standard deviation.

Let's calculate step by step:

1. Add up all the returns: 5% + 12% + 8% + 11% = 36%
2. Divide the sum by the number of returns to get the average: 36% / 4 = 9%
3. Subtract the average from each return and square the result:
   • (5% - 9%)² = 16%
   • (12% - 9%)² = 9%
   • (8% - 9%)² = 1%
   • (11% - 9%)² = 4%
4. Add up the squared differences: 16% + 9% + 1% + 4% = 30%
5. Divide the sum by the number of returns: 30% / 4 = 7.5%
6. Take the square root of the result: sqrt(7.5%) ≈ 2.74%

Therefore, the standard deviation of these returns is approximately 2.74%.