Mutual Fund Return Lies: Average Annual Return vs Compound Annual Growth Rate

The mutual fund industry has a dirty little secret: the returns many fund companies advertise in the financial media and promotional materials are wrong. Well, not technically wrong but definitely misleading. Mutual fund companies love to quote their Average Annual Return numbers, which, not surprisingly, practically always over-state their funds’ actual returns. The difference comes down to simple math. Average Annual Returns are calculated using the simple arithmetic mean.

The Arithmetic Mean (or simple average)

Everybody is familiar with the arithmetic mean: it’s just the sum of all values in a series divided by the number of values in the series. Take the following series of mutual fund returns: 4%, 8%, 13%, 3%, -6%. The arithmetic mean of this series is simply (4 + 8 + 13 + 3 – 6) / 5 = 4.4%. So far so good, right? Problem is, taking a simple average of mutual fund returns will yield incorrect (and artificially high) results. Say you invested $10,000 in mutual fund A which proceeded to gain 100% the first year and lose 50% the second year. Simple math will tell you that you’ll end up right where you started: with $10,000 ($10,000 * 2.0 * 0.5 = $10,000). You haven’t gained or lost anything. The average annual return, though, is 25% (100% gain – 50% loss) /2 = 25%. Clearly, this is incorrect because you only have $10,000 in your account, not $12,500.

False promises
Unfortunately, some unethical mutual fund companies flaunt their average returns in their marketing materials even though they are misleading to investors. Let’s revist the above example. Say you bought $10,000 of mutual fund A on Januray 1st, 2003 and experienced the following returns:

• 2003: 4%
• 2004: 8%
• 2005: 13%
• 2006: 3%
• 2007: -6%

As we saw above, the average return of this mutual fund is 4.4%, but that doesn’t tell the whole story. To figure out your REAL rate of return, you will need to calculate the geometric mean, or Compound Annual Growth Rate (CAGR). In this case, you look at your year-end statement and see that you have $12,288 in your account at the end of 2007 ($10,000 * 1.04 * 1.08 * 1.13 * 1.03 * 0.94 = $12,288). This works out to a CAGR of 4.21%, which is significantly lower than the 4.4% your mutual fund company likely promotes in their TV ads. You can use the following form to calculate the CAGR return of your portfolio using the starting balance, ending balance, and time period.