The Curious Investor

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Every person who graduated the third grade has heard of the Fibonacci numbers - 1, 1, 2, 3, 5, 8, 13, 21, etc. Each new number in the sequence is created by adding the two numbers preceding it. Surprisingly enough, this sequence has been studied by various cultures throughout history, but its first appearance in Western mathematics was in 1202 by Leonardo of Pisa (a.k.a. Fibonacci).

Ratios of the Fibonacci numbers tend to appear in nature quite often and, mathematically, the limit of successive numbers in this series is known as the the Golden Ratio which is defined as:

Interestingly enough, many patterns that appear in nature follow some form of the Fibonacci sequence or ratios created by the Fibonacci sequence. The Golden Ratio in particular seems to govern the growth patterns in many things in nature from the way branches and veins grow to the geometry of crystals. As a result, some traders have adopted Fibonacci ratios as a method of predicting pricing actions. The most popular of these methods is Fibonacci Retracements.

Retracement Charting

It’s believed that after a stock moves strongly in one direction or another, it will reverse its momentum in the form of a retracement. These reversals do not happen linearly. As we all know, despite having a general trend one way or another, stocks prices tend to zig zag up and down from day to day. So, in order to identify possible levels of support and resistance in the future, some traders will apply Fibonacci ratios to the stock chart.

The principle ratios used are 23.6%, 38.2%, and 61.8%. These ratios are the limits of dividing one Fibonacci number by the number three places to the right, the number two places to the right, and the successive number in the series respectively. Two other popularly used ratios are the 50% and 78.6% ratios. 50% is simply 1/2 and 78.6% is the square root of the inverse of the Golden Ratio.

To construct Fibonacci lines, you simply pick a peak and a trough in the stock chart and calculate the vertical distance between the two points. Then, you multiply this number by the aforementioned ratios and draw horizontal lines on the stock chart going up from the trough.

Here, I’ve constructed a few Fibonacci retracement lines for the S&P500 between the crash after the internet bubble and the subsequent retracement. From this chart, we find that that the S&P fell approximately 740 points between its peak and where it finally seemed to bottom out. We also find that most of Fibonacci retracement lines do, in fact, act as pretty good resistance points along the S&P 500’s retracement over the last few years. It seemed that the S&P 500 zoomed past the 61.8% as well as the 78.6% line, but what we find is that these lines later act as support lines when the market pulled back during its uptrend.

Does this stuff really work?

Fibonacci Retracements are very interesting but they take a bit of a leap of faith to jump into. Ultimately, there’s no rigorous reason for these ratios to signify any sort of future support or resistance points. Even assuming the relevance of the Fibonacci Sequence to investing (a leap in and of itself), the selection of these ratios is, for the most part, arbitrary.

For example, the two most powerful Fibonacci retracement levels are typically 50% and 78.6%. Yet, these two are the most arbitrary of the Fibonacci retracement ratios. The first three mentioned, 23.6%, 38.2%, and 61.8% come directly from the Fibonacci sequence. The 50% ratio is simply the decision to divide the first two numbers of the series. One could logically argue that the 50% retracement level does not have anything to do with the mystical power of the Fibonacci sequence, but instead that it is simply a byproduct of human psychology. Upon regaining 50% of a loss, many people who invested in a stock may begin to sell their positions happy to have recouped a bit of their position. The 78.6% ratio obtained by taking the square root of .618 is even more dubious. This seems a completely arbitrary choice in hopes of filling in the section between 61.8% and 100%. Yet, despite this, many believe this 78.6% area to be the most important testing ground of a retracement.

So, is Fibonacci Retracement a worthwhile tool for technical analysis? These days, it has gained a pretty significant popularity. So, regardless of any scientific merit, it is possible that these levels are a self-fulfilling prophecy as many market movers are inclined to set their own targets in tune with Fibonacci levels. Furthermore, barring any other methods of projection, it would seem that Fibonacci Retracement does provide at least a little bit of insight for someone hoping to anticipate a reversal in a stock and trade it successfully.

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