From the May 2014 issue of Futures Magazine • Subscribe!

Fibonacci and stock analysis

We’ve recently examined how more advanced aspects of Fibonacci retracements combine with cycle analysis to provide a powerful big-picture view of the markets. Written with those new to Fibonacci in mind, this article will offer a more basic overview that also covers fans and arcs in both individual stocks and popular equity indexes.

For those unfamiliar with the basics of Fibonacci, the term most often is used to refer to a series of numbers that were popularized by Italian mathematician Leonardo Pisano Fibonacci who lived in the 12th century. The numbers are more than just a series of relationships, however. Fibonacci discovered that these numbers and the relationships between them were found throughout nature.

The Fibonacci numbers themselves are a sequence in which each successive number is the sum of the two previous numbers:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, etc.

After you advance past the first few numbers, the ratio of any number to the next approaches 0.618%, and the ratio of any number to the one prior becomes approximately 1.618%. Traders and investors use these numbers and ratios to identify points of action (new positions, liquidate positions, add to positions, etc.) in the markets.

There Fibonacci studies are most popular among traders: 

  1. Fibonacci arcs
  2. Fibonacci fans 
  3. Fibonacci retracements and extensions

These three studies help in predicting trend changes in prices for stocks, commodities and currencies.

Fibonacci arcs

Fibonacci arcs mark potential support or reversal zones to watch as prices pull back after the advance. The interpretation of Fibonacci arcs involves anticipating support and resistance as prices approach the arcs. After a decline, Fibonacci arcs are used to anticipate resistance or reversal zones for the counter-trend bounce.

Fibonacci arcs are half circles that extend out from a trendline. The first and third arcs are based on the Fibonacci ratios 0.382 (38.2%) and 0.618 (61.8%), respectively. The middle arc is set at 0.50 or 50%. 

The first step to creating a Fibonacci arc is to draw a trendline between two extreme points, such as a swing high and swing low. Three arcs are then drawn, centered on the second extreme point so they intersect the trendline at the Fibonacci levels of 38.2%, 50.0% and 61.8%.

As seen in the chart of Apple Inc. (“Breaking the fall,” below), after the significant bull market, from a low of 522 on May 18, 2012, until the high of 704 on Sept. 21, Apple stock started correcting. At that point, we can use the low and high to draw Fibonacci arcs as shown. 

The price correction first stopped at the 38.2% retracement, had a small pullback and again started moving lower near the next Fibonacci arc at 61.8%. The 61.8% arc retracement acted as temporary support. 

After price broke through, price continued to move lower with this particular arc now serving as resistance. After several attempts to break back above the 61.8% arc, price moved to the next significant Fibonacci ratio, 100%, where it found support yet again.

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