Average Annual Return of 25%, but $0 of Growth?

Imagine you have $1,000,000 in an investment account (one day, right). Over the course of two years you generate the following returns:

Start of Year 1  ➡  End of Year 1: +100%
Start of Year 2  ➡︎  End of Year 2:  -50%​

What is your average annual return?

​Well, let's do the math:
(100% - 50%) ÷ 2 = +25%

​Now, let's look at the actual movement of money for each period:

Start of Year 1: $1,000,000  ➡︎  +100%  ➡︎  End of Year 1: $2,000,000
Start of Year 2: $2,000,000  ➡︎    -50%    ➡︎  End of Year 2: $1,000,000

So, you started Year 1 with $1,000,000 and ended Year 2 with $1,000,000 (i.e. $0 of growth)...but your average annual return is 25%?

The Point
Two things can be true at once, and that working with data is both art and science. In the hypothetical above, it's true that the arithmetic average annual return is 25%. It's also true that this is definitely not an accurate portrayal of how our investment portfolio has performed. When possible, make sure to look at the underlying data that's producing a descriptive statistic (like the average in our hypothetical). If access to the data isn't an option (either the dataset is too large, or simply unaccessible), it's helpful to at least inquire about a statistic's composition and the data source.