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:

- Fibonacci arcs
- Fibonacci fans
- 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.

**Fibonacci fans**

The first step to drawing Fibonacci fan lines also involves drawing a trendline between two extreme points, which are basically a swing high and swing low of a recent move. Then an “invisible” vertical line is drawn through the second extreme point. Three trendlines are then drawn from the first extreme point so they pass through the invisible vertical line at the Fibonacci levels of 38.2%, 50.0% 61.8% and 78.6%.

The Fibonacci fan lines can then be used to estimate support levels or potential reversal zones. Fibonacci fans are also useful to measure the speed of a trend’s movement, higher or lower. The more steep the fan, the faster the trend.

“Fanning out” (below) shows how prices in the S&P 500 found support and resistance at the fan lines. As soon as S&P 500 prices move below a Fibonacci fan line, price falls until the next Fibonacci Fan trendline level. Because of this, traders expect Fibonacci fan lines to serve as support for uptrending markets.

The chart of the S&P 500 (CME:SPM14) shows an uptrend that retraced to the 38.2%, 50% and 61.8% Fibonacci fan lines. These points are marked by blue circles.

In “Euro bounce” (below), we can see how these lines might be used to manage a trade, even when the odds are stacked against you in the form of a strong counter trend. This euro/dollar currency pair daily chart shows how long trades might be initiated after prices move through the 38.2% line and continue through the 50% retracement level. Once price resumes its drop and touches the 38.2% again, a low-risk entry is taken with a stop loss of a close below the 38.2% line. We target the 50% and 61.8% line. The targets were achieved. Note that this is meant as an illustration of the technique. It is not advisable to trade against the prevailing trend.

**Retracements and extensions**

Fibonacci retracements and extensions are displayed by first drawing a trendline between two extreme points, which usually are a swing high and swing low of recent move. A series of 11 horizontal lines (sometimes fewer, depending on the scale of the chart and the size of the moves being assessed) is drawn intersecting the trendline at the Fibonacci levels of 0.0%, 23.6%, 38.2%, 50%, 61.8%, 78.6%, 100%, 123.6%, 138.2%, 150% and 161.8%.

After a significant price move (either up or down), prices will often retrace a significant portion (if not all) of the original move. As prices retrace, support and resistance levels often occur at or near the Fibonacci retracement levels.

Fibonacci extensions work best when stocks are at new highs or new lows, where there aren’t any obvious support or resistance levels on the chart. If you are long a stock and it begins to make new highs, and you want to take profits, you can calculate the extension levels to get a general idea of where it may begin to fall.

In “Line break” (below), Fibonacci retracement lines were drawn between $1,334.00 and $1341.50, which were a swing high and a swing low. The rally from the lowest low ($1,334.00) to the high ($1341.50) was a difference of $7.50. The most common Fibonacci ratios are 0.382, 0.50 and 0.618, which allow us to calculate the key Fibonacci support levels.

38.2% Support: $1341.5 – (0.382 x $7.5) = $1338.6

**50% Support: $1341.5 – (0.50 x $7.5) = $1337.5**

**61.8% Support: $1341.5 – (0.618 x $7.5) = $1336.8 **

As a result, those who went short once gold was unable to break the swing high for 15 minutes could have used a stop at swing high of 1341.5, for a target of 38.2%, 50% and 61.8%, respectively. As seen above, shorts all three targets were achieved.

We can see how Fibonacci extensions work in a recent example using the CNX Nifty. The Indian stock index breached its all-time high of 6415 on March 7, 2014. Traders might use Fibonacci extensions to identify the next target. As seen in “How high?” (below), the next day the index made a new high at exactly the 123.6% extension.

Fibonacci studies are used to identify potential support, resistance or reversal points. No indicator is perfect. This is why chartists must use other tools to confirm what Fibonacci analysis is telling us. Some useful tools include oscillators, moving averages and traditional chart patterns, such as triangles, head-and-shoulders formations and candlestick relationships. Any time one of these indicators corresponds at a specific price point with another, it adds to the importance of that level especially if it occurs with strong volume.

*Bramesh Bhandari writes at www.brameshtechanalysis.com and provides online tutoring on technical analysis. He can be reached via e-mail at bhandaribrahmesh@gmail.com.*