A hypothetical value rises by 10% in one period and falls by 10% in the next. The arithmetic average of those two rates is zero. Yet a starting value of 100 finishes at 99.
Follow the value, not just the rates
The first step is 100 × 1.10 = 110. The second is 110 × 0.90 = 99. The loss applies to 110, so it removes 11 after the earlier gain added 10.
The example assumes no cash flows, fees, tax or distributions. It illustrates a calculation distinction rather than the performance of any actual product.
Ask what average means
An arithmetic average summarises the listed rates. It does not, by itself, reproduce the compounded path of the starting amount. A financial table should explain which measure it reports and over what periods.
Do not assume every figure labelled average uses the same method. Look for the definition or calculation notes before comparing two tables.
Rebuild a tiny example
Use two or three periods and carry the ending value of each into the next. If the printed explanation remains unclear, keep the question open rather than guessing its intended method.
The exercise extends following two years of compounding. Small numbers make it easier to see why a summary statistic and an actual sequence can answer different questions.