Fibonacci Numbers and Lines Definition and Uses

What are Fibonacci Numbers and Lines?

Fibonacci numbers are used to create technical indicators using a mathematical sequence developed by the Italian mathematician, commonly referred to as "Fibonacci," in the 13th century. The sequence of numbers, starting with zero and one, is created by adding the previous two numbers. For example, the early part of the sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,144, 233, 377, and so on.

This sequence can then be broken down into ratios which some believe provide clues as to where a given financial market will move to.

The Fibonacci sequence is significant because of the so-called golden ratio of 1.618, or its inverse 0.618. In the Fibonacci sequence, any given number is approximately 1.618 times the preceding number, ignoring the first few numbers. Each number is also 0.618 of the number to the right of it, again ignoring the first few numbers in the sequence. The golden ratio is ubiquitous in nature where it describes everything from the number of veins in a leaf to the magnetic resonance of spins in cobalt niobate crystals.


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Key Takeaways

  • Fibonacci numbers and lines are created by ratios found in Fibonacci's sequence.
  • Common Fibonacci numbers in financial markets are 0.236, 0.382, 0.618, 1.618, 2.618, 4.236. These ratios or percentages can be found by dividing certain numbers in the sequence by other numbers.
  • While not officially Fibonacci numbers, many traders also use 0.5, 1.0, and 2.0.
  • The numbers reflect how far the price could go following another price move. For example, if a stock moves from $1 to $2, Fibonacci numbers can be applied to that. A drop to $1.76 is a 23.6% retracement of the $1 price move (rounded).
  • Two common Fibonacci tools are retracements and extensions. Fibonacci retracements measure how far a pullback could go. Fibonacci extensions measure how far an impulse wave could go.

Formulas for Fibonacci Numbers and Levels

Fibonacci numbers don't have a specific formula, rather it is a number sequence where the numbers tend to have certain relationships with each other.

How to Calculate Fibonacci Retracement Levels

The Fibonacci number sequence can be used in different ways to get Fibonacci retracement levels or Fibonacci extension levels. Here's how to find them. How to use them is discussed in the next section.

Fibonacci retracements require two price points to be chosen on a chart, usually a swing high and a swing low. Once those two points are chosen, the Fibonacci numbers/lines are drawn at percentages of that move.

If a stock rises from $15 to $20, then the 23.6% level is $18.82, or $20 - ($5 x 0.236) = $18.82. The 50% level is $17.50, or $15 - ($5 x 0.5) = $17.50.

Fibonacci extension levels are also derived from the number sequence. As the sequence gets going, divide one number by the prior number to get a ratio of 1.618. Divide a number by two places to the left and the ratio is 2.618. Divide a number by three to the left and the ratio is 4.236.

A Fibonacci extension requires three price points. The start of a move, the end of a move, and then a point somewhere in between (the pullback).

If the price rises from $30 to $40, and these two price levels are points one and two, then the 161.8% level will be $16.18 (1.618 x $10) above the price chosen for point three. If point three is $35, the 161.8% extension level is $51.18 ($35 + $16.18).

The 100% and 200% levels are not official Fibonacci numbers, but they are useful since they project a similar move (or a multiple of it) to what just happened on the price chart.

What Do Fibonacci Numbers and Lines Tell You?

Some traders believe that the Fibonacci numbers play an important role in finance. As discussed above, the Fibonacci number sequence can be used to create ratios or percentages that traders use.

These include: 23.6%, 38.2%, 50% 61.8%, 78.6%, 100%, 161.8%, 261.8%, 423.6%.

These percentages are applied using many different techniques:

  1. Fibonacci Retracements. These are horizontal lines on a chart that indicate areas of support and resistance.
  2. Fibonacci Extensions. These are horizontal lines on a chart that indicate where a strong price wave may reach.
  3. Fibonacci Arcs. These are compass-like movements stemming from a high or low that represent areas of support and resistance.
  4. Fibonacci Fans. These are diagonal lines created using a high and a low that represent areas of support and resistance.
  5. Fibonacci Time Zones. These are vertical lines into the future designed to predict when major price movements will occur.

Fibonacci retracements are the most common form of technical analysis based on the Fibonacci sequence. During a trend, Fibonacci retracements can be used to determine how deep a pullback could be. Impulse waves are the larger waves in the trending direction, while pullbacks are the smaller waves in between. Since they are smaller waves, they will be a percentage of the larger wave. Traders will watch the Fibonacci ratios between 23.6% and 78.6% during these times. If the price stalls near one of the Fibonacci levels and then starts to move back in the trending direction, a trader may take a trade in the trending direction.

Fibonacci levels are used as guides, possible areas where a trade could develop. The price should confirm prior to acting on the Fibonacci level. In advance, traders don't know which level will be significant, so they need to wait and see which level the price respects before taking a trade.

Arcs, fans, extensions and time zones are similar concepts but are applied to charts in different ways. Each one shows potential areas of support or resistance, based on Fibonacci numbers applied to prior price moves. These support or resistance levels can be used to forecast where price may stop falling or rising in the future.

The Difference Between Fibonacci Numbers and Gann Numbers

W.D. Gann was a famous trader who developed several number-based approaches to trading. The indicators based on his work include the Gann Fan and the Gann Square. The Gann Fan, for example, uses 45-degree angles, as Gann found these especially important. Gann's work largely revolved around cycles and angles. The Fibonacci numbers, on the other hand, mostly have to do with ratios derived from the Fibonacci number sequence. Gann was a trader, so his methods were created for financial markets. Fibonacci's methods were not created for trading, but were adapted to the markets by traders and analysts.

Limitations of Using Fibonacci Numbers and Levels

The usage of the Fibonacci studies is subjective since the trader must use highs and lows of their choice. Which highs and lows are chosen will affect the results a trader gets.

Another argument against Fibonacci number trading methods is that there are so many of these levels that the market is bound to bounce or change direction near one of them, making the indicator look significant in hindsight. The problem is that it is difficult to know which number or level will be important in real-time or in the future.

Article Sources
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  1. James Chen. "Essentials of Foreign Exchange Trading." John Wiley & Sons, 2009.

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