Numbers never lie, but they sure can deceive

When measuring how your investments have performed, you sometimes need to take a closer look behind the headline numbers.

Suppose someone told you that for the last 10 calendar years ending Dec. 31, 2011, the TSX Total Return index had an annualized rate of return of 7.04 per cent. Then they provided you with a chart of the last 10 years of mutual fund X's returns, which averaged 8.5 per cent for that time period.

Based on that data, You might think that $1 invested with the mutual fund would have outperformed $1 invested in an index fund that tracked the TSX.

And you could be wrong.

There is a big difference when it comes to annualized returns and average returns. Annualized returns measure the rate of growth of a lump sum investment had it grown at the same amount every year. The average return, on the other hand, is simply the average of calendar year returns.

While the annualized returns of the TSX Total Return index was indeed 7.04 per cent for the past 10 calendar years, the average return was 9.1 per cent. (Add up the following returns in the second column and divide by 10, the result is 9.1 per cent.)

If we know that if a $100,000 investment earning the index returns would have left you with $197,408.84 at the end of 10 years, then we can calculate the compound annual growth rate.

Without getting into the nitty-gritty of how those calculations are made, let's take an example to really drive home the difference between these two measures.

Suppose you only had two years worth of returns. In Year One, your fund grows by 25 per cent and in Year Two it loses 20 per cent. $100,000 would have grown to $125,000 then promptly lost $25,000 (20 per cent of $125,000) to end up right back at $100,000. Even though you didn't make any money, the average return was 2.5 per cent per year. However, the annualized return was clearly 0 per cent, as you didn't make any money over the two years.

The reason it's important to know the difference between average returns and annualized returns is so that you can ensure that you're comparing apples to apples when evaluating competing investments.

If someone shows you a table of an average returns, then proceeds to show you how it beat the annualized return of a benchmark, index fund, or competing investment strategy, you'll know that they aren't making a fair comparison.