Fibonacci Sequence Explained
The Fibonacci sequence is our subject here, but first we will look at the history of the man who discovered these numbers — a discovery that took hold in financial markets and drew close attention from currency and stock traders, because of the large role it plays in reading market direction, especially in Elliott waves and harmonic trading.
The Fibonacci sequence is used to build technical indicators from a mathematical sequence developed by the Italian mathematician commonly known as Fibonacci in the 13th century. The number sequence is created starting from zero and one by adding the two previous numbers. For example, the first part of the sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, and so on. This sequence can then be divided into ratios that some believe give clues about where a given financial market will move.
Who Was Fibonacci?
Leonardo Pisano, or Leonardo Fibonacci as he is widely known, was a medieval European mathematician who wrote Liber Abaci (Book of Calculation) in 1202 AD.
In this book he discussed a variety of topics, including how to convert currencies and measurements for trade, profit and interest calculations, and a number of mathematical and geometric equations.
Two important points that stand out in the discussion:
First: at the beginning of Liber Abaci, Fibonacci discussed the benefits of using the Arabic numeral system. At that time the influence of the old Roman Empire was still strong, and most European citizens preferred to use Roman numerals. However, in Liber Abaci, Fibonacci made a very strong, persuasive and easy-to-understand argument for using the Arabic numeral system. From that point the Arabic numeral system gained a firm foothold in European society and soon became the dominant method of mathematics in the region, and eventually throughout the world — so much so that we still use the Arabic numeral system to this day.
The second important part of Liber Abaci that we use today is the Fibonacci sequence: a series of numbers in which each number equals the sum of the two numbers before it.
The Fibonacci sequence
and so on, to infinity… 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144
As you can see from the Fibonacci sequence, we need to start with two initial numbers, 0 and 1. Then we add 0 and 1 to get the next number in the sequence, which is 1. Then you take that value and add it to the number before it to get the next number in the Fibonacci sequence. If we keep following this pattern, we get this:
1+1=2, 1+2=3, 2+3=5, 3+5=8, 8+5=13, 13+8=21, 21+13=34, 34+21=55, 55+34=89 … and so on
The Fibonacci sequence is very important to this discussion because we need these numbers to get the Fibonacci ratios — without the Fibonacci ratios, the Fibonacci sequence would not exist.
What Are Fibonacci Ratios?
With the rise of the internet there has been a lot of misinformation about the values that make up the Fibonacci ratios, which led Fibonacci analysis — especially in trading — to misinterpretation and misunderstanding of how and what a Fibonacci ratio is. Let us look at what a Fibonacci ratio is, how it is created, and some examples of those that are not Fibonacci ratios at all.
Fibonacci Ratios
The math behind the Fibonacci ratios is fairly simple. All we have to do is take certain numbers from the Fibonacci sequence and follow a pattern of division throughout. As an example, let us 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 the developing pattern here? Starting from 21 divided by 34 and on to infinity, you will always get 0.618!
We can do this with other numbers in the Fibonacci sequence too. For example, by taking a number in the sequence and dividing it by the number that precedes it, we see another constant number develop.
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 Fibonacci numbers. Now, 1.618 actually carries greater significance, because it is also called the golden ratio, the golden number, or the divine proportion — but I could keep writing many pages on this topic.
Examples of the Patterns That Develop
Here are some examples of the patterns that develop by taking numbers in the Fibonacci sequence and dividing them, in a pattern, by other numbers within the sequence:
As you can see, we can get many different numbers just by taking the numbers within the Fibonacci sequence and developing a division pattern within the sequence. However, this is not the only way to arrive at Fibonacci ratios once you have the numbers from the division.
What makes these numbers Fibonacci ratios is simply converting them into percentages. Using this rationale, 0.236 becomes 23.6% after converting to a percentage, 0.382 becomes 38.2%, and so on.
If we look at our analysis, we can then see that 23.6%, 38.2%, 48.6%, 61.8%, 78.6%, 127.2%, 161.8%, 161.8%, 205.8%, 261.8%, and 423.6% are bona fide Fibonacci ratios.
But the useful thing is that you do not need to do all these calculations to draw Fibonacci levels on the chart. Every trading platform, including MetaTrader, provides that at the push of a button, as we will see later.
What About 50%?
While 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 W. D. Gann in the early 1900s.
Others describe the 50% level as a “sacred ratio,” just like the Fibonacci ratios. Many people will take the inverse square root or the square of these “sacred ratios” to form more values. Some examples can be found in the table below.
Regardless of the source, the 50% ratio appears to be an important and relevant level when trading, and it is often included in Fibonacci analysis as if it were a Fibonacci ratio. Some of the other numbers listed in the table have been understood as Fibonacci ratios too, but clearly they are not.
The Fibonacci Sequence and Its Applications
When price moves in a financial market from point A to point B, it rarely moves in a straight line. Generally price moves in waves, and one of the main goals of technical traders is to identify how far these waves retrace. One of the most popular tools for doing this is the Fibonacci sequence.
The Origins of the Fibonacci Sequence
The Fibonacci sequence is a naturally occurring sequence that can be observed in various physical phenomena and in financial markets. Price tends to retrace according to these ratios. For example, if price is moving from point A to point B, it will generally retrace to point C between point A and point B.
The image above shows a move from point “A” to point “B.” Now, as price begins to retrace against point “A,” it is likely to move to a “Fibonacci ratio.” The most common retracements are 38%, 50%, 62% and 79%. The fact is that a large number of forex traders use the Fibonacci sequence when applying technical analysis to price charts, and this is one of the main reasons Fibonacci levels tend to act as support and resistance on a consistent basis. Let us look at some real examples.
In the image above, you can see that after price moved from LO to HI, it retraced to 38% at circle 1, then to 50% at circle 2, and to 62% at circle 4. In this example, each of these circles pushed price to the upside.
One of the things that makes the Fibonacci sequence more powerful is that its use is not limited to financial markets — it extends to other areas of life, including engineering uses and even environmental science. Anyone who researches this knows well the importance of this sequence in nature generally, and in financial markets specifically.
A Fibonacci Trading Strategy
Most traders use the Fibonacci sequence together with other technical tools. For example, traders might use some key moving averages, candlestick analysis, the stochastic, and so on, then use the Fibonacci sequence as an overall tool to identify areas where the market may reverse.
One of the most basic ways to use the Fibonacci sequence is to first use a trend-identifying indicator. Here are the steps to follow in this strategy:
- Choose a currency pair with a clear trend.
- Wait for price to start moving against that trend.
- Then draw the Fibonacci sequence from the last swing HI to the swing LO.
- As price retraces against the overall trend and reaches a Fibonacci level, check whether any other technical tools confirm the entry.
- If the Fibonacci level lines up with some other technical indicator, enter the trade in the direction of the overall trend, expecting the overall trend to resume.
This is the very basic Fibonacci strategy, which — when used with other technical tools — can improve the odds on a setup, though no trade is ever guaranteed.
Add to the above that some analysis methods rely heavily on Fibonacci, such as harmonic patterns. When studying harmonic patterns, you need to be familiar with the Fibonacci sequence in order to apply it on the chart.
How Currency Pairs React to Fibonacci Levels
Interestingly, some Fibonacci ratios tend to work better with specific currency pairs in the forex market. GBP/USD tends to respect the 50% level. EUR/USD tends to respect the 38% level. A more advanced way to use Fibonacci is to think in reverse. For example, when price retraces to the 38% Fibonacci level, price should find support. However, if it breaks the 38% retracement level and continues to pull back deeper, the 38% retracement now becomes general resistance when price starts to move back up.
The Fibonacci sequence can be used to place entry orders, set stop-loss levels, or define price targets. A trader might see a stock rise, and after the rise it retraces to the 61.8% level, then starts climbing again.
Because the retrace happened at a Fibonacci level during an uptrend, the trader decides to buy, and might set a stop-loss at the 61.8% level, since a return below this level could signal that the rally has failed.
The Fibonacci sequence also shows up in other ways in technical analysis. It is common in Gartley patterns and Elliott wave theory. After a large price move up or down, these forms of technical analysis find that reversals tend to happen near certain Fibonacci levels.
Fibonacci is an impressive tool for identifying major reversals in a market of probabilities, but always keep in mind that this theory, and any other trading theory, is purely hypothetical. Past performance cannot guarantee future results, and you should always get extensive training and knowledge before trying it.
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Frequently Asked Questions
Why is it called Fibonacci?
The sequence is named after its discoverer, the European mathematician Leonardo Fibonacci.
Who is the scholar who discovered these sequences?
The discoverer of this series, or sequence, is the mathematician Leonardo Fibonacci, who described it in his book Liber Abaci.
What are Fibonacci levels?
They are a set of levels derived from the sequence, used widely in financial markets, and they also feature in some other mathematical calculations.
What is the Fibonacci theory?
The math behind the Fibonacci ratios is fairly simple: all we have to do is take certain numbers from the Fibonacci sequence and follow a pattern of division throughout.
Disclaimer
This article is for educational purposes only and is not investment advice or a recommendation to trade. Fibonacci levels are analytical tools, not predictions — signals can and do fail, and past performance does not guarantee future results. Trading forex and CFDs involves leverage and a high risk of losing money rapidly. Some links on this site may be affiliate links, which means we may earn a commission at no extra cost to you. Do your own research and consider your risk tolerance before trading.
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