Let’s start with what average annual rate of return (or annualized return) is NOT:

The above is an *arithmetic average*, and can work out to be very different than *annualized return*. If you make an investment, the annualized return at the end is what you will use to pay bills or buy groceries. **Annualized return is what you eat.**

Now, you know that the return you make on an investment is Value at the End vs. the Value at the Beginning. Or, to state it mathematically:

`Return = End / Beginning - 1`

You invest $1,000. And 3 years later you sell that investment for $1,100. You made:

`1100 / 1000 - 1 = 0.10`

or **10% cumulative return**

But that 10% is the return for the whole 3 years. You want to know what equivalent rate you compounded at *annually*, in order to end up making 10% total.

`Annualized Return = (End / Beginning)`

^{(1 / Num Years)} - 1

Or, continuing our example above:

`(1100 / 1000)`

or ^{(1 / 3)} - 1 = 0.032**3.2% annualized return**

Dirt simple. And note that it works for fractional years too.

Great article. I’m just getting into understanding my IRA/401K portfolio and this is one of the clearest explanations of how to calculate average annual returns I’ve read. Talking to our financial people only gave me a headache!

yes I think luminous is correct

This is good… now what if you are regularly adding to your position? For example, re-investing dividends, employee stock purchase plan, or regular contributions to your portfolio? Is it still easy to computer the average ROR?

Hi JB,

Pressed for time at the moment, but the short answer is that I think you’re looking for dollar-weighted return, time-weighted return, or internal rate of return. There’s a good post on that here:

http://www.usatoday.com/money/perfi/columnist/krantz/2006-06-27-tota-return_x.htm

Really nice. Thankyou

a very useful example for my students

excellent!!!

But in table 2, how did you calculate the annual ROR?

kate, annual ROR is price this year divided by price a year ago. for example, for 2001:

97.80/111.19 -1 = -.1204 or -12.04%

Thank you, clear and simple.

.

The way the formula is written, the expression “1 / num years” is shown as an exponent. How do I calculate 1.1 to the 1/ 3 power?

Never mind, I just remembered computers

GG bra thanks mate its alright. explanantion is clearish