Final answer:
The dollar-weighted average is typically the most precise measure for mutual fund performance when cash flows are irregular, while the geometric average accurately reflects long-term performance. The arithmetic average is simpler but less accurate for variable performance periods.
Step-by-step explanation:
When considering which measure best describes the performance of a mutual fund, we need to look at the arithmetic average, geometric average, and dollar-weighted average. The arithmetic average is simply the sum of returns in each period divided by the number of periods. It may give a clear picture if mutual fund performance is consistent over time. The geometric average takes into account the compounding effect of the returns and offers a more accurate measure of the fund's performance over time, particularly for long-term investments. The dollar-weighted average, also known as the internal rate of return (IRR), considers the timing and amount of all cash flows, making it the most accurate representation when additional purchases or redemptions have occurred.
To truly reflect the mutual fund's performance, especially if there are irregular cash flows, the dollar-weighted average may provide the best insight. However, for overall simplification and comparison purposes, the geometric average can be useful. Index funds, which aim to mimic the market performance, are often tracked against these averages for performance assessment.