Beginner traders unfamiliar with Fibonacci numbers and ratios should know that they are widely known tools used to analyse trends and predict the price of any instrument.

As traders of the new millennia, we might think of Fibonacci numbers and the golden ratio of something that belongs to technical analysts and traders. However, the reality is that Fibonaccis were here way before the markets even existed.

A bit of History

Although Fibonacci numbers have been most popular since the Roman Empire, they root back to Greek mathematician Diophantus who lived in c. 250 AD, and the founder of geometry Euclid, who lived in mid-4^th century BC.

The Fibonacci sequence first appeared to solve mathematical problems involving rabbits and art, evidently known in Leonardo Da Vinci’s Vitruvian Man.

It is a formula created by a man named Leonardo Bonacci, Leonardo di Pisa or Leonardo Bigollo Pisano about 1200 AD, in Liber Abaci, the book of Abacus. It was not accepted as an accurate method until 1753 when a Scottish mathematician named Robert Simson discovered the golden ratio.

Still, the Fibonacci sequence was only used by scientists later in the 1800s after a French mathematician named Edouard Lucas found the numbers in nature, like in pine cones, genealogy, et cetera.

What are Fibonacci Numbers?

The Fibonacci numbers are simply a series of numbers that progress towards infinity. The sequence starts from 0 and 1. The sequence is built when one adds the last number to its preceding, which gives the new number in the sequence, looking like the following:

0,1,2,3,5,8,13,21,34,55,89,144,233,

so on and so forth.

Interestingly, the division of each number in the sequence with its preceding number always results in a ratio of c. 0.618. This is precisely what we call the Golden Ratio.

The golden ratio is widely known in mathematics, represented by the Greek letter φ (phi). However, we traders know this as the most significant retracement level in a market trend. The inverse of 0.618 is 1.618, which we traders use as the most critical extension level in a market trend. Similarly, the following extended ratio of 2.618 is the inverse of 0.382, 4.236 of 0.236, 6.854 of 0.146, and 11.089 of 0.09.

Where do Retracement and Extension Levels Come From?

Apart from the division and inverse of numbers in the Fibonacci sequence, we use several mathematically-related relationships to derive additional significant retracement and extension levels to analyse the markets.

If we divide alternate numbers in the sequence to infinity, for example, 1/3 and not ½, we will find the second ratio, which is 0.382, and if we divide by the second alternate, then the 0.236. The 0.786 Fibonacci retracement comes from the square root of 0.618, whereas the 1.272 of 1.618. Finally, the 0.50 retracement is a Fibonacci number; however, it only appears in the first numbers of the sequence – i.e., 2/1.

With that said, all Fibonacci retracement and extension levels have now been identified. Let’s see how the simplest Fibonacci retracement and extensions provide the best results.

How Can Traders Master Fibonaccis?

There are three ways to use the modern Fibonaccis in the market to find trade setups. As retracement support or resistance entry and as an extension and expansion exit, whether in profit or loss. Let’s go over them one by one.

Price Retracements

Fibonacci retracement levels often depict where markets could find support or resistance, depending on the direction of the primary trend. As a rule of thumb, a market that just reversed from one direction to the other will often retrace 0.618 of the new short-term trends. However, if the retracement is shallow, it hints at an extended trend.

The contrary is valid for deep retracements. If the market retraces to 0.618 or 0.782, confidence in the short-term trend is lost, and the conviction declines, making the case of an extension not only limited but possibly nonexistent.

In the following example, we see the DXY vs. the USDJPY chart. We can notice that a retracement of 0.382 in the index has led to an extension and a fresh high of around 1.2 Fibonacci in 82 days. Whereas the 0.8 retracement on the dollar against the yen, took 176 days instead.

Price Extensions and Expansions

Fibonacci extensions and expansions are similar but not the same as they provide different targets. And you may ask yourself why to use both.

First, we are interested in both targets as the one closest to the entry offers less risk, whereas the one farther, higher. Second, we are primarily interested in identifying clusters, a zone/area where both tools indicate the same target. This makes the level much stronger and worth considering closing the total trade at such levels. And third, both tools give us an exit strategy if markets turn against us after reaching the first target, offering a risk-control mechanism.

As a rule of thumb, prices that extend to 1.618 have more chances to make it past that level after they retrace down to the 1.272/ 1.382 extension or expansion levels. And in case that happens, the 2.618 extension lies ahead next.

Using the same example above, you will notice that the Fibonacci expansion (inverse Fibonacci retracement) in DXY reached a price above 1.618 and halted, whereas the USDJPY charts point at a less extended move, finding resistance only at around 1.35 expansion as the retracement down at 105.62 was deep.

You will also notice that the DXY has found support at a cluster between the 1.38 expansion and 0.786 extension at ~95.30. However, such relationship has not been (yet) established in USDJPY as the pair looks more prone to downside risk than the index due to the depth in its initial retracement. The pair has found support at the 1 extension; however, this is not a cluster, making weak support. On the contrary, a cluster may be higher at around 116, where the 1.38 expansion and 1.272 extensions meet. This means that USDJPY could go up to that cluster as it is a magnet zone.

Closing Words

After knowing the most significant relationships, project entry and exit levels, and adequately managing profits and losses, you can generate your own high-confidence Fibonacci trading strategy.

To make money in the markets you first must ensure you don’t lose running profits. And there’s no more effective way from using Fibonaccis, whether a retracement, an expansion, or an extension.

Apply the above mathematical relationships to your method and see why expert traders are ‘experts’.

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