Fibonacci theory

1. What is the fibonacci sequence?
2. What are fibonacci ratios?
3. Gann ratio
4. Fibonacci retracements

The fundamentals of Fibonacci theory form the basis for a wide range of analytical tools, indicators, and trading strategies. In this lesson, we will focus on Fibonacci ratios, retracements, and other techniques used in market analysis.

History of the fibonacci sequence

Before we dive deeper into what Fibonacci is, let's first answer the question, "Who is Fibonacci?" Leonardo Pisano, also known as Leonardo Fibonacci, was a European mathematician in the Middle Ages who, in 1202 AD, wrote Liber Abaci (The Book of Calculations). In this book, he discussed various topics, such as currency conversion, measurements for trade, profit and interest calculations, and a variety of mathematical and geometric equations.

However, there are two things from this book that stand out in today’s context. First, in the early parts of Liber Abaci, he discussed the advantages of using the Arabic numeral system. At that time, the influence of the fallen Roman Empire was still strong, and most Europeans preferred using Roman numerals. However, Fibonacci made a strong, influential, and easily understandable argument for using the Arabic numeral system in Liber Abaci. From this point on, the Arabic numeral system became firmly established in European society and quickly became the dominant method of mathematics in the region, and eventually worldwide. The influence was so strong that we still use the Arabic numeral system today.

The second important part of Liber Abaci that we still use today is the Fibonacci sequence.

What is the fibonacci sequence?

The Fibonacci sequence is a series of numbers where each new number is the sum of the two preceding ones. It starts with zero and one, known as the "seed numbers." The next number is simply the sum of these two numbers: (0 + 1) = 1, (1 + 1) = 2, and so on.

The first few numbers in this sequence are:

Fibonacci sequence

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...

At first, this may seem a bit confusing, but it becomes clearer when we look at the formula behind this number pattern.

The math behind the fibonacci sequence

Each number in this sequence is simply the sum of the two preceding ones.

For example:

0 + 1 = 1
1 + 1 = 2
1 + 2 = 3
2 + 3 = 5
3 + 5 = 8

And it continues like this.

However, the Fibonacci sequence itself is not particularly important for traders. The key aspect for traders are the Fibonacci ratios derived from this sequence, which are used in technical analysis.

What are fibonacci ratios?

Fibonacci ratios are specific percentages that are calculated by dividing the numbers in the Fibonacci sequence. While there are many different ratios, the most important ones are 23.6%, 38.2%, 61.8%, 78.6%, and 161.8%.

To better understand how these ratios work, let's look at the mathematics behind the 61.8% ratio.
To calculate the 61.8% ratio, you simply divide each number in the Fibonacci sequence by the number that follows it. If you repeat this process for several numbers in the sequence, you'll get a value of approximately 0.618, especially with numbers larger than 21 ÷ 34.

Example:

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 = 0.615
21 ÷ 34 = 0.618
34 ÷ 55 = 0.618
55 ÷ 89 = 0.618

When we convert 0.618 into a percentage, we get 61.8%.

To calculate the 161.8% ratio, simply divide each number by the number that precedes it.

Example:

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 = 1.618
55 ÷ 34 = 1.618
89 ÷ 55 = 1.618

61.8% and 161.8% are very significant Fibonacci ratios, often referred to as golden ratios. These values appear in many fields of mathematics, geometry, architecture, art, and more.

There are also other Fibonacci ratios derived from different division patterns. Here are a few of them:

Another method of obtaining Fibonacci ratios is by calculating the square root of a given number. For example, the square root of 0.618 is 0.786. When we convert this value to a percentage, we get 78.6%, which is one of the key Fibonacci ratios.

Here are some other common Fibonacci ratios that can be derived using square roots.

Gann ratio
50%

There is another ratio often used in Fibonacci analysis, though technically it's not a Fibonacci ratio — the 50%. This ratio doesn’t appear in the original sequence but, similar to key values, it frequently appears in market analysis.

Some claim that the 50% ratio is a "Gann ratio," developed by WD Gann in the early 20th century. Regardless of its origin, the 50% level is considered a crucial and relevant level in trading, and as such, it is often included in technical analysis as if it were a Fibonacci ratio.
Just like with Fibonacci ratios, many traders use the inverse value or the square root of these "sacred ratios" to create additional values. Some examples of these values are shown in the table below.

Regardless of the origin of this ratio, the 50% level proves to be key and significant in trading, which is why it is often included in Fibonacci analysis, even though it technically isn’t a Fibonacci ratio. Some other numbers in the table have also been mistakenly considered Fibonacci ratios, but in reality, they are not.

Fibonacciho retracements

So, how can you apply Fibonacci theory to your trading? Most commonly, traders use Fibonacci retracements to predict support and resistance levels when the market retraces after a significant move.

Example: Let’s say the price of Brent oil drops by 150 points during a bearish trend. You anticipate a countertrend, where buyers temporarily halt the price drop. According to Fibonacci theory, this countertrend might encounter support or resistance levels at the Fibonacci ratios of the original move, typically at 23.6%, 38.2%, 61.8%, or 78.6%.

You can add these ratios to any trading chart on the Y4Trade.com platform using the Fibonacci retracement drawing tool. This tool will automatically draw lines at key Fibonacci levels (including 50%), allowing you to visualize where a reversal might occur during the next countertrend. It also helps you predefine potential support and resistance levels.

Fibonacci retracement overview