Technical Analysis: Fibonacci
Leonardo Pisano, aka Fibonacci, is credited with devising the Fibonacci sequence that bears his name. Fibonacci analysis, which we will explain after an introduction to the Fibonacci sequence itself, is an application of Fibonacci's 11th century discovery to 21st century price trends. The resultant tool enables traders to identify the levels at which price levels support and resistance are likely to form-in effect, they provide guidance on when to buy and when to sell.
The Fibonacci sequence commences with the numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 and 55. Each number in the sequence is the sum of the two preceding numbers. So the number that follows 55 is the sum of 55 + 34 (34 being the number preceding 55). Thus 89 follows 55. And then 89 is followed by 144, 203, 347 and 550. Clearly the sequence is infinite.
What intrigued Fibonacci about this sequence was not the numbers themselves but rather that the ratios have proved to have applications in fields as diverse as botany, psychology and astronomy. For example these ratios correspond even more exactly to the distances between the planets in our solar system and the sun than the ratio using Bode's Law (aka Titius-Bode Law, the flawed sequence which was used by astronomers almost 600 years after Fibonacci's birth to predict a planet between Mars and Jupiter that appears to have been reduced to asteroids, and a sequence which anyway breaks down for Neptune and Pluto). So Fibonacci was ahead of his time, and he could never have dreamed of the applications to which his sequence would be put.
What is perhaps more relevant than whether the Fibonacci sequence predicted the whereabouts of Neptune and Pluto is that it is widely used as a predictor of the values of stocks and CFDs. It seems curious, but historically using Fibonacci analysis has proven to be effective. And that is why you need to know about it.
This section explains how you can apply Fibonacci ratios to stocks and CFDs, predicting continued growth or even the consequences of downturns, using the following tools:
When a stock or CFD price reverses a trend, traders naturally want to know how far the stock price is likely to move in its new direction. A system employing what is known as 'Fibonacci retracement' can help.
Technical analysts use the Fibonacci sequence to create two sets of three critical ratios. We are going to explain how the ratios are created. Do not worry about remembering the explanations of the calculations because they are not so important. But the handful of percentages shown in bold are essential and ought to be committed to memory.
The first set of three ratios used for retracement analysis is 61.8 percent, 38.2 percent and 23.6 percent. And this is how we arrive at those figures:
- 61.8 percent is arrived at after dividing 55 by 89. These numbers are immediately adjacent to each other.
- 38.2 percent is arrived at after dividing 34 by 89. These numbers are not immediately adjacent since one number, 55, is missing.
- 23.6 percent is arrived at after dividing 21 by 89. These numbers are not immediately adjacent since two numbers, 34 and 55, are missing.
The second set of three ratios used for retracement analysis is 50 percent, 76.4 percent and 100 percent. The second set of three ratios contains derivations from the first set. And this is how we arrive at those figures:
- 50 percent is arrived at by identifying the midpoint between 61.8 percent and 38.2 percent ((61.8% + 38.2%) ÷ 2 = 50%).
- 76.4 percent is arrived at by identifying the distance between 38.2 percent and 23.6 percent (38.2% - 23.6% = 14.6%). And that 14.6 percent is then added to 61.8 percent.
- 100 percent is arrived at by identifying where the previous trend began.
Taken together, these six Fibonacci retracement percentages form support and resistance benchmarks that can help you determine which trading tactics you are going to use at each price level..
You can see these Fibonacci levels in action very clearly on the daily Boeing (BA:xnys) chart below (see Figure 1 ). Each of the illustrated levels is based on the trend highlighted by the red arrow. If you were trading here, you could have used each level to help you determine whether to buy or sell as the stock price fluctuated.
Figure 1-Fibonacci Retracement Levels
In particular you should take note of how the stock price moved up and down, bouncing off both the 23.6 percent and 38.2 percent retracement levels.
Trends are usually not straight-line affairs. They are prone to temporary reversals, which could be compared with the natural ebb and flow of a tide.
When a stock price resumes its previous trend, stock and CFD traders want to predict how far the stock price is likely to continue moving. Fibonacci projection levels can help.
The sharp-eyed reader will notice that these calculations are actually the reverse of those used to create the first set of three ratios for the Fibonacci retracements we dealt with earlier. But as before, the method of calculation is not so important. Remembering the key ratios, marked in bold, is all that you ought to do.
The projection levels that you need to know are as follows:
- 161.8 percent is arrived at after dividing 89 by 55. These numbers are immediately adjacent to each other.
- 261.8 percent is arrived at after dividing 89 by 34. These numbers are not immediately adjacent since one number, 55, is missing.
- 423.8 percent is arrived at after dividing 89 by 21. These numbers are not immediately adjacent since two numbers, 34 and 55, are missing.
Knowing all three Fibonacci projection levels, and setting them as benchmarks, is a great way to predict support and resistance levels for stock and CFD trading.
You can see these Fibonacci levels in operation on the daily Coca Cola (KO:xnys) chart below (see Figure 2 ). The upward trend is highlighted by the red arrow. It has already bounced off the 161.8 percent level. If Coca Cola resumes the anticipated upward trend, you can assume that the stock will now continue to rise through and beyond the 161.8 percent level, until it bounces back down, with an adjustment, from the 261.8 percent level. Knowing the theory of this should help you to determine where to set your profit targets and, potentially, your exit levels-the levels at which Coca Cola may turn around and cause you to sell and take your profits.
Figure 2-Fibonacci Projection Levels
Notice that the stock price, based on the previous trend, is likely to move up to the 161.8 percent projection level in the near future. If it reaches this level then the 261.8 percent projection level becomes the next profit target level.
Fibonacci levels provide both horizontal and diagonal levels of support and resistance. So far we have looked at horizontal levels with retracements and projections.
The diagonal levels of support and resistance are called Fibonacci fans.
Fibonacci fans are based on three Fibonacci retracement levels, at 61.8 percent, 50 percent and 38.2 percent All three of these, as you've hopefully remembered, were among the six percentages used for retracements.
To construct a Fibonacci fan, you need to do the following, all of which is clearly explained by Figure 3 .
- Identify a recent trend, pinpointing where it started and ended.
- Draw two horizontal lines across the chart that go through the start-point and the end-point of that trend. These two horizontal lines equate to the highest and lowest prices that occurred during the trend.
- Draw a vertical line at the point where the trend ended. This will, in effect, run perpendicular between the horizontal lines that you've just drawn.
- Identify three horizontal Fibonacci levels (61.8 percent, 50 percent and 38.2 percent) as they relate to that trend.
- 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 line intersects one of the three horizontal Fibonacci levels.
This may seem complicated at first, but it is essentially simple. Once you can create a Fibonacci fan, you will be able to use it to anticipate critical support and resistance levels.
We have drawn a Fibonacci fan on the daily Coca Cola (KO:xnys) chart below (see Figure 3 ). Each of the illustrated levels was calculated based on the trend highlighted by the red arrow. Had you been the owner of Coca cola stock, this fan could have helped you determine the optimum moments to buy and sell.
Figure 3-Fibonacci Fan
You should notice how the stock price bounced off the middle ray of the Fibonacci fan in early January and is currently at the resistance level formed by the bottom ray of the fan. At this point, that bottom ray of the fan has a good chance of acting as resistance and sending the price of Coca Cola lower.
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