Technical Analysis: Fibonacci
Fibonacci analysis is the study of identifying potential support and resistance
levels in the future based on past price trends and reversals. Fibonacci analysis
is based on the mathematical discoveries of Leonardo Pisano - also known as Fibonacci.
He is credited with discovering a sequence of numbers that now bears his name:
the Fibonacci sequence.
The Fibonacci sequence is a series of numbers that progresses as follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 …
To arrive at each subsequent number in the sequence, you simply find the sum of the two
preceding numbers in the sequence. For example, to find the number that follows 55 in
the sequence, you find the sum of 55 + 34 (the two preceding numbers in the sequence).
The sum of 55 + 34 is 89. This is the next number in the sequence.
What intrigued Fibonacci about this sequence was not the numbers themselves but rather the
relationships among the numbers, or the ratios created by various numbers in the sequence.
Similar relationships are known to exist throughout nature, in botany and even psychology,
and very notably in astronomy because the Fibonacci sequence has a high correlation with the
respective distances between the planets in our solar system and the sun around which they turn.
Although the ratios between adjacent numbers vary throughout the sequence, in respect of
the numbers 21, 34, 55 and 89 the ratio is very similar and is around 1.618, which traders
often refer to as 'the golden ratio'. They therefore make use of just those four numbers in
the Fibonacci sequence, 21, 34, 55 and 89, in a predictive manner.
The golden ratio and the other ratios that exist within the Fibonacci sequence represent
the natural ebb and flow of life. They also apply to the natural ebb and flow of futures contracts.
In this section, you will learn how Fibonacci ratios can be applied to
Futures contracts using the following analysis tools:
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Fibonacci Retracements |
When a Futures price reverses trend, Futures traders naturally want to know
how far the price is most likely to move in its new direction. Fibonacci retracement
levels can help. Certain Fibonacci ratios are useful when you are trying to
determine how far a Futures contract price is going to retrace, or move against,
a previous trend.
The ratios you will be using in your Futures trading will help you find the following retracement levels:
| 61.8 percent | This level is found by dividing a number in the Fibonacci sequence by the number immediately following it in the sequence (55 / 89 = 61.8%). |
| 38.2 percent | This level is found by dividing a number in the Fibonacci sequence by the second number following it in the sequence (34 / 89 = 38.2%). |
| 23.6 percent | This level is found by dividing a number in the Fibonacci sequence by the third number following it in the sequence (21 / 89 = 23.6%). |
You will also use three other levels in your retracement analysis. While the following levels are not
calculated using numbers within the Fibonacci sequence, they are based on the Fibonacci levels above:
| 50 percent | This level is determined by finding the middle between 61.8 percent and 38.2 percent [(61.8% + 38.2%) / 2 = 50%]. |
| 76.4 percent | This level is determined by finding the distance from 38.2 percent and 23.6 percent (38.2% - 23.6% = 14.6%) and adding it to 61.8 percent (61.8% + 14.6% = 76.4%). |
| 100 percent | This level is determined simply by finding where the previous trend began. |
Determining all six Fibonacci retracement levels provides you with potential support and
resistance levels you can use in your Futures trading.
You can see these Fibonacci levels on the daily Euro FX (ECM8) chart below (see Figure 1).
Each of the illustrated levels was calculated based on the trend highlighted by the red arrow.
You could have used each level to help you determine when to enter and exit your trades as
the price began to turn around and move higher.
Figure 1 - Fibonacci Retracement Levels
Notice how the price dropped down to the 38.2 percent retracement level just below 1.5400 (at 1.5371)
before turning back around and bouncing higher again.
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Fibonacci Projections |
Trends never go straight up or straight down. Trends move in one direction initially,
then they pull back and move in the opposite direction for a while, and then they turn
around and resume moving in the original direction. This is the natural ebb and flow of a trend.
When a Futures price resumes its original trend, Futures traders naturally want to
know how far the price is most likely to continue moving in that self-same direction.
Fibonacci projection levels can help. Certain Fibonacci ratios are useful when you are
trying to determine how far the price is going to move once it resumes its original trend.
The ratios you will be using in your Futures trading will help you find the following projection levels:
| 161.8 percent | This level is found by dividing a number in the Fibonacci sequence by the number immediately preceding it in the sequence (89 / 55 = 161.8%). |
| 261.8 percent | This level is found by dividing a number in the Fibonacci sequence by the second number preceding it in the sequence (89 / 34 = 261.8%). |
| 423.8 percent | This level is found by dividing a number in the Fibonacci sequence by the third number preceding it in the sequence (89 / 21 = 423.8%). |
Determining all three Fibonacci projection levels provides you with potential support and resistance
levels that you can use in your Futures trading.
You can see these Fibonacci levels on the daily Euro FX (ECM8) chart below (see Figure 2).
Each of the illustrated levels was calculated based on the trend highlighted by the black
arrow. If the Euro FX resumes its upward trend you can use each level to help you determine
where to set your profit targets (potential exit levels) if you buy the Futures contract.
Figure 2 - Fibonacci Projection Levels
Notice that the Euro FX price, based on the previous trend, has the potential to move up to the 161.8 percent
projection level at 1.7000 in the Future. If it reaches this level, you could set the 261.8 percent projection
level at 1.8600 as your next long-term profit target level.
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Fibonacci Fans |
Fibonacci levels provide diagonal levels of support and resistance as well as
horizontal levels of support and resistance. The diagonal levels of support
and resistance are called Fibonacci fans.
Fibonacci fans are based on three Fibonacci retracement levels - 61.8 percent,
50 percent and 38.2 percent. To construct a Fibonacci fan you have to do the following:
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Identify a recent trend, pinpointing where it starts and ends.
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Draw two horizontal lines across the chart which go through the start-point
and the end-point of that trend. These two horizontals equate to the highest
and lowest prices that occurred during the trend.
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Drop a vertical line from the very peak of the trend. This will, in effect,
run vertically between the horizontals that you've just drawn.
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Identify three horizontal Fibonacci levels (61.8%, 50% and 38.2%) as they
relate to that trend. This is done by assuming that the previously-drawn horizontal
through the peak of the trend is 0% (where prices had 0% potential), and that the
other previously-drawn horizontal at the foot of the trough before the trend is
100% (where prices had 100% potential). The three new levels and their corresponding
horizontals are therefore calculated as percentages of the difference between the
lowest and highest prices.
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Finally draw three diagonal lines. All three must begin in the same place,
the point where the trend began. But the three all follow separate paths to where
the vertical below the peak intersects one of the three horizontal Fibonacci levels.
Now that you have your Fibonacci fans drawn, you can use them to project potential
support and resistance levels that you can use in your Futures trading.
You can see a Fibonacci fan on the daily Euro FX (ECM8) chart below (see Figure 3).
Each of the illustrated levels was calculated based on the trend highlighted by the
red arrow. You could have used the rays from the fan to help you determine when to
enter and exit your trades as the price began to turn around and move higher.
Figure 3 - Fibonacci Fan
Notice how the Euro FX price bounced off of the middle ray of the Fibonacci fan in May
and is currently at the resistance level formed by the top ray of the fan.
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