Leonardo FIBONACCI was an Italian mathematician who lived in the 12th and 13th centuries ((1175 – 1250). He is known to have highlighted the famous Fibonacci sequence.

The sequence of fibonacci numbers is, after 0 and 1, a sequence in which each new digit is the sum of the two previous ones: 0, 1, 1, 1, 2, 3, 5, 8, 13, 21, 34, 34, 55, 89, 144, 233, 377, 610. This suite can continue indefinitely and has many properties, especially in mathematics.

It is thanks to this sequence that the golden number 1.618 and it’s opposite, the golden ratio 0.618 were found.

However, this figure is very present all over the world around us: from starfish to sunflowers, cactus, galaxies, molluscs and even galaxies… The numbers of the Fibonacci sequence and the golden number are everywhere.

I greatly invite you to take an interest in this exciting issue.

To get to the heart of the matter at hand, these figures are also present in finance and particularly in technical analysis.

Indeed, FIbonacci retracements generally correspond to resistance or support objectives during the corrective phases. Since these figures are well known and used by everyone, these levels of support and resistance often play their role since all traders operate in these same price areas!

**Calculation **

Tracing can be configured in different ways depending on the trader’s choice on the different technical analysis platforms but the most used and therefore most followed by the market are 14.6%, 23.6%, 32.2%, 50%, 61.8%, 78.6% and finally 85.4%.

A small clarification concerning 78.6%: some use 76.4% which is the reciprocal of 23.6% rather than 78.6% which is the true figure because it is the square root of 61.8.

Why these figures? Indeed, they are not directly related to the Fibonacci sequence. In fact, they were obtained with mathematical relationships between certain numbers and this famous sequence. The basis of the gold ratio is 61.8% and comes from the division of 89 by 144 (which are numbers from the famous sequence) and gives 0.618.

–> 14.6 is obtained by dividing 89 by 610 which gives 0.1459 rounded to 14.6%.

–> 23.6 is the division of 89 by 377 and gives the result of 0.2360.

–> 38.2 is obtained by dividing 89 by 233 which gives 0.3519 which is rounded to 38.20%.

–> 50% is not linked to the continuation of Leonardo but it is often a technical level that is quite monitored by the market because it is a retracement that is widely used in the range: the average level of the range is often a level on which stakeholders take profits.

–> 61.8 is the inverse of the golden number (1.618 – 1)

–> 76.4 is the reciprocal of 23.6

–> 78.6 is the square root of 0.618

–> 85.4 the reciprocal of 14.6

**How are these numbers almost out of the hat relevant? **

As explained earlier, these are what we call in finance “self-fulfilling prophecy’’ everyone thinks that these levels will work so everyone acts on these levels: taking a position, stopping a position, modify stops loss… and it works!

**Trading strategy **

Fibonacci retracements are mainly used as technical zones like support areas and possible resistances. Indeed, when stakeholders draw their retracements, they are particularly attentive to the **levels 23.6% – 38.2% – 50% – 78.6%** (or 76.4) and sometimes even 14.6% and its reciprocal 85.4%.

These levels are used as technical areas for profit taking, position taking, etc….

These are therefore interesting areas because, graphically, they often produce price reactions: volume is executed on these levels.

To trace Fibonacci retracements, it is necessary to identify the peak and trough of the trend. Then we take this tool available on all technical analysis platforms and draw from the trough to the top for a bullish trend and from the top to the bottom for a bearish trend.

We get this kind of plot:

*It is clear that during the BTC crash in 2018, the sharp downward trend was clearly stopped at the 78.6% level before rising to the 50% level and then falling again.*

If we look a little more closely at this crash, we can obtain a rather interesting graphical reading of the retracements of fibonacci.

*Indeed, if we extend our retracements from the high point to the low point, we easily realize that the upward corrective retracement was stopped on the 38.2% level twice. However, this technical level corresponds to the 50% retracement level of the entire ”bubble” at the end of 2017! (see previously)*

If we trace our retracements from the low point to the high corrective point during the crash, we see that some levels are still respected.

*On this graph, the 38.2% level was used as price support before a second attempt to raise prices. On the second failure (double top), prices found support on the 78.6% level.*

**How I use the Fibonacci retracements **

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–> Fibonacci levels are very useful, provided you don’t miss the information when it comes up. So, I recommend drawing all the main levels on his graph to avoid wrangles like 78.6% or 76.4%. Indeed, it will often happen that prices mark one level rather than another and vice versa depending on the markets. Knowing which level will work is not important. We simply have to be aware of what the prices tell us in order to benefit from them.

–> Retracements between 61.8% and 76.4% are quite interesting to buy (in a bullish trend) and sell (in a bearish trend), quite often they are significant retracements and prices like to start rising again after this kind of correction. If, for example, prices fail on the 76.4% retracement, the 78.6% level can be used to place a stop loss.

–> Finally, prices rarely fall below the 85.4% level, which is, in itself, a very deep retracement. If this is the case, it is probably not a retracement (which is normally only a temporary correction in a trend) and the trader will probably have to review his scenario.

–> Of course, it goes without saying that Fibonacci retracements should not be used as signals as such. They **must be used** with other techniques to allow the trader to obtain a better chance of winning when he enters the position: chartist figures, indicators, oscillators, price action (Japanese candlesticks) … the possibilities are endless, so let’s take advantage of them!

*Want to learn more? The following articles may be of interest to you
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*“Volume and liquidity analysis”*