Fibonacci Theory: Understanding the Sequence, Ratios, and Retracements in Trading

The Fibonacci theory is a cornerstone of technical analysis, widely used by traders to identify potential support and resistance levels in the market. Based on mathematical principles, the theory provides multiple tools and strategies that help traders predict market movements. In this article, we’ll explore the Fibonacci sequence, ratios, retracements, and even the Gann ratio, delving into how these concepts can be used in trading.

A Bit of History of Fibonacci

Before we dive into the technical aspects, it’s important to understand the origin of Fibonacci theory. So, who exactly is Fibonacci? Born as Leonardo Pisano, he was a European mathematician from the Middle Ages, most commonly known as Fibonacci. He is best remembered for his groundbreaking work in 1202 AD when he authored Liber Abaci (Book of Calculation). In this book, Fibonacci discussed numerous mathematical topics, including methods for converting currencies, calculating profit and interest, and solving complex mathematical and geometric problems.

Two notable contributions from Liber Abaci stand out today: Fibonacci’s advocacy for the Arabic numeral system and the introduction of the Fibonacci sequence. At that time, most Europeans still used Roman numerals, but Fibonacci argued that Arabic numerals were far more efficient and practical for calculations. Thanks to Fibonacci, the Arabic numeral system gained a foothold in Europe, eventually becoming the global standard.

His second major contribution, the Fibonacci sequence, is what traders primarily focus on today. This sequence of numbers underpins various trading strategies, especially in identifying market retracements and projections.

What is the Fibonacci Sequence?

The Fibonacci sequence is a series of whole numbers where each number is the sum of the two numbers preceding it. The sequence starts with zero and one, which are referred to as ‘seed numbers.’ From there, the sequence continues indefinitely. Here’s an example of how the sequence progresses:

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

To break it down further, each number is generated by adding the two numbers before it. For instance:

• 0 + 1 = 1
• 1 + 1 = 2
• 1 + 2 = 3
• 2 + 3 = 5
• 3 + 5 = 8
• And so on…

At first glance, this might seem like a simple mathematical sequence, but it forms the foundation for some essential concepts in trading, particularly Fibonacci ratios.

What are Fibonacci Ratios?

Fibonacci ratios are derived from the Fibonacci sequence and are calculated by dividing certain numbers in the sequence by others. These ratios are crucial in technical analysis because they are used to determine potential levels of support and resistance. The most commonly used Fibonacci ratios in trading are 23.6%, 38.2%, 50%, 61.8%, 78.6%, and 161.8%.

The 61.8% ratio, often referred to as the “golden ratio,” holds particular significance in trading and beyond. To calculate this ratio, you divide a Fibonacci number by the number that follows it in the sequence. As you move further along the sequence, the result gets closer and closer to 0.618. For instance:

• 1 ÷ 1 = 1
• 1 ÷ 2 = 0.5
• 2 ÷ 3 = 0.666
• 3 ÷ 5 = 0.6
• 5 ÷ 8 = 0.625
• 13 ÷ 21 = 0.619
• 21 ÷ 34 = 0.618
• 55 ÷ 89 = 0.618

By converting 0.618 into a percentage, we get 61.8%. This ratio appears repeatedly in various areas of life, including mathematics, art, and architecture.

The 161.8% ratio, another important Fibonacci ratio, is calculated by dividing a number in the sequence by the one that precedes it. For instance:

• 2 ÷ 1 = 2
• 3 ÷ 2 = 1.5
• 5 ÷ 3 = 1.666
• 13 ÷ 8 = 1.625
• 55 ÷ 34 = 1.618

The result of these calculations is approximately 1.618, which when converted to a percentage is 161.8%. This ratio is also known as the “golden ratio” and is used in identifying potential price extensions in trending markets.

Fibonacci ratios are not limited to just these two. Traders often use other ratios as well, derived from dividing numbers in the sequence by other numbers that either follow or precede them. For instance, dividing a number by the second number following it gives you the 38.2% ratio, while dividing it by the third number following it results in the 23.6% ratio.

Other key ratios like 78.6% are derived by taking the square roots of these Fibonacci numbers. The square root of 0.618, for example, is 0.786, which equals 78.6%.

Gann Ratio

Alongside Fibonacci ratios, traders also use another important ratio, the 50% retracement level. Though not technically a Fibonacci ratio, it is often treated as one in practice. This 50% level is known as the Gann ratio, named after W.D. Gann, a famous trader from the early 1900s who developed various market forecasting techniques.

The 50% retracement is considered a key psychological level in markets, reflecting the tendency for prices to retrace half of a significant move before continuing in their original direction. Many traders consider the 50% retracement as an essential level for identifying potential reversals.

Fibonacci Retracements in Trading

Now that we have explored Fibonacci ratios, how can we apply them in trading? The most common way traders use Fibonacci theory is through Fibonacci retracements. These retracements are a technical analysis tool used to identify potential support and resistance levels during price pullbacks within a trend.

For example, after a significant price movement, markets often retrace some of the gains or losses. Fibonacci retracement levels help traders identify potential points where these retracements might reverse and resume the original trend. The most commonly used retracement levels are 23.6%, 38.2%, 50%, 61.8%, and 78.6%.

Imagine that the price of a commodity, such as Brent crude oil, drops 150 points as part of a bearish trend. As traders expect a countertrend to form, Fibonacci retracement levels can help pinpoint where this countertrend may face resistance or support. According to Fibonacci theory, this countertrend may encounter significant resistance at 23.6%, 38.2%, 61.8%, or 78.6% of the initial move. These levels provide potential entry points for traders looking to join the trend.

In modern trading platforms, Fibonacci retracement tools are readily available. Traders can simply use these tools to plot the Fibonacci retracement levels automatically on their charts, making it easier to identify possible reversal points.

The Fibonacci theory, with its sequence, ratios, and retracements, provides valuable tools for traders. Whether you are identifying potential support and resistance levels, projecting price targets, or analyzing market reversals, Fibonacci retracements and extensions play a crucial role in technical analysis. Furthermore, the inclusion of the Gann ratio adds another layer of analysis, helping traders make informed decisions. Understanding and utilizing these concepts can greatly enhance your trading strategy and give you a better edge in navigating the markets.