People who study the stock market tend to form very strong opinions about how it works.

FoolsMy stock market education was inaugurated by the

Motley Fools, beginning with their

first book and ending with a couple of newsletters. The Motley Fools are fundamental investors, meaning they are concerned about things like earnings growth, price to earnings ratios (P/E), and management of individual companies. Their investing strategy is to pick individual stocks that have the best combination of low price and high future earnings potential. Although they have developed a dizzying array of sub-strategies and newsletters, their goal in every case is to choose a set of stocks which, on average, will beat the market in the long run.

The Motley Fools have pure contempt for other methods. They view technical analysis as the equivalent of reading tea leaves, and

market-timing as an impossible dream. The irony is that the Fools often recommend buying strategies which contribute to the very support lines that technical analysts look for. Most of the stock recommendations in their newsletters include recommended purchase prices; in other words, "buy at price X or lower." When there's a population of potential buyers who only buy a stock below a certain price, then that price will show up in the chart as a support line.

The 'Fools have managed to beat the market with their methods, but this is not as great an accomplishment at it might seem. Beating the market in a bear market like today means you can still be losing money -just not as quickly as everyone else is. Remember, cash beats the market in a bear market!

More to the point, their yardstick for measuring success is questionable. The 'Fools like to compare their returns to the S&P 500 when it isn't appropriate. Their

small-cap newsletter is beating the S&P 500 by 22% right now, (cumulatively, not even annually) but anyone could have done almost as well by simply purchasing a

Russell 2000 ETF, which contains

all of the small cap companies in the U.S. Their flagship newsletter,

Stock Advisor, has been beating the S&P 500 mostly because it picks mid-cap stocks, which anyone could have accomplished with a

single mid-cap fund. In this latter case they don't even acknowledge the mid-cap selectivity of the newsletter.

FundamentalsFundamental analysis may work more often than it fails for finding superior individual stocks, but it's almost useless when it comes to predicting the future behavior of the overall market. In the past 25 years alone, the P/E ratio of the S&P 500 varied between 8 and 42! Even if it were possible to accurately forecast the future earnings (E) of the S&P 500 companies, (it isn't) there's still a factor of 5 uncertainty in the future P/E ratio. Yet despite this incontrovertible evidence, there are legions of investors out there trying to predict the market based on fundamentals.

Not all fundamental analysis is equally useless, however. The dividend yield of the S&P 500 is a concrete measure of cash actually returned to investors, whereas earnings (profit) can be fudged with accounting tricks and

wasted on stock buybacks. Not all earnings numbers are alike, either.

As-reported earnings are more conservative and generally more accurate than

operating earnings. For instance, the projected P/E ratio of the S&P 500 for the end of 2009 is 18.7 using as-reported earnings, but only 11.6 using operating earnings!

So you can see why I've chosen to side with the technical analysis camp over the fundamental one.

FibonacciAlas, technical analysis (TA) is equally vulnerable to human misconceptions and wishful thinking. One of the most widely used art forms in TA today involves Fibonacci grids and the related field of Elliot Wave Theory.

A Fibonacci grid is an attempt to

predict lines of support and resistance before they occur, using the number .618, which is also known as the

golden ratio. (By contrast, I only identify a support line on a chart after a price has already bounced off of it at least twice.) Without going into too much detail, the number .618 arises from a sequence of mathematically- related numbers called Fibonacci numbers. Presumably it is the pure mathematical origin of the golden ratio that makes it meaningful to people who use Fibonacci grids.

Here's how the simplest Fibonacci grid works: Suppose a stock price or market index has been rising for a while. When it eventually changes direction, a line is drawn across the most recent peak price, and a second line is drawn at the earlier low price which occurred at the beginning of the rally. This chart of the S&P 500 will be used to demonstrate:

I don't claim to be doing this by the book, and I'm sure some purists will complain, but this is just to demonstrate the basic idea to non-practitioners.

Now two more lines are drawn between these two extremes, one at 61.8% of the way through the interval, and another at 38.2%. (100-61.8)

Remember, Fibonacci practitioners don't draw lines at .6 and .4, nor even .62 and .38. They draw them at exactly .618 and .382.

The idea is that these lines

might be support lines off of which the S&P 500 will bounce and change to a bull market. As you can see from the above chart, the upper line didn't hold in this case. That leaves 1076 as a possible turning point for the S&P 500, according to this theory. The problem is that, were the S&P 500 to continue rising from today's price, Fibonacci followers would probably claim success, since the bounce was

close to the 1267 line. I'll demonstrate this with some actual examples.

The following stock charts appear on websites where Fibonacci grids are treated seriously, and where they already have the lines drawn on them. (I haven't added anything.)

There are two things to notice in the above chart. First, there is another line drawn in at the 50% mark. All Fibonacci charts seem to include this extra line, even though .50 is not related to the golden ratio in any way. I suspect that it's used in order to increase the chances of a successfully-predicted bounce.

The second thing to notice is that, despite the closely-packed triad of lines, the stock price failed to bounce off of any of them. In fact, the two bounces occurred

exactly in-between the lines, which is a perfect miss in my book. Even so, this chart is not seen as a failure of the Fibonacci system by the faithful. Typically a charter will say that a bounce was "close to" a line, which is validation enough:

It's perplexing that a bounce

close to a line is significant, given the precision (.38

2!) with which the lines are drawn. If "close enough" counts, then why bother with lines at all? In practice, the Fibonacci grid users that I've seen are satisfied if a bounce occurs anywhere in the middle 30% of the range or so, which means that the golden ratio (.618) really has nothing to do with any of it.

In an apparent attempt to further improve the odds of a Fibonacci bounce, some people add even more lines to the chart. This one adds lines at 78.6% and 23.6%, which come from additional permutations of the golden ratio:

The next one replaces the 23.6% line with a 25% line, (I guess it's close enough!) and adds another line at 88.6%:

It's comical that even with seven lines and no fewer than seven bounces in the above chart, only two bounces managed to hit a target. One wonders how crowded a Fibonacci grid would have to be for a believer to question the relevance of the lines.

Confidence Versus BeliefI only use market indicators that have objective and provable track records of predicting market behavior. I don't fudge sentiment data or trend lines, and I spend considerable effort to keep my own biases and wishes out of the interpretation of the signals. The day may come, for instance, when the S&P 500 stops forming channels and stops bouncing off of support and resistance lines. (I don't know why it would happen - this is just by way of example.) If sufficient evidence were to accumulate indicating that this had happened, then I would stop using these lines in my analysis. However, I doubt that Fibonacci fans would even notice. That's the difference, I suppose, between confidence and belief.