Compound Returns vs. Average Returns

A reader asked me to explain my comment in the previous post about investors only being able to eat compound returns not average returns. Simple enough.

Let's say a mutual fund quotes you an "average annual return" from date of inception of 7.0% to the end of 2008. Let's say that fund has been around for the extraordinarily long time of 109 years. Call it the "Methuselah Growth Fund". Well, what they are describing to you is a calculation done by the addition of the annual figures for its returns divided by the number of such observations, or 109. That's the simple part.

Now let's say that all those years ago that fund began with an offering price of $10 per share. "So", you say. "Lemme just plug that in to my TI calculator" as the beginning value and then let's take that annual return of 7% and multiply the year end value each and every year by 1.07. Or, even better just use a handy function provided by the calculator that will do the same thing. Much faster than 109 separate hand calculations!

"Whoa!" you exclaim. "That's not the value of the fund I'm showing! My data show it's WAY lower than that! What happened?" Well, I'll let you in on a little secret. Our fictitious Methuselah Growth Fund is a fund that tracks the return of the Dow Jones Industrial Average. What happened was that negative returns from time to time degraded the fund's performance. Sometimes these negative numbers were quite large. Minus 33% in 1937, minus 28% in 1974 and minus 34% last year for example. And as they deviate farther and farther from zero, the degradation in the compound returns becomes more pronounced. For example, a series averaging 5% that goes 15%, minus 10%, and 10% has a higher compound return (4.419%) than a series that goes 30%, minus 25%, 10% (2.361%).So, instead of that 7% return you were expecting, the actual compounded returns were 4.6%! This is the actual compound annual growth rate of the DJIA from 1900-2008.You can see all this graphically at the Crestmont Research site here. And the order of those returns doesn't matter, a fact you can prove yourself by playing around with the calculator.

So when I say that an investor "can't eat arithmetic returns", it just means that arithmetic returns are not what end up in the mailbox in the 401k statement. Compound returns do. And if that investment is at all volatile in its return series, the compound return -- what that investor can eat--will be much lower than the arithmetic return.