The world is awash with hot stock tips and investment advisers pitching the next great investment idea. These ideas seem to come out of every corner of the financial markets. When I sit down with a client, or get them on the phone, one of the first things they want to talk about is investing.

That's fine.

Investing is not where I would start, personally. I chuckle a little on the inside when someone asks me what stock they should buy or whether they should invest in a particular asset class. It's not because I think they're dumb. I've talked to engineers and CFOs of corporations who love to crunch numbers and see hypothetical on a spreadsheet.

...and I used to accommodate their hopes and dreams of perpetual stock market returns of 10 percent annually. I would, of course,caution each and every one of them that I thought that it was unlikely they would see that rate of return. Especially if they were asking me what stock to invest in.

I am convinced that the financial planning industry has trained the general public to become overly reliant on financial advisers and investment gurus. If you are familiar with Julian Jaynes's theory of bicamerality, it's understandable to think that people would be attracted to automatic answers by external authorities. It's in our evolutionary history.

Whether or not Jaynes was correct in his assumptions, one thing seems clear: many people are looking to be told what to invest in. They're also being told that investing is necessary.

#### The Cult Of Averages

Pick up any financial planning magazine, prospectus or financial industry trade journal, and there's bound to be a discussion of either "Monte Carlo simulations" or "average investment returns" at some point.

Averaging investment returns is supposedly a great way to understand what you can expect out of your investments over the long term. I already smashed that myth a while ago and finally published it after agonizing over the mistakes I made as a "green pea" in the industry.

But, just a quick refresher:

Let's say that you give me $25,000. I show you where to invest it. You earn 100 percent returns on that money. What do you have? That's right, $50,000. Now, let's say I am a stinker and I keep you invested in that volatile investment and you lose 50 percent the next year. Wait a second, don't get so angry, I still made you money didn't I?

Let's see...100 percent minus 50 percent equals 50 percent. Now, let's average those returns together. Divide 50 percent by two and that equals 25 percent. Come on, that's pretty good. That's Peter Lynch good.

What's that you say? You only have $25,000 when the dust settles? Let's see. $25,000 plus 100 percent equals $50,000. Now subtract 50 percent. You have...$25,000. By gosh, you're right!

But, I made an average rate of return of 25 percent for you. Aren't you happy? Wait, I must deduct .5 percent or 1 percent for my investment adviser fee. Now you have $24,875 or $24,750, respectively. There, is that better? No?

This is not a devilish trick that financial planners sit at home scheming over. I don't think that most advisers really understand what they're promoting. If they did, they would snap out of it and stop running their investment software hypothetical illustrations. They would stop promoting Monte Carlo simulators as predictive. They would stop pitching average investment returns. But, they don't. They remain in the fog of rationalism, which is beat into them by universities and by industry intellectuals, that guides them towards offering bad financial advice to their clients. Until they wake up and start thinking more clearly, you might want to ignore the siren song of averages.

#### What to do?

In a previous post, I discussed whether it's really worth your time to invest. I am not a math genius, but I do think a little differently than most financial guys pitching their services. Think about it this way for a moment: if you were really great at investing, why not ditch your career and make money as a professional investor? If you're only so-so at investing, are you earning enough money to compensate for the time you put in? In other words, when you add up the hours you spend researching investments, are you earning more per hour than your day job? If not, perhaps you should adopt a different strategy that makes more financial sense.

..but that's a post for another time.

Justice// Aug 23, 2011 at 11:30 amThe naive formula for average return on investment seems indeed to be flawed.

A better formula might be the following. Suppose the following sequence of percentage yearly returns for n years: y_1, y_2, …, y_n. A percentage loss in any year i would be a negative number for y_i. Then the return ratio for any year i is (y_i + 1). The geometric average return ratio would be ((y_1 + 1) x (y_2 + 1) x … (y_n + 1))^(1/n). And the geometric average percentage yearly return would be ((y_1 + 1) x (y_2 + 1) x … (y_n + 1))^(1/n) – 1.

Taking the example in your post of a 100% gain in year 1 followed by a 50% loss in year two (before fees), we have the geometric average percentage yearly return as ((100% + 1) x (-50% + 1))^(1/2) – 1 = sqrt(2 * 0.5) – 1 = 1 – 1 = 0% (before fees), which means an initial $25,000 investment with the yearly percentage returns listed above will come out with a 0% geometric average percentage yearly return (no gain and no loss), giving back $25,000 after two years.

The rationale for this substitution is that returns compound on each other, rather than adding together, and therefore that compounding is a multiplication rather than an addition.

The naive formula with the arithmetic mean approximates the formula here with the geometric mean when the yearly returns are close to zero (1% to 5%, say), and diverges spectacularly and gives very wrong answers for total return on investment when the yearly returns are far away from zero (100% and -50%). Likewise, the formula with the arithmetic mean is a good approximation when the investment occurs over just a few years (1 to 5 years) and diverges spectacularly and gives very wrong answers for total return on investment when the investment occurs over a long period of time (30 to 99 years). That is why the formula works decently well for investments with returns near zero over just a few years.

This formula, obtained by substituting geometric mean for arithmetic mean in the naive formula, seems to provide much better insight.

Cheers,

Justice

David C Lewis, RFC// Aug 25, 2011 at 8:43 pmJustice,

Thanks for your post. Yes, leaving aside the “Monte Carlo” problem, your formulas do provide better insight.