Question

An investor purchased shares in a large cap mutual fund 5 years ago. The returns were 10%, 10%, 9%, 10%, and 11%, respectively. Which of the following statements regarding average returns is most accurate?

Select one:
A. The geometric average equals the arithmetic average.
B. The actual IRR the investor earned over the five years must equal the geometric mean percentage.
C. The standard deviation of returns is zero.
D. The arithmetic average is 10%.

Answer 1

The arithmetic average of the investor's mutual fund returns over 5 years is 10%, which matches option D. The arithmetic average is not equal to the geometric mean, and the standard deviation is not zero since the returns were not identical each year. The correct answer is option d.

Step-by-step explanation:

Understanding Average Returns in Mutual Fund Investments

An investor who purchased shares in a large cap mutual fund 5 years ago with annual returns of 10%, 10%, 9%, 10%, and 11% would need to calculate both the arithmetic average and the geometric average to understand the performance of their investment fully.

The arithmetic average of the returns is calculated by summing the percentage returns and dividing by the number of years. In this case, (10% + 10% + 9% + 10% + 11%) / 5 = 50% / 5 = 10%. Thus, the arithmetic average is indeed 10%, which corresponds to option D – The arithmetic average is 10%.

However, the arithmetic average is not necessarily the same as the geometric mean, which takes into account the effect of compounding. The standard deviation measures the variability of the returns, which in this case is not zero, because not all annual returns are the same. And the investor's actual internal rate of return (IRR) over five years will likely align with the geometric mean rather than the arithmetic average due to the effects of compounding.