Saturday, August 09, 2008

Fools, Fundamentals, and Fibonacci

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


My 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.


Fundamental 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.


Alas, 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 (.382!) 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 Belief

I 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.


hindawg said...

All the makings of a healthy debate here. Our trading styles are similar, we both tend to avoid ind stocks. As you know I place a large emphasis on Fib. I have never tried to use fib on an individual stock. ACV is a perfect example of fib used incorrectly. I could put endless charts up of TA gone bad. With ACV it’s clearly uptrending, to forecast with fib you need a change in trend. ACV, in your chart, has clear support at 49.20. I’d be curious to see how much volume there was at that level using a VWAP. The fib lines are useless where placed. The example of SPX is more in line with accurate fib use. If you look at the bull run of the DOW. Without exact numbers in front of me 02 low 7700 and 07 high 14000 a perfect .5 (yes 5 is a fib number, 1,2,3 (5) 8, retrace of 6300 points is 3150. 3150-14000 is 10850. July low= 10827. Interesting that we spent nearly 2.5 years at that level. That’s a lot of support and an obvious successful fib projection. Trendlines are great, but I draw mine with a crayon, not a straight edge. I believe the market does work in a mathematical harmony laced with symmetry and human emotions that present themselves time and time again.

Jody, I have to wonder though, 1576-768=808, 808 * .786 = 635, 1576-635= ((940)) hmmm

Have a good Saturday night,


Anonymous said...

Your review and analysis was to say the least, incredible and extensive.
Do I interpret this correctly, that "trend lines" are more important & accurate than other lines sub as the fibs? How much weight do you give to the trend lines vs. the other factors you follow?
Let's say the S&P breaks out of the trend lines significantly; what about the other factors you follow? How much are they weighted vs. trend lines?
Again - great blog, and great analysis.
the kd

Anonymous said...

The fact is that, technical market strategies tend to "work" only because they are better than randomly selecting a upward or downward bias at the beginning and throughout the day. In other words they apply discipline and order to a perfectly disorderly time series. The first strategy that has worked pretty well is "buy & hold." Including dividends and tax benefits, over the decades, it's really hard to beat.

Jody said...

Hi John,

Much of your reply actually supports my critique.

[1] The Dow low was 7197 on October 10, 2002, and the high was 14198 on October 11, 2007. The difference is 7001 points. A .5 retraction from 14,198 would take it to 10,697. The July 15 low of 10,827 was therefore a .481 retraction. That's different than .500. On the other hand, if .481 is "close enough" to .500, then why specify a level there at all?

[2] If .5 is a Fib grid number because 5 is in the Fibonacci number sequence, then why aren't the following numbers also used in charts? .2, .3, .8, .13, .21, .34, .55, etc?


Jody said...

The KD,

I think the S&P 500 has been forming clean trend lines more often than usual lately, and as long as they're that obvious it makes sense to pay attention to them. It's not a question of giving them more importance than sentiment or volume. The latter tell you *what* is going to happen eventually, while a trend line break signals *when* the new trend has begun.

Remember, when the S&P 500 was breaking out of the declining channel pattern earlier, I was noticing that other market indicators were more or less neutral. No surprise then that the market hasn't gone very far since breaking out of the channel.

Jody said...


Buy and hold works great when stocks are undervalued and in bull markets. Unfortunately we're in an overvalued bear market right now. Besides, the dividend yield of the S&P 500 has been 2% or lower for more than a decade now, which is anemic compared to the historical average of 4.0% to 4.5%.

John said...

.481? Think “they” will make it more obvious?

The good news is there’s lots of ways to skin a cat. Fib is only part of the equation. Lots of indicators, sentiment, price, time and fib- if you get confluence all you can do is trade it and hope you’ve increased your odds.

If you’re dialed in more than that sell your method. With any TA it’s near impossible to time or price the exact penny an index will turn on. I’ve been very public about forecasts on multiple timeframes. Called an int bottom at 1220, looked for 1270-1240-1292 and we got 1200, 1267-1248-1291. Not perfect but profitable.

Off by .019%? Will you be that critical of 940?


Jody said...

Hi John,

My critique has nothing to do with your ability to trade the market - you may be the best trader on the web for all I know. My complaint is that a method which claims to use the golden ratio (.618, .382) and Fibonacci numbers (3,5,8...) actually ends up using neither of them when put into practice.

If any retractment from .35 to .65 counts, then the name of the method should reflect this more honestly. Maybe something along the lines of "half-way retractment" method, or "middle third retractment" method. But having "Fibonacci" in the name and printing ".618" on the charts invites just the kind of skepticism that I've leveled at it.


John said...

I agree with that, I’ve heard people say 1/3 or 2/3 retrace to give estimates. That’s all my 1291 forecast was. There are purists. Most oscillators are set with true fib # sequences and a very popular/conservative trading system is the 13/34 MA crossover.(.382) It’s everywhere.

Let’s see if it caps this rally on 8/13- at .5- :)just kidding!

Best to yours.

Dan said...


Watch this video and please comment.

Thank you

Jody said...

OK. Although the blog entry you pointed to was posted on July 10, the interview of Barton Biggs was recorded earlier on March 14.

Biggs was basically correct at the time. Investor sentiment was pessimistic in mid-March, a quasi-double bottom was completed on March 18, and the Dow ended up rallying more than 1000 points from about 11,800 to 13,100.

However, it was obviously not the end of the bear market, as the Dow turned around at the end of the rally and reached a new low of 10,900 in July.