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Fibonacci and the Golden Ratio
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.” Here, we take a look at some technical analysis tools that have been developed to take advantage of the pattern.
The Mathematics
Mathematicians, scientists, and naturalists have known about the golden ratio for centuries. It’s derived from the Fibonacci sequence, named after its Italian founder, Leonardo Fibonacci (whose birth is assumed to be around 1175 A.D. and death around 1250 A.D.). In the sequence, each number is simply the sum of the two preceding numbers (1, 1, 2, 3, 5, 8, 13, etc.).
Key Takeaways
 The golden ratio describes predictable patterns on everything from atoms to huge stars in the sky.
 The ratio is derived from something called the Fibonacci sequence, named after its Italian founder, Leonardo Fibonacci.
 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.
But this sequence is not all that important; rather, the essential part is the quotient of the adjacent number that possess an amazing proportion, roughly 1.618, or its inverse 0.618. This proportion is known by many names: the golden ratio, the golden mean, PHI, and the divine proportion, among others. So, why is this number so important? Well, almost everything has dimensional properties that adhere to the ratio of 1.618, so it seems to have a fundamental function for the building blocks of nature.
Prove It
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 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.
Are you still having trouble believing it? Need something that’s easily measured? Try measuring from your shoulder to your fingertips, and then divide this number by the length from your elbow to your fingertips. Or try measuring from your head to your feet, and divide that by the length from your belly button to your feet. Are the results the same? Somewhere in the area of 1.618? The golden ratio is seemingly 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.
The Fibonacci Studies and Finance
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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Created Using MetaTrader
2. Fibonacci Arcs
Finding the high and low of a chart is the first step to composing Fibonacci arcs. Then, with a compasslike 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.
Created Using MetaTrader
3. Fibonacci Fans
Fibonacci fans are composed of diagonal lines. After the high and low of the chart is located, an invisible vertical 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.
Created Using MetaTrader
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.
Created Using MetaTrader
The Golden Ratio can be applied to everything from nature to human anatomy to finance.
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 studies and add it to your set of investment tools.
Technical Analysis: Using Fibonacci Retracement On The Trading Floor
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Last Updated on November 17, 2020
Fibonacci tools utilize special ratios that naturally occur in nature to help predict points of support or resistance. Fibonacci numbers are 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, etc. The sequence occurs by adding the previous two numbers (i.e. 1+1=2, 2+3=5) The main ratio used is .618, this is found by dividing one Fibonacci number into the next in sequence Fibonacci number (55/89=0.618). The logic most often used by Fibonacci based traders is that since Fibonacci numbers occur in nature and the stock, futures, and currency markets are creations of nature – humans. Therefore, the Fibonacci sequence should apply to the financial markets. There are many Fibonacci tools used by traders, they include:
Fibonacci Retracements
Arguably the most heavily used Fibonacci tool is the Fibonacci Retracement. To calculate the Fibonacci Retracement levels, a significant low to a significant high should be found. From there, prices should retrace the initial difference (low to high or high to low) by a ratio of the Fibonacci sequence, generally the 23.6%, 38.2%, 50%, 61.8%, or the 76.4% retracement.
For the examples of this section, the S&P 500 Depository Receipts (SPY) will be used based on the logic that the S&P 500 is a broad measure of human nature, thus the Fibonacci sequence should apply very well. Nevertheless, the Fibonacci sequence is applied to individual stocks, commodities, and forex currency pairs quite regularly. The chart above shows the 38.2% retracement acting as support for prices.
Note that a trendline was drawn from a significant low (beginning of trend) to a significant high (end of trend); the trading software calculated the retracement levels.
The chart below of the SPY’s shows that Fibonacci Retracements can be used to retrace downtrend moves as well:
Notice after the bottom in the S&P 500, that price rallied to the 23.6% retracement level and then was promptly rejected downwards. After breaking resistance a few months later, the 23.6% retracement became support (see: Support & Resistance). Price rallied up to the 50% retracement level, where it ran up against resistance. Price continued to fluctuate between the 38.2% retracement level (acting as support) and the 50% retracement level (acting as resistance).
There are many other Fibonacci tools available to stock, forex, or futures traders. Fibonacci Arcs are discussed next.
Fib Retracement
Contents
APPLICATION
The Fib Retracement tool is not included in your favorites by default, so you can add it by selecting the hollow star next to the tool icon and name. A favorites toolbar will then appear.
Fibonacci Retracements are an extremely popular tool in technical analysis. They are created by first drawing a trend line between two extreme points. The vertical distance between those two points is then divided up vertically with horizontal lines placed at key levels. Those levels are placed at the key Fibonacci Ratios of 23.6%, 38.2%, 61.8% and 100%.
The Fib Retracement tool includes the ability to set 24 different Fibonacci levels (including the 0% and the 100% levels that are defined by the two extremes of the trend line that is originally drawn). Values between 0 and 1 are internal retracement levels. Values greater than 1 are external retracement levels while values less than 0 are extensions. A checkbox is available for each defined level which allows that level to be turned on or off for display purposes.
The main use of these levels is that they act as levels of support and/or resistance when price is retracing back from an original advance or decline. These are key levels to take note of when price is correcting or experiencing a countertrend bounce. The idea is that after an initial move (either a decline or an advance), price will often retrace back towards the direction it came from. The areas or levels defined by the retracement values can give the analyst a better idea about future price movements. Remember that as price moves, levels that were once considered to be resistance can switch to being support levels. The opposite is also true.
HOW TO USE IN TRADINGVIEW
 Navigate to https://www.tradingview.com/
 On the landing page, enter a symbol and click “Launch Chart”
 Drawing Tools are located along the left hand side of the chart. Select the Drawing Tool that you would like to add to your chart.
 You can access the Formatting Window by right clicking on the Drawing Tools in the chart itself and selecting “Format”.
Style
Trend Line
Can change the visibility and color of the trend line as well as its thickness and style.
Additional Levels
Can toggle the visibility of additional levels. Can also change their color and line thickness.
Extend Lines
Extends lines indefinitely.
Reverse
Reverses the direction of the fib retracement.
Labels
Changes the positioning of the labels.
Background
Can toggle the visibility of background colors as well as change their opacity.
Levels
Can toggle the visibility of text displaying level values.
Prices
Can toggle the visibility of text displaying price values.
Coordinates
Price 1
Allows for the precise placement of the fib retracement’s first point (Price 1) using a bar number and price.
Price 2
Allows for the precise placement of the fib retracement’s second point (Price 2) using a bar number and price.

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