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Mathematics has some fascinating applications in everyday life. The stock market is no exception: movements in price, volume and time are fertile ground for mathematical work. One of the most “familiar” applications of this dry discipline is the Fibonacci sequence and its properties. Let’s explore Fibonacci retracements with Green Chart and add a genuinely useful mathematical tool to your investing toolkit.
What is the Fibonacci sequence?
Fibonacci retracement is a fascinating topic. To fully understand and appreciate the concept, we first need to understand the Fibonacci sequence. The origins of the Fibonacci sequence can be traced back to ancient Indian mathematical texts, with some findings dating from 200 BC. Later, in the 12th century,, Leonardo Pisano Bogollo, an Italian mathematician from Pisa known to his friends as Fibonacci, discovered the Fibonacci numbers.
The Fibonacci sequence is a series of numbers starting from 0, arranged so that each number is the sum of the two numbers before it.
The simple Fibonacci sequence looks like this:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610…
Note the following:
233 = 144 + 89
144 = 89 + 55
89 = 55 + 34
The sequence goes on forever. Once the numbers are large enough, a property emerges: divide any number in the sequence by the one before it, and the ratio is always approximately 1.618.
For example:
610/377 = 1.618
377/233 = 1.618
233/144 = 1.618
The ratio 1.618 is known as the golden ratio, also called Phi. Fibonacci numbers are linked to nature. The ratio can be found in human faces, flower petals, animal bodies, fruit, vegetables, rock formations, galaxy formations and more. Back to the main topic: if you are interested, I recommend searching online for examples of the golden ratio – you will find plenty of surprises. Digging deeper into the ratio’s properties, you find remarkable consistency when a number in the Fibonacci sequence is divided by the number immediately after it.
For example:
89/144 = 0.618
144/233 = 0.618
377/610 = 0.618
At this point, remember that 0.618 expressed as a percentage is 61.8%.
The same consistency appears when any number in the Fibonacci sequence is divided by the number two places higher.
For example:
13/34 = 0.382
21/55 = 0.382
34/89 = 0.382
0.382 expressed as a percentage is 38.2%.
There is also consistency when a number in the Fibonacci sequence is divided by the number three places higher.
For example:
13/55 = 0.236
21/89 = 0.236
34/144 = 0.236
55/233 = 0.236
0.236 expressed as a percentage is 23.6%.
Fibonacci and the stock market
Many believe that the Fibonacci ratios – 61.8%, 38.2% and 23.6% – can be applied to stock charts. Fibonacci analysis can be used whenever there is a notable move up or down in price. Whenever a stock rises or falls sharply, it usually tends to retrace before continuing the trend. For example, if a stock has risen from 50 to 100, it may pull back to around 70 before rising to 120.
“Retracement forecasting” is a technique for identifying how far a retracement is likely to go. These retracement levels give traders good opportunities to enter new positions in the direction of the trend. The Fibonacci ratios – 61.8%, 38.2% and 23.6% – help traders identify likely retracement levels. Traders can use these levels to position themselves for a trade.
I will now take the 20-point move (39 → 59) as the Fibonacci upswing. According to Fibonacci retracement theory, after an advance one can anticipate that the stock’s subsequent correction will equal one of the Fibonacci ratios. For example, the first level the stock may correct to could be 23.6%. If the stock corrects further, traders can watch the 38.2% and 61.8% levels.
Note that in the example shown below, the stock fell back to the 61.8% level, at 46.8, before continuing higher.
We can also arrive at 46.8 with simple arithmetic
Total size of the upswing = 20
61.8% of the Fibonacci upswing = 61.8% × 20 = 12.3
61.8% retracement level: 59 – 12.3 = 46.7
In the same way, we can calculate the 38.2% level and the other ratios. There is no need to do this by hand, however, because charting tools do it for us.
Here is another example, in which the price of DGC rose from 42 to 180. The 138-point move therefore forms the Fibonacci upswing. The stock fell back 38.2%, to 127, before continuing higher.
Fibonacci retracements can also be applied to falling stocks to identify the levels to which a stock may rebound. In the chart below (FCN), the stock fell from 37 to 20, creating a 17-point Fibonacci downswing.
After the decline, the stock tried to recover and climbed back to 26.4, the 61.8% Fibonacci retracement level.
Drawing a Fibonacci retracement
As we know, Fibonacci retracement levels are moves on the chart that run against the trend. To use Fibonacci retracements, we first need to define the 100% Fibonacci move. The 100% move can be either a rise or a fall in price. To mark the 100% move, we pick the most recent peak and trough on the chart. Once these are identified, we connect them with the Fibonacci Retracement tool, available in most technical analysis software packages and in brokerage firms’ online price boards.
Here is a step-by-step guide:
Step 1: Identify the starting and ending trough and peak. In this case, the trough is at 10 and the peak at 37. The 27-point rise corresponds to 100%.
Step 2: Select the Fibonacci retracement tool from the charting tools
Step 3: Use the Fibonacci retracement tool to connect the trough and the peak.
How should you use Fibonacci levels?
Imagine you want to buy a particular stock but have missed it because it rallied sharply. In that situation, the most prudent course of action is to wait for the stock to retrace. Fibonacci retracement levels such as 61.8%, 38.2% and 23.6% act as potential levels to which the stock may correct.
By plotting Fibonacci retracement levels, investors can identify these levels and position themselves for a trading opportunity. Note, however, that like any indicator, Fibonacci retracements should be used as a confirmation tool, not as the deciding factor.
I will only buy a stock once it has met the other criteria on my checklist. In other words, I am more inclined to buy if the stock has:
- Formed a recognisable candlestick pattern
- A stop-loss that coincides with a support or resistance level
- Above-average volume.
Along with the points above, if the stop-loss also coincides with a Fibonacci level, I have a trade setup that lines up well on every count, so I will buy. The word “strong” describes how much confidence a trade setup carries. The more confirming factors we use to study the trend and reversals, the stronger the signal. The same logic applies to short-term trading.
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Happy Trading!!
