The Tortoise & The Hare

When I was working as a stockbroker, a mutual fund representative came into my office one day for a visit. He left me with essentially an interesting twist on the old fable of the tortoise and the hare, focusing the story on investments of course, and I thought it was worth sharing.
On a sheet of paper he wrote "Mutual Fund A" and "Mutual Fund B" side-by-side. Fund A was a "rock 'n roll" type fund providing a 70% return in Year 1, but then lost 80% the next year, and gave a 31% return the next. (It sounds reminiscent of the tech funds of the late 90's, doesn't it?)
Fund B provided a consistent 7% return each of the three years.
Now, here is where you pull out your calculators!
You can see by adding the returns of each of the three years for the funds and dividing by three, you get the "average" annual yield. Each fund had a 21% overall return, and a 7% average annual return. So, they're the same, right?
Nope. Do the actual math, and you will see.
Put $1,000 in Fund A. After Year 1, you have $1,700. Of course, in Year 2 you lose 80% or $1,360, so you're left with only $340. Year 3 gives you a 31% return on that amount, so you end Year 3 with $445.40.
Put $1,000 in Fund B. After Year 1, you have $1,070. With another 7% return in Year 2, you have $1,144.90. And in Year 3, you end up with another 7% to end with $1,225.04 -- or $779.64 more than Fund A.
Of course, this doesn't have to be labeled "Mutual Fund A" or "Mutual Fund B" as you can substitute "Stock A" or "Investment B" or really anything. When looking at prospectuses for mutual funds, the often-quoted figure is the average annual return, so be aware that not all "averages" are created equal.