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In his historic 13th century novel Liber Abaci (Book of the Abacus), Leonardo Fibonacci brought a special sequence of numbers known as the Fibonacci series to Western civilization. Before we look into how Fibonacci numbers and ratios are used in the financial markets to predict future support and resistance levels, let's have a look at where they came from and how they were created.
A simple mathematical expression that describes a Fibonacci series is given as follows:
F(n+1)=Fn+ F(n-1)
where Fn represents the current number, F(n-1)the previous number, and F(n+1) the next number in the Fibonacci series. Any integer in the Fibonacci series is the sum of its two previous whole numbers, regardless of how it is represented mathematically.
Starting with F(n-1) = 0 as the previous number and Fn = 1 as the current number in the sequence, we can get F(n+1), the next number in the Fibonacci series, by repeating or iterating the process for each new Fn:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, ...
The ratio of the current Fibonacci number to its immediate previous number, that is, the ratio (F(n+1)/Fn) or (Fn/F(n-1)), is a special and somewhat mysterious characteristic of the Fibonacci sequence. When we move farther out into the Fibonacci sequence, this ratio reaches 1.618 (to three decimal places). In truth, it turns out that it doesn't matter which two numbers were chosen to start the series in the first place. It will still hit 1.618 as we proceed along with the list! This unique ratio is referred to as the Golden Ratio, or "Phi".
We already know that Phi = 1.618 (to three decimal places). Here are some other important ratios related to Phi:
a. (1/Phi) = 0.382
b. Phi x Phi = 2.618
c. (2/Phi)-1 =0.236
d. √ (1/Phi) = 0.786
e. √ Phi = 1.272
The items in this list of Phi‐related ratios are regarded as significant ratios in technical analysis and are used widely by technical traders and analysts.
Fibonacci Retracements, Extensions, and Projections
Fibonacci numbers and ratios are often used to time future market reversals, or as time forecasts, as we can see in the following pages. Before going any further, it's a good idea to define the terms retracement, extension and projections in broad terms.
Price Retracements
A market drop or reversal from a significant high, or a rebound from a significant trough, is referred to as a retracement. The amount of retracement is normally expressed as a percentage of the observed price range, and is calculated by comparing the peak to a previous significant trough or a trough to a previous significant peak. In other words, we have both downside and upside retracements. Popular Fibonacci percentage retracements include:
a. 23.6 percent
b. 38.2 percent
c. 61.8 percent
d. 78.6 percent
Price Extensions
A downside extension is any downside retracement that is greater than 100 percent, that is, the downside retracement extends below the previous significant trough, that is, beyond the observed price range. In similar fashion, an upside extension is any upside retracement that is greater than 100 percent, that is, the upside retracement extends above the previous significant peak that is beyond the observed price range. Popular Fibonacci price percentage extension levels include:
a. 127.2 percent
b. 161.8 percent
c. 261.8 percent
d. 361.8 percent
e. 423.6 percent
f. 461.8 percent
Price Projection
An upside price projection is a projection of an observed price range from a higher significant trough. A 100 percent price projection is simply a one to one (1:1) projection of the observed price range from some new higher significant trough. Similarly, Fibonacci downside price projections use the phi‐related percentages for forecasting potential support in a downtrend.
The main Fibonacci percentages associated with projections are:
a. 61.8 percent
b. 161.8 percent
c. 261.8 percent
d. 361.8 percent
e. 423.6 percent
f. 461.8 percent
Trade with care.
If you like our content, please feel free to support our page with a like, comment & subscribe for future educational ideas and trading setups.
A simple mathematical expression that describes a Fibonacci series is given as follows:
F(n+1)=Fn+ F(n-1)
where Fn represents the current number, F(n-1)the previous number, and F(n+1) the next number in the Fibonacci series. Any integer in the Fibonacci series is the sum of its two previous whole numbers, regardless of how it is represented mathematically.
Starting with F(n-1) = 0 as the previous number and Fn = 1 as the current number in the sequence, we can get F(n+1), the next number in the Fibonacci series, by repeating or iterating the process for each new Fn:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, ...
The ratio of the current Fibonacci number to its immediate previous number, that is, the ratio (F(n+1)/Fn) or (Fn/F(n-1)), is a special and somewhat mysterious characteristic of the Fibonacci sequence. When we move farther out into the Fibonacci sequence, this ratio reaches 1.618 (to three decimal places). In truth, it turns out that it doesn't matter which two numbers were chosen to start the series in the first place. It will still hit 1.618 as we proceed along with the list! This unique ratio is referred to as the Golden Ratio, or "Phi".
We already know that Phi = 1.618 (to three decimal places). Here are some other important ratios related to Phi:
a. (1/Phi) = 0.382
b. Phi x Phi = 2.618
c. (2/Phi)-1 =0.236
d. √ (1/Phi) = 0.786
e. √ Phi = 1.272
The items in this list of Phi‐related ratios are regarded as significant ratios in technical analysis and are used widely by technical traders and analysts.
Fibonacci Retracements, Extensions, and Projections
Fibonacci numbers and ratios are often used to time future market reversals, or as time forecasts, as we can see in the following pages. Before going any further, it's a good idea to define the terms retracement, extension and projections in broad terms.
Price Retracements
A market drop or reversal from a significant high, or a rebound from a significant trough, is referred to as a retracement. The amount of retracement is normally expressed as a percentage of the observed price range, and is calculated by comparing the peak to a previous significant trough or a trough to a previous significant peak. In other words, we have both downside and upside retracements. Popular Fibonacci percentage retracements include:
a. 23.6 percent
b. 38.2 percent
c. 61.8 percent
d. 78.6 percent
Price Extensions
A downside extension is any downside retracement that is greater than 100 percent, that is, the downside retracement extends below the previous significant trough, that is, beyond the observed price range. In similar fashion, an upside extension is any upside retracement that is greater than 100 percent, that is, the upside retracement extends above the previous significant peak that is beyond the observed price range. Popular Fibonacci price percentage extension levels include:
a. 127.2 percent
b. 161.8 percent
c. 261.8 percent
d. 361.8 percent
e. 423.6 percent
f. 461.8 percent
Price Projection
An upside price projection is a projection of an observed price range from a higher significant trough. A 100 percent price projection is simply a one to one (1:1) projection of the observed price range from some new higher significant trough. Similarly, Fibonacci downside price projections use the phi‐related percentages for forecasting potential support in a downtrend.
The main Fibonacci percentages associated with projections are:
a. 61.8 percent
b. 161.8 percent
c. 261.8 percent
d. 361.8 percent
e. 423.6 percent
f. 461.8 percent
Trade with care.
If you like our content, please feel free to support our page with a like, comment & subscribe for future educational ideas and trading setups.
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