# Fibonacci Ratio in Forex Market

Before we delve into what Fibonacci is, let's first answer the question: who is Fibonacci? Leonardo Pisano, or Leonardo Fibonacci as he is better known, was a European mathematician in the Middle Ages who wrote Liber Abaci (Book of Calculus) in 1202 AD.

First published in 1202, Fibonacci's Liber abaci was one of the most important books on mathematics in the Middle Ages, introducing Arabic numerals and methods across Europe. Its author, Leonardo Pisano, now known as Fibonacci, was a citizen of Pisa, an active maritime power, with trading posts on the Barbary Coast and other parts of the Muslim Empire. As a young man, Fibonacci was instructed in mathematics at one of these outposts; he continued his mathematics studies while traveling. See more here.

In this book, he discussed a variety of topics, including how to convert currencies and measures for trade, profit and interest calculations, and a series of mathematical and geometric equations. However, there are two things that leap to the forefront of our discussion in today's world.

First, in the early parts of Liber Abaci, he discussed the benefits of using the Arabic numeral system.

At the time, the influence of the defunct Roman Empire was still strong, and the preference of most European citizens was the use of Roman numerals.

However, in Liber Abaci, Fibonacci provided a very powerful, influential, and easy-to-understand argument for the use of the Arabic numeral system.

From there, the Arabic numbering system gained a strong presence in the European community and soon became the dominant method of mathematics in the region and eventually throughout the world. It was so strong that we still use the Arabic numbering system today.

The second important section of the Liber Abaci that we will use is the Fibonacci sequence. This Fibonacci sequence is a series of numbers where each number in the series is equivalent to the sum of the two preceding numbers.

As you can see in the image above, in this sequence we need to start with two “seed” numbers, which are 0 and 1.

Then we add 0 and 1 to get the next number in the sequence, which is 1. You then take that value and add it to the previous number to get the next number in the sequence. If we continue to follow this pattern, we get the following:

The Fibonacci sequence is very important to this discussion because we need these numbers to get our Fibonacci ratios. Without the Fibonacci sequence, Fibonacci coefficients would not exist.

## What makes a Fibonacci relationship?

With the advent of the Internet, there has been a lot of misinformation about what values ​​make up the Fibonacci ratio.

The proliferation of Fibonacci analysis, particularly in the commercial realm, has encouraged interpretations and misunderstandings about how and what constitutes a Fibonacci relationship.

Let's look at what a Fibonacci ratio is, how it's created, and some examples of those that aren't really Fibonacci ratios.

### Fibonacci ratios

The math involved behind Fibonacci ratios is quite simple. All we have to do is take certain numbers from the Fibonacci sequence and follow a pattern of division along it. As an example, let's take a number in the sequence and divide it by the number that follows it.

• 0 ÷ 1 = 0
• 1 ÷ 1 = 1
• 1 ÷ 2 = 0,5
• 2 ÷ 3 = 0,67
• 3 ÷ 5 = 0,6
• 5 ÷ 8 = 0,625
• 8 ÷ 13 = 0,615
• 13 ÷ 21 = 0,619
• 21 ÷ 34 = 0,618
• 34 ÷ 55 = 0,618
• 55 ÷ 89 = 0,618

Notice a pattern that develops here? Starting with 21 divided by 34 going to infinity, you will ALWAYS get 0,618!

We could also do this with other numbers in the Fibonacci sequence. For example, when taking a number in the sequence and dividing it by the number that precedes it, we see another constant number that develops.

• 1 ÷ 0 = 0
• 1 ÷ 1 = 1
• 2 ÷ 1 = 2
• 3 ÷ 2 = 1,5
• 5 ÷ 3 = 1,67
• 8 ÷ 5 = 1,6
• 13 ÷ 8 = 1,625
• 21 ÷ 13 = 1,615
• 34 ÷ 21 = 1,619
• 55 ÷ 34 = 1,618
• 89 ÷ 55 = 1,618
• 144 ÷ 89 = 1,618

Another pattern develops from the numbers in the Fibonacci sequence. Now 1.618 actually has even more meaning because it is also called Golden Ratio, Golden Number or Divine Proportion, but I could go on for many more pages on this subject.

Here are a few more examples of patterns that develop by taking numbers in the Fibonacci sequence and splitting them into a pattern with other numbers in the sequence.

DIVIDE BY THE 2nd NEXT DIVIDE BY THE 2nd BEFORE DIVIDE BY THE 3nd NEXT DIVIDE BY THE 3rd BEFORE
0 ÷ 1 = 0 1 ÷ 0 = 0 0 ÷ 2 = 0 2 ÷ 0 = 0
1 ÷ 2 = 0,5 2 ÷ 1 = 2 1 ÷ 3 = 0,33 3 ÷ 1 = 3
1 ÷ 3 = 0,33 3 ÷ 1 = 3 1 ÷ 5 = 0,2 5 ÷ 1 = 5
2 ÷ 5 = 0,4 5 ÷ 2 = 2,5 2 ÷ 8 = 0,25 8 ÷ 2 = 4
3 ÷ 8 = 0,375 8 ÷ 3 = 2,67 3 ÷ 13 = 0,231 13 ÷ 3 = 4,33
5 ÷ 13 = 0,385 13 ÷ 5 = 2,6 5 ÷ 21 = 0,238 21 ÷ 5 = 4,2
8 ÷ 21 = 0,381 21 ÷ 8 = 2,625 8 ÷ 34 = 0,235 34 ÷ 8 = 4,25
13 ÷ 34 = 0,382 34 ÷ 13 = 2,615 13 ÷ 55 = 0,236 55 ÷ 13 = 4,231
21 ÷ 55 = 0,382 55 ÷ 21 = 2,619 21 ÷ 89 = 0,236 89 ÷ 21 = 4,231
34 ÷ 89 = 0,382 89 ÷ 34 = 2,618 34 ÷ 144 = 0,236 144 ÷ 34 = 4,235
55 ÷ 144 = 0,382 144 ÷ 55 = 2,618 55 ÷ 233 = 0,236 233 ÷ 55 = 4,236
89 ÷ 233 = 0,382 233 ÷ 89 = 2,618 89 ÷ 377 = 0,236 377 ÷ 89 = 4,236
144 ÷ 377 = 0,382 377 ÷ 144 = 2,618 144 ÷ 610 = 0,236 610 ÷ 144 = 4,236

As you can see, we could get a lot of different numbers just by taking the numbers in the Fibonacci sequence and developing a division pattern in the sequence.

However, this is not the only way to get Fibonacci indices. Once we have the division numbers, we can take the square roots of each of these numbers to get more numbers.

See the table below for some examples of these values:

FIBONACCI RATIO OPERATION RESULT
0,236 Square root of 0,236 0,486
0,382 Square root of 0,382 0,618
0,618 Square root of 0,618 0,786
1.618 Square root of 1,618 1.272
2.618 Square root of 2,618 1.618
4,236 Square root of 4,236 2.058

The last part of making these Fibonacci ratios of numbers is simply turning them into percentages. Using this reasoning, 0,236 becomes 23,6%, 0,382 becomes 38,2%, etc. So, analyzing our analysis, we can see that 23,6%, 38,2%, 48,6%, 61,8%, 78,6%, 127,2%, 161,8%, 205,8%, 261,8 .423,6% and XNUMX% are our true Fibonacci ratios.

Although the 50% ratio is often used in Fibonacci analysis, it is not a Fibonacci ratio.

Some say the 50% level is a Gann ratio, created by WD Gann in the early 1900s.

Others call the 50% level of inverse a “sacred relationship”. Like Fibonacci proportions, many people will take the inverse or square root of “sacred proportions” to form more values.

Some of these examples can be seen in the table below:

SACRED RELATIONSHIP OPERATION RESULT INVERSE OF THE SACRED RELATIONSHIP
1 Square root of 1 1 1
2 Square root of 2 1.414 0,5
3 Square root of 3 1.732 0,333
4 Square root of 4 2 2.236
5 Square root of 5 0,25 0,2

Whatever the source, the 50% ratio seems to be a very important and relevant level when trading, it is often included in Fibonacci analysis as if it were a Fibonacci ratio.

Some of the other numbers included in the table have also been confused with Fibonacci ratios, but obviously they are not.

Regardless of the source, the 50% ratio appears to be a very important and relevant level when traded, it is often included in Fibonacci analysis as if it were a Fibonacci ratio.

Some of the other numbers included in the table have also been confused with Fibonacci ratios, but obviously they are not.

## How does Fibonacci retracement work?

In trading, these ratios are also known as retracement levels.

Traders expect prices to approach these levels and act on their strategy.

They typically look for a reversal signal at these widely watched retracement levels before opening their positions.

The most commonly used of the three levels is 0,618 — the reciprocal of the golden ratio (1,618), denoted in mathematics by the Greek letter.

### How to draw Fibonacci retracement levels

Drawing Fibonacci retracements is a simple three-step process:

#### On an upward trend:

• Step 1 — Identify the market direction: uptrend;
• Step 2 — Attach the Fibonacci retracement tool to the bottom and drag it to the right towards the top;
• Step 3 — Monitor the three potential support levels: 0,236, 0,382 and 0,618.

#### In a downtrend:

• Step 1 — Identify the market direction: downtrend;
• Step 2 — Attach the Fibonacci retracement tool to the top and drag it to the right, all the way to the bottom;
• Step 3 — Monitor the three potential resistance levels: 0,236, 0,382 and 0,618.

Obviously, it is more reliable to look for a confluence of signals (ie, more reasons to act on a position).

Don't fall into the trap of assuming that just because the price has reached a Fibonacci level, the market will automatically reverse.

Combine Fibonacci levels with candlestick patterns Japanese, oscillators and indicators for a stronger signal.

As you can see in the chart below, the “Three White Soldiers” pattern is confirmed by the fact that prices are trading above the Moving Average line and additionally that the MACD (Moving Average/Convergence Divergence) is above the zero line.

## Summarizing the Fibonacci relation

Every trader, especially beginners, dreams of mastering the Fibonacci theory.

Many traders use it to identify potential support and resistance levels on a price chart, which suggests that a reversal is likely.

Many enter the market just because the price has reached one of the Fibonacci levels on the chart. This is not enough!

It is best to look for more signals before entering the market, such as Japanese candlestick reversal formations or oscillators crossing the baseline, or even a moving average confirming your decision.

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