Capturing the Moment with Charting Tools
Twenty or thirty years ago, technical analysis (TA) was considered on par with reading tea leaves as a type of financial analysis, and its reliability was doubted by almost every type of investor on Wall Street. The widespread availability of personal computers has changed that. Their processing power has allowed the masses access to complex types of mathematical analyses of equities, thereby making technical analysis mainstream.
The increasing familiarity with TA has created a thirst for more. One of the latest areas of the field to be appreciated is based on a very old mathematical observation. Although the math is quite well-established, this was only discovered lately because it involves multiple complex calculations. As more software and charting programs include it as a basic feature, it is easy to perform these calculations and see their uncanny correlation to price action.
This area of technical analysis is known by its discoverer, Leonardo Fibonacci, a 12th century mathematician. “Fibonacci numbers” and the “Golden Ratio” are based on a set of specific mathematical equations. For centuries, this mathematician’s discovery was repeatedly discovered in the physical world, and it has since been discovered in the world of investing. The basic equations are quite simple, but they are repetitive, and that’s where software has helped make the Fibonacci numbers easily accessible.
Fibonacci called his original concept the “Golden Ratio.” He observed that adding two consecutive numbers to derive a third number, and then repeating this exercise, would create a series with interesting properties. For example:
1 2 3 5 8 13 21 34 55 . . .
Each number in the series above is the sum of the two prior numbers. (The precise numbers aren’t important. In fact, any string is valid so long as it sums each two prior numbers.) Next, divide each number above by the one preceding it to see how the Golden Ratio is derived:
0.500 0.667 0.600 0.625 0.615 0.619 0.618 0.618 0.618
Notice something about the ratios as they get further into the series? They gradually approach 0.618, or 61.8%. The rest of Fibonacci is really just variations of the ratio. For example, the same formula applied to two non-consecutive numbers approaches 38.2%, another “Fibonacci number.” Or, the formula’s variables can be reversed to approach 161.8%.
Pretty neat stuff, huh? Not nearly so neat as how commonly Fibonacci ratios appear in price patterns. Perhaps that is because price is the product of mass psychology, and psychology is a form of nature. More important than predicting price action, the ratios can help to anticipate a directional change or a consolidation in an equity price. It never ceases to amaze me when trending suddenly reverses direction upon touching a Fibonacci number.
Despite their usefulness, Fibonacci numbers still remain somewhat controversial. Since the idea assumes that a single universal calculation can be applied uniformly among various situations, patterns, and markets to identify influential price levels in advance, Fibonacci numbers come across as esoteric or metaphysical to critics. Critics would also argue that it is only coincidental when a consolidation in Soybeans futures, and a pullback in the NASDAQ stock index, each rally suddenly upon retracing 61.8% of their prior legs. After all, what could the two disparate markets possibly have in common?
Of course, the answer is found not by comparing what products the two markets represent. This, after all, is technical analysis. The common thread among all markets is that their price action is the product of mass psychology. While individuals change throughout their lives, people generally do not. Not much, not when acting out fear or greed.
Fibonacci is applied to the investment world as either Retracements, or as Extensions. “Retracements” are pullbacks inside of a range or in a trend. “Extensions” are the trending, itself.
Retracements appear eventually in every trend, when it reverses direction to temporarily “retrace” the trend back toward its origin. That’s also known as a “correction.” Interestingly, corrections tend to end after retracing the trend by 38.2% or 61.8%. So, if the original trend was a 10-point rally, then its retracement is likely to end after falling around $3.82, or $6.18.
Retracements can also describe legs within a trading range or consolidation. For example, as price fluctuates within a narrowing range, one leg may retrace 61.8% of its prior leg, and then that leg may also be retraced by 61.8% of the next leg (forming a Triangle).
Extensions are based on the difference between the high and low of a consolidation range. That difference is extrapolated out by Fibonacci numbers to identify resistance (or support) that the trending is likely to encounter. For example, a rally up to $30 might be reversed back down to $24. Its reaction up stops short of touching $30 before reversing back down toward $24 while volume dwindles. The consolidation measures $6 wide, 61.8% of which equals $3.70. So, its eventual breakout above $30 might be expected to encounter resistance at $33.70.