Is an 'Annualized' Return the Same as an Average?

Is an 'Annualized' Return the Same as an Average?

The Short Answer

Is an 'Annualized' Return the Same as an Average?

By Karen Wallace | 09-20-11 | 06:00 AM | E-mail Article

Question: Morningstar's longer-term return data are all "annualized" returns. Is annualized return the same as average return?

Answer: Well, the short answer is yes. But it's a certain type of average, and that distinction matters.

To use a simple example, let's pretend you invested exactly $1,000 in an S&P 500 Index fund on Jan. 1, 2008. The fund promptly lost 37% that year (ouch!). But then it reversed course and shot up 26.5% in 2009, and then it gained nearly 15% in 2010. What is the annualized three-year return of your investment? And more important, have you made money?

You might be tempted to add these three numbers and divide by three to produce an average yearly return (negative 37% + 26.5% + 15%) ÷ 3, which would mean an average three-year return of 1.5%. At the end of three years, your initial $1,000 investment is worth about $1,046. Not great, but not bad, right? But your statement says you have around $920--$80 less than you started with three years ago! How did that happen?!

The reason is that a simple arithmetic average is not appropriate for calculating investment returns. It works perfectly to determine the central tendency of a series of numbers that are independent of one another, however. For instance, perhaps an investment team comprises three members: The portfolio manager, who has been running the fund for 30 years, and two analysts, who have been there for eight and seven years, respectively. This team could perhaps claim an average of 15 years' investment experience on the fund, which is the arithmetic average (or mean) of their three tenures. (At Morningstar, we'd still be more comfortable knowing the old hand had final say on buys and sells here, but I digress.)

Investment returns, however, need to be calculated using a geometric mean, or average. Don't be put off by the term: It simply means that because investment returns are compounded, they are dependent on one another.

Let's take a look at our example investment. In the first year you held your investment, it lost 37%, so the $1,000 you invested at the beginning of 2008 was worth only $630 by year-end. Your fund had a good year in 2009, gaining 26.5%; remember, however, that because you started the year with only $630, the 26.5% gain only brought you to $796.95 by Dec. 31, 2009. Then you gained 15% in 2010, but because you only had around $800 at the beginning of the year, you finished the year with around $920. Your three-year annualized return is a less cheerful but more accurate negative 2.86%.

To calculate a geometric mean for an investment over a period of years, you add 1 to the percentage returns for each calendar year (to get them all to be positive), then multiply them all together, and take the Nth root of the product of n numbers. ("N" depends on the number of years you want to annualize.) So, for the example above, the formula for calculating geometric average would look like this: (0.63 x 1.265 x 1.15)^1/3 - 1. The factors in the equation are found by adding 1 to the yearly return percentage expressed as a decimal (so, 1 + (negative 0.37) = 0.63, and so on).

Essentially, the example illustrates that if you lose half of your money, you have to double it just to get back to where you started. Those losses really sting! That's why our proprietary Morningstar Risk rating, which is a component of our Morningstar Rating for funds, emphasizes downside variations; it is based on the expected utility theory, which recognizes that investors are concerned enough about potential losses that they are willing to trade a portion of their potential upside in exchange for a greater certainty of return. For more on how to use Morningstar ratings (and how not to), check out What's Behind the Morningstar Ratings?

Karen Wallace is an editor with Morningstar.