Fibonacci, the mathematical sequence behind a whole series of technical indicators

The Fibonacci mathematical sequence is at the origin of trading tools that are  essential in trading rooms.  

What is the Fibonacci sequence?

0, 1, 1, 2, 3, 5, 8, 13... The Fibonacci sequence is a mathematical sequence of integers where each number corresponds to the sum of the two preceding numbers (except for the first two 0 and 1). This sequence, discovered by the mathematician Leonardo Fibonacci, has several surprising features: for example, the fact that the quotient of two consecutive numbers of the Fibonacci sequence converges to the golden number 1.618. Well-known to mathematicians, this golden ratio is omnipresent in nature (the proportions of a snail's shell, the structure of tree branches, or the reproduction rate of a colony of rabbits), but also in many human constructions such as the pyramids of Egypt. However, if for some people, this golden ratio has a mystical origin, for scientists, its omnipresence is mainly linked to purely mathematical factors, and to the accuracy of Leonardo Fibonacci's intuition. Intrigued by the omnipotence of the Fibonacci sequence, technical analysts and traders transposed the use of the golden ratio to the financial markets in order to create multiple tools and technical indicators.   

Fibonacci retracement levels

Fibonacci retracements are one of the most famous technical indicators derived from the Fibonacci sequence. It is indeed possible to calculate several coefficients with amazing mathematical properties. The coefficients of Fibonacci retracements are:

  • 23,6%
  • 38,2%
  • 61,8%
  • 78,6%

In addition, although not Fibonacci retracements per se, the 0%, 50% and 100% coefficients are also widely used. Following a bullish or bearish price movement, traders use their trading platform to draw Fibonacci retracements. To do this, they just have to click on the starting point of the impulse movement and then on its end point.  The end point of the trend movement corresponds by definition to a 0% retracement, while a return to the initial point corresponds to a 100% retracement of the movement. Between these two extreme retracements, the intermediate retracements of 23.6%, 38.2%, 61.8%, and 78.6% are then calculated and automatically represented as horizontal lines projected on the trader's chart. In practice, investors often prefer to wait for the end of an impulse to enter a position in favour of a correction movement in order to profit thereafter from the next impulse movement in the direction of the current trend. 

Once the first impulse movement is identified, the trader waits for the market to “retrace” in order to enter a position in contact with one of the Fibonacci retracements. If the current trend is strong, the retracement will be relatively small, and the trader will look to enter the 23.6% ratio, for example. Conversely, if the trend is not yet well established, the trader may be more patient and wait for the 78.6% ratio. In short, Fibonacci retracements are used as real support and resistance zones.  

Fibonacci extensions

In the same way that Fibonacci retracements allow a trader to detect potential entry points in the direction of a current trend, Fibonacci extensions allow them to set targets for the current trend.  Indeed, depending on the size of the initial impulse and the proportion of the retracement, Fibonacci extensions allow traders to find the right exit points (if they trade in the direction of the trend) or the right entry points (if they adopts a contrarian approach and chooses to trade in the opposite direction of the trend).

Coefficients of Fibonacci extensions are :

  • 161,8%
  • 200%
  • 261,8%

Fibonacci circles

Fibonacci circles (or Fibonacci arcs) are calculated in the same way as Fibonacci retracements and extensions, i.e. starting from the starting point of an impulse movement to the end point of this movement. Concentric semicircles (whose center point is the end point of the impulse) are then drawn automatically by the graphical interface of the trading platform. Fibonacci circles make it possible to ensure the relevance of the calculation based on its ability to accurately identify the intermediate points of the trend movement that has taken place, but also and above all to project into the future supports and resistances whose level depends on the passage of time (which is not the case for retracements and extensions).  

Trading strategies: how to use Fibonacci

Several trading strategies can be implemented using Fibonacci. In all these strategies, Fibonacci indicators always play the same role: support and resistance. Everything depends on the approach chosen by the trader, who can exploit these levels to enter positions in the direction of the current trend or use them to anticipate reversal movements. Due to the increasing use of trading algorithms, Fibonacci tools are becoming more and more appealing because of their deeply mathematical nature, in the manner of pivot points. Unlike historical supports and resistances, Fibonacci levels can be useful even in price areas that have never been explored by historical trading.

Of course, as with any technical analysis, it is up to the trader to build their own strategy and to cross-check information provided by Fibonacci tools with other sources of technical, economic or behavioural information.