Fibonacci and the Golden Ratio: Technical Analysis to Unlock Markets (2024)

There is a unique ratio that can be used to describe the proportions of everything from nature's smallest building blocks, such as atoms, to the most advanced patterns in the universe, like the unimaginably large celestial bodies. Nature relies on this innate proportion to maintain balance, but the financial markets also seem to conform to this "golden ratio."

The golden ratio is derived from the Fibonacci numbers, a series of numbers where each entry is the sum of the two preceding entries. Although this sequence is associated with Leonardo of Pisa, the Fibonacci numbers were actually formulated for the first time by the Indian mathematician, Virahanka, 600 years prior to their introduction to the Western world.

Here, we take a look at some technical analysis tools that have been developed to take advantage of the pattern.

Key Takeaways

  • The golden ratio is an irrational number that is equal to (1+√5)/2, or approximately 1.618...
  • The ratio is derived from an ancient Indian mathematical formula which Western society named for Leonardo Fibonacci, who introduced the concept to Europe.
  • Nature uses this ratio to maintain balance, and the financial markets seem to as well.
  • The Fibonacci sequence can be applied to finance by using four main techniques: retracements, arcs, fans, and time zones.
  • Fibonacci numbers have become famous in popular culture, although some experts say their importance is exaggerated.

History of the Mathematics

Mathematicians, scientists, and naturalists have known about the golden ratio for centuries. It's derived from the Fibonacci sequence, named after the Pisan mathematician Leonardo Fibonacci, who lived from around 1175 A.D. until around 1250 A.D.

Although Fibonacci introduced these numbers to the Western world, they were actually discovered by Indian mathematicians hundreds of years earlier. The poet Pingala used them to count the syllables of Sanskrit poetry around 200 B.C., and the method for calculating them was formulated by the Indian mathematician Virahanka around 800 years later.

In this sequence, each number is simply the sum of the two preceding numbers (1, 1, 2, 3, 5, 8, 13, etc.).

Fibonacci borrowed heavily from Indian and Arabic sources. In his book Liber Abaci, he described the Hindu-Arabic numeral system represented by the numbers 0 through 9. He called this the "Modus Indorum," or the method of the Indians.

But this sequence is not all that important. The essential part is that as the numbers get larger, the quotient between each successive pair of Fibonacci numbers approximates 1.618, or its inverse 0.618. This proportion is known by many names: the golden ratio, the golden mean, ϕ, and the divine proportion, among others.

So, why is this number so important? Well, many things in nature have dimensional properties that adhere to the ratio of 1.618, so it seems to have a fundamental function for the building blocks of nature.

The exact value of the golden ratio can be calculated by:

ϕ = (1+√5) / 2

Examples of the Golden Ratio

Don't believe it? Take honeybees, for example. If you divide the female bees by the male bees in any given hive, you will get a number around 1.618. Sunflowers, which have opposing spirals of seeds, have a 1.618 ratio between the diameters of each rotation. This same ratio can be seen in relationships between different components throughout nature.

The golden ratio also appears in the arts, because it is more aesthetically pleasing than other proportions. The Parthenon in Athens, the Great Pyramid in Giza, and Da Vinci's Mona Lisa all incorporate rectangles whose dimensions are based on the golden ratio. It seems to be unavoidable.

But does that mean it works in finance? Actually, financial markets have the very same mathematical base as these natural phenomena. Below we will examine some ways in which the golden ratio can be applied to finance, and we'll show some charts as proof.

Trading and Investing With the Golden Ratio

The golden ratio is frequently used by traders and technical analysts, who use it to forecast market-driven price movements. This is because the Fibonacci numbers and the golden ratio have a strong psychological importance in herd behavior. Traders are more likely to take profits or cover losses at certain price points, which happen to be marked by the golden ratio.

Curiously, the widespread use of the golden ratio in trading analysis forms something of a self-fulfilling prophecy: the more traders rely on Fibonacci-based trading strategies, the more effective those strategies will tend to be.

Thanks to books like Dan Brown's The Da Vinci Code, the golden ratio has been elevated to almost mystical levels in popular culture. However, some mathematicians have stated that the importance of this ratio is wildly exaggerated.

The Golden Ratio and Technical Analysis

When used in technical analysis, the golden ratio is typically translated into three percentages:38.2%, 50%, and 61.8%. However, more multiples can be used when needed, such as 23.6%, 161.8%, 423%, and so on. Meanwhile, there are four ways that the Fibonacci sequence can be applied to charts: retracements, arcs, fans, and time zones. However, not all might be available, depending on the charting application being used.

1. Fibonacci Retracements

Fibonacci retracements use horizontal lines to indicate areas of support or resistance. Levels are calculated using the high and low points of the chart. Then five lines are drawn: the first at 100% (the high on the chart), the second at 61.8%, the third at 50%, the fourth at 38.2%, and the last one at 0% (the low on the chart). After a significant price movement up or down, the new support and resistance levels are often at or near these lines.

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2. Fibonacci Arcs

Finding the high and low of a chart is the first step to composing Fibonacci arcs. Then, with a compass-like movement, three curved lines are drawn at 38.2%, 50%, and 61.8%from the desired point. These lines anticipate the support and resistance levels, as well as trading ranges.

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3. Fibonacci Fans

Fibonacci fans are composed of diagonal lines. After the high and low of the chart is located, an invisible horizontal line is drawn through the rightmost point. This invisible line is then divided into 38.2%, 50%, and 61.8%, and lines are drawn from the leftmost point through each of these points. These lines indicate areas of support and resistance.

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4. Fibonacci Time Zones

Unlike the other Fibonacci methods, time zones are a series of vertical lines. They are composed by dividing a chart into segments with vertical lines spaced apart in increments that conform to the Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, etc.). Each line indicates a time in which major price movement can be expected.

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What Is the Relationship Between the Fibonacci Series and the Golden Ratio?

The golden ratio is derived by dividing each number of the Fibonacci series by its immediate predecessor. In mathematical terms, if F(n) describes the nth Fibonacci number, the quotient F(n)/ F(n-1) will approach the limit 1.618... for increasingly high values of n. This limit is better known as the golden ratio.

Why Is the Fibonacci Sequence So Important?

The Fibonacci sequence is a recursive series of numbers where each value is determined by the two values immediately before it. For this reason, the Fibonacci numbers frequently appear in problems relating to population growth. When used in visual arts, they are also aesthetically pleasing, although their significance tends to be highly exaggerated in popular culture.

Why Is 1.618 So Important?

The number 1.61803... is better known as the golden ratio, and frequently appears in art, architecture, and natural sciences. It is derived from the Fibonacci series of numbers, where each entry is recursively defined by the entries preceding it. The golden ratio is also used in technical analysis because traders tend to behave in a predictable way near the psychologically-important Fibonacci lines.

The Bottom Line

Fibonacci studies are not intended to provide the primary indications for timing the entry and exit of a position; however, the numbers are useful for estimating areas of support and resistance. Many people use combinations of Fibonacci studies to obtain a more accurate forecast. For example, a trader may observe the intersecting points in a combination of the Fibonacci arcs and resistances.

Fibonacci studies are often used in conjunction with other forms of technical analysis. For example, Fibonacci studies, in combination with Elliott Waves, can be used to forecast the extent of the retracements after different waves. Hopefully, you can find your own niche use for the Fibonacci studiesand add it to your set of investment tools.

Fibonacci and the Golden Ratio: Technical Analysis to Unlock Markets (2024)


Is Fibonacci a good trading strategy? ›

That said, many traders find success using Fibonacci ratios and retracements to place transactions within long-term price trends. Fibonacci retracement can become even more powerful when used in conjunction with other indicators or technical signals.

How to enter a trade using Fibonacci? ›

We can create Fibonacci retracements by taking a peak and trough (or two extreme points) on a chart and dividing the vertical distance by the above key Fibonacci ratios. Once these trading patterns​ are identified, horizontal lines can be drawn and then used to identify possible support and resistance levels.

What is the success rate of Fibonacci? ›

Our Fibonacci Testing Results
Fibonacci LevelsSuccess Rate
Failure Rate63%
3 more rows
May 4, 2024

What is the highest win rate trading strategy? ›

If you're looking for a high win rate trading strategy, the Triple RSI Trading System is definitely worth checking out. This system uses three different Relative Strength Index (RSI) indicators to identify potential buy and sell signals in the market.

What is the best Fibonacci setting for day trading? ›

The most commonly used Fibonacci retracement levels are 38.2%, 50%, and 61.8%. The Fibonacci retracement level gives technical traders a good edge in the market. The Fibonacci retracement tool is one of the most common trading tools on charting software – MT4.

What is the easiest way to solve the Fibonacci sequence? ›

Remember, to find any given number in the Fibonacci sequence, you simply add the two previous numbers in the sequence. To create the sequence, you should think of 0 coming before 1 (the first term), so 1 + 0 = 1.

What is the best time frame for Fibonacci retracement? ›

What time frame is best for Fibonacci retracement? The 30-60 minute candlestick chart is best suited to analyse the Fibonacci retracements to watch the daily market swings closely.

What is the God number in nature? ›

The golden ratio is 1.618, represented by the Greek letter 'phi', is said to be is a mathematical connection between two aspects of an object. It is also called the Fibonacci sequence and it can be found across all of nature: plants, animals, weather structures, star systems – it is ever-present in the universe.

Do professional traders use Fibonacci retracement? ›

Every foreign exchange trader will use Fibonacci retracements at some point in their trading career. Some will use them just some of the time, while others will apply them regularly.

Can you use Fibonacci for day trading? ›

Fibonacci retracements are derived from Fibonacci sequences. Retracement levels are 23.6%, 38.2%, 61.8%, and 78.6%. In day trading these retracement levels help define levels between highs and lows where prices may stall or reverse.

How to use Fibonacci for stop loss? ›

Usually, traders place a Stop Loss order just below the next Fibonacci level after they buy an asset or above the next level after they sell one. This way, if the trend gets reversed, your losses are minimized.

What are the disadvantages of Fibonacci? ›

A disadvantage is that due to buildup of entropy/debt as described above, the actual cost of a given call could be as much as O(n). Another disadvantage of the Fibonacci heap is that it uses more memory per element than alternatives like binary heap.

How does Fibonacci work in real life? ›

We observe that many of the natural things follow the Fibonacci sequence. It appears in biological settings such as branching in trees, phyllotaxis (the arrangement of leaves on a stem), the fruit sprouts of a pineapple, the flowering of an artichoke, an uncurling fern and the arrangement of a pine cone's bracts etc.

What is the Fibonacci channel strategy? ›

A Fibonacci channel is a technical analysis tool used by traders to identify potential future levels of support and resistance. It is similar to Fibonacci retracement, but the lines are drawn diagonally and run parallel to two selected highs in a downtrend, or two selected lows in an uptrend.

Is Fibonacci retracement a good indicator? ›

Fibonacci retracements are popular tools that traders can use to draw support lines, identify resistance levels, place stop-loss orders, and set target prices. Fibonacci retracements suffer from the same drawbacks as other universal trading tools, so they are best used in conjunction with other indicators.

Is Fibonacci good for scalping? ›

As so many traders use Fibonacci levels as part of their strategies, a lot of price activity happens at these levels, which can create the ideal conditions for scalping Fibonacci levels.

Is Fibonacci a lagging indicator? ›

Is a Fibonacci Channel a Leading or Lagging Indicator? A Fibonacci channel is a technical tool used by traders to analyze support and resistance levels, where a trend pause or reversal might be likely to occur. Because it is used to predict future movement of trends, it can be considered a leading indicator.

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