Learn Forex: Fibonacci Levels

Technical analysis can be a helpful, albeit involved, method of determining price trends in foreign exchange trading. How can a trader know, for example, where a price trend is going and what are good price levels at which to buy and sell? One of the more widely utilised methods of making predictions of the movements of forex trends is using Fibonacci levels.

Fibonacci levels are trading levels based on mathematical ratios from what are known as Fibonacci numbers. Fibonacci numbers date back to the origins of modern mathematics in renaissance Europe. They were discovered by Renaissance era mathematician Leonardo Pisano Bigollo early in the 13th century. His family name was Bonacci and his pen name was Filius (son) Bonacci, thus the contraction “Fibonacci.”

In a treatise on mathematics published in 1202, Bonacci revealed what has come to be known as the “Fibonacci sequence” of numbers. It is determined by the following mathematical expression: ƒ1= f2=1; ƒn+2=ƒn + ƒn+1, where ƒ is a term in the sequence and n is an integer.1)Retrieved 30 November 2015 http://www.fq.math.ca/Books/Primer/basin2.pdf

In simpler terms, the expression says that certain significant numbers are found by adding integers. Each term in the Fibonacci sequence is the sum of the two terms before it, as:
1+1=2, 1+2=3, 2+3=5, 3+5=8, etc. With this, the numbers in the sequence turn out to be 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and onward to infinity.

As the sequence moves toward infinity, the ratio of each number to the previous number tends toward 1.618. This ratio has been found to be especially significant over time, describing many patterns found in nature such as the growth patterns of tree branches and leaves, the shapes of flowers, shells, DNA molecules, etc.

Because of its significance, the ratio has come to be known as the “golden ratio,” and it is represented by the greek letter Phi φ. The ratio has also been found to be significant in patterns found in financial calculations, including applications in accounting, corporate income, calculations of loans with interest, and charting of asset prices.

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Fibonacci Levels In Forex Trading: Retracement

Beginning in the 20th century, Fibonacci numbers have been used to identify successful trading entrance and exit levels for numerous asset classes, including currencies. Since the early days of financial charting pioneered by Charles Dow and other proponents of the Dow Theory, analysts have noted that when prices reverse trajectory they tend to “retrace” a portion of their previous movements. Mr. Dow himself suggested that the retracement was between 33% and 66%.2)Retrieved 13 November 2015 http://www.jstor.org/stable/pdf/40981862.pdf?seq=1#page_scan_tab_contents

That proposal was refined further several years later by Ralph Nelson Elliott, the author of the Elliott Wave Theory, who found that more accurate retracement levels occurred at 38.2% and 61.8% based on the Fibonacci sequence. In addition, Elliott found that 50% was a common retracement level.3)Retrieved 13 November 2015 http://www.lbma.org.uk/assets/alch40_elliott.pdf

Elliott and other, later analysts applied these numbers to charts. They found that the trend lines described by the percentages frequently predicted where and when on the charts that price support or resistance levels would be reached, and where price reversals would occur. Thus, it was determined that they’re reliable constants for predicting when assets should be bought or sold.

To make the forecast, a trader, for example, could start to plot a hypothetical price trend line at a particular peak or trough on a chart for a buy or sell order. Then, they could trace a line to one of the percentage price increases or decreases suggested by the Fibonacci numbers to determine when the next likely best price move would occur for buying or selling.

Other Fibonacci Level Charting Techniques

In addition to simple charting retracement, other techniques using Fibonacci numbers have also been found to be useful. Among these are Fibonacci Arcs, Fibonacci Fans, Fibonacci Expansions, Fibonacci Channels and Fibonacci Time Zones.


With arcs, analysts choose a trend line between two extreme points in a price movement between a low and a high, and draw arcs across the chart at the levels of 38.2%, 50% and 61.8%. As a result, they plot all the potential support or resistance levels that are likely to occur over time in the future period that is graphed on the chart.


With fans, an invisible vertical line is drawn through the second extreme point in a price movement and trend lines are drawn from the first extreme point to intersect the invisible vertical line at the levels of 38.2%, 50% and 61.8%. As with arcs, the trend lines from the “fan” of three new trend lines will project into future points on the graph where support or resistance levels will likely appear.


Expansion is a technique for determining the likely second and third “waves” of a longer price movement trend. The height of a movement between two price extremes is used as a reference unit interval, and it is considered to be 61.8% of the three wave movement. When the price rebounds to a new peak or trough, an invisible vertical line is drawn. From there, the new price reversal will be expected to move to support or resistance levels of 100% and 161.8% of the distance described by the reference unit interval.


For channels, a peak and trough of a price movement are chosen to represent a unit width. Then, a series of parallel lines is drawn on the chart based on multiples to the unit width of 0.618, 1.00, 1.618, 2.618, 4.236, etc. The multiples represent the likely points of future support or resistance levels.

Time Zones

Unlike the other charting techniques, Time Zones focus on the timing, rather than the price component of price movements. With this technique, a unit time interval is chosen as a reference, and vertical lines are plotted at Fibonacci intervals of 1, 2, 3, 5, 8, 13, 21, 34, etc., where new support or resistance levels can be expected.

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