Understanding how your investments work requires some basic math skills which anyone can master with a little bit of effort.

CAGR (Compound Annual Growth Rate) is a concept that all investors must grasp.  Investments compound geometrically over time (they multiply on each other), but frequently the way they are described can be downright misleading.

Imagine I offered the choice between two investments to hold for two years.  Our first investment (Rabbit) earns an average return of 25%; the second investment (Tortoise) earns an average return of 2%.  Which one would you rather own?

Of  course it’s a trick question.  I have not given you enough information to decide.  I have only given you the arithmetic mean of returns. What’s missing is the volatility of these returns.  The difference between average returns and CAGR is found in the volatility of the investments.  Average returns are how investments are often described, but it is the CAGR that investors actually get.

If there was no volatility involved we would buy Rabbit every time.  25% compounded annually equals a total return of 56.25%, where 2% compounded for Tortoise only equals 4.04% after two years.

That is rarely (if ever) the case.  Almost always higher returns are closely linked to higher volatility. Consider an alternative scenario:

Rabbit returns:

Year 1: 100%

Year 2: -50%

Do you see what I did there? In this example, the average return of Rabbit is still 25%: (100 – 50)/2 = 25.  The total return to the investor is zero!  In my first year the investment doubled and in the second it was cut in half. This puts us right back where we started. If Tortoise earned 2% per year without this volatility, we would have more money there after two years than with our failed investment in Rabbit.

In figuring returns and trying to grow your investments, knowing the expected volatility is just as important as knowing the expected returns.