CAGR -- Compounded Annual Growth Rate

What is CAGR (Compounded Annual Growth Rate)?

Compounded Annual Growth Rate, AKA annualized return, is the actual yearly return you're making on your money. It is more complex than just averaging yearly returns -- which is misleading.

How can I calculate the compounded annual growth rate?

Like this: CAGR = (Future Value/Beginning Value)^(1/number of years) - 1

Don't be intimidated by the ugly formula. You don't need to memorize it or even understand it, you just need to know how to recognize when someone is using AAR and use a tool to get the Compounded Annual Growth Rate.

For example, in my best way to invest money I look at the returns of different portfolio balances (down at the bottom of the page). I state that they all have a Compounded Annual Growth Rate of between 6.75% and 7.5%. I calculated that by a starting portfolio balance of 100 for the all bond portfolio. Its future value is 348 and number of years is 19. When you plug in the numbers, you get 6.78% -- 3.48^(1/19) - 1 = 6.78%. I don't know and I don't care what the average annual return is.

What's wrong with just averaging the yearly returns?

It doesn't give you an accurate reflection of how well you've really done over the years. For example, if you gain 50% one year and then lose 50% the next year, you've got an average annual return of 0%. But, but, but you lost money over those two years from start to finish! You went from $100 to $150 to $75. How can that be? Because the real way to measure returns over several years is by Compounded Annual Growth Rate. Average annual returns are meaningless.

The use of AAR is downright criminal. Yet, is commonplace by even the biggest and most respected investment firms. Knowing that average annual return numbers are meaningless is a big step towards protecting yourself and investing wisely.

Why are average annual returns and compounded annual growth rate confusing?

There is confusion between AAR and Compounded Annual Growth Rate because they can be the same. Over a time period where you have the same return every year they will be the same. Most of the time this comes in the form of people calculating hypothetical future returns.

For example, lets say I'm trying to plan for retirement and I wanted to see how much money I would have. I would use the expected total CAGR every year in the future for the estimation. In this case, the CAGR and AAR are the same.

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