What Makes a Fibonacci Ratio? How to Draw Fibonacci Retracement Levels with eToro
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History of Fibonacci
Before we get in too much about what Fibonacci is, let’s first answer the question “who is Fibonacci?” Leonardo Pisano, or Leonardo Fibonacci as he is most widely known, was a European mathematician in the Middle Ages who wrote Liber Abaci (Book of Calculation) in 1202 AD. In this book he discussed a variety of topics including how to convert currencies and measurements for commerce, calculations of profit and interest, and a number of mathematical and geometric equations. However, there are two things that jump to the forefront of our discussion in today’s world.First, in the beginning portions of Liber Abaci he discussed the benefits of using the Arabic numeral system. At the time, the influence of the defunct Roman Empire was still strong, and the preference of most European citizens was to use Roman numerals. However, in Liber Abaci, Fibonacci provided a very powerful, influential, and easytounderstand argument for using the Arabic numeral system. From that point on, the Arabic numeral system got a strong foothold in the European community and soon became the dominant method of mathematics in the region and eventually throughout the world. It was so strong that we still use the Arabic numeral system to this day.
The second important section of Liber Abaci that we use today is the Fibonacci sequence. The Fibonacci sequence is a series of numbers where each number in the series is the equivalent of the sum of the two numbers previous to it.
As you can see from this sequence, we need to start out with two “seed” numbers, which are 0 and 1. We then add 0 and 1 to get the next number in the sequence, which is 1. You then take that value and add it to the number previous to it to get the next number in the sequence. If we continue to follow that pattern we get this:
The Fibonacci sequence is so important to this discussion because we need those numbers to get our Fibonacci ratios. Without the Fibonacci sequence, the Fibonacci ratios wouldn’t exist.
What Makes a Fibonacci Ratio?
With the advent of the internet, there has been a lot of misinformation on which values make up Fibonacci Ratios. Proliferation of Fibonacci analysis, particularly in the realm of trading, has encouraged misinterpretations and misunderstandings of how and what makes a Fibonacci ratio. Let’s look at what a Fibonacci ratio is, how it is created, and some examples of those that are not really Fibonacci ratios at all.
Fibonacci Ratios
The math involved behind the Fibonacci ratios is rather simple. All we have to do is take certain numbers from the Fibonacci sequence and follow a pattern of division throughout it. As an example, let’s take a number in the sequence and divide it by the number that follows it.0 ÷ 1 = 0
1 ÷ 1 = 1
1 ÷ 2 = 0.5
2 ÷ 3 = 0.67
3 ÷ 5 = 0.6
5 ÷ 8 = 0.625
8 ÷ 13 = 0.615
13 ÷ 21 = 0.619
21 ÷ 34 = 0.618
34 ÷ 55 = 0.618
55 ÷ 89 = 0.618
Notice a pattern developing here? Starting at 21 divided by 34 going out to infinity you will ALWAYS get 0.618!
We could do this with other numbers in the Fibonacci sequence as well. For instance by taking a number in the sequence and dividing it by the number that precedes it, we see another constant number that develops.
1 ÷ 0 = 0
1 ÷ 1 = 1
2 ÷ 1 = 2
3 ÷ 2 = 1.5
5 ÷ 3 = 1.67
8 ÷ 5 = 1.6
13 ÷ 8 = 1.625
21 ÷ 13 = 1.615
34 ÷ 21 = 1.619
55 ÷ 34 = 1.618
89 ÷ 55 = 1.618
144 ÷ 89 = 1.618
Another pattern develops out of the numbers of the Fibonacci sequence. Now 1.618 actually holds even more significance because it is also called the Golden Ratio, the Golden Number, or the Divine Ratio, but I could go on for many more pages about that subject.
Here are some more examples of patterns that develop by taking numbers in the Fibonacci sequence and dividing them in a pattern with other numbers within the sequence.
DIVIDE BY 2ND FOLLOWING  DIVIDE BY 2ND PRECEDING  DIVIDE BY 3RD FOLLOWING  DIVIDE BY 3RD PRECEDING 

0 ÷ 1 = 0  1 ÷ 0 = 0  0 ÷ 2 = 0  2 ÷ 0 = 0 
1 ÷ 2 = 0.5  2 ÷ 1 = 2  1 ÷ 3 = 0.33  3 ÷ 1 = 3 
1 ÷ 3 = 0.33  3 ÷ 1 = 3  1 ÷ 5 = 0.2  5 ÷ 1 = 5 
2 ÷ 5 = 0.4  5 ÷ 2 = 2.5  2 ÷ 8 = 0.25  8 ÷ 2 = 4 
3 ÷ 8 = 0.375  8 ÷ 3 = 2.67  3 ÷ 13 = 0.231  13 ÷ 3 = 4.33 
5 ÷ 13 = 0.385  13 ÷ 5 = 2.6  5 ÷ 21 = 0.238  21 ÷ 5 = 4.2 
8 ÷ 21 = 0.381  21 ÷ 8 = 2.625  8 ÷ 34 = 0.235  34 ÷ 8 = 4.25 
13 ÷ 34 = 0.382  34 ÷ 13 = 2.615  13 ÷ 55 = 0.236  55 ÷ 13 = 4.231 
21 ÷ 55 = 0.382  55 ÷ 21 = 2.619  21 ÷ 89 = 0.236  89 ÷ 21 = 4.231 
34 ÷ 89 = 0.382  89 ÷ 34 = 2.618  34 ÷ 144 = 0.236  144 ÷ 34 = 4.235 
55 ÷ 144 = 0.382  144 ÷ 55 = 2.618  55 ÷ 233 = 0.236  233 ÷ 55 = 4.236 
89 ÷ 233 = 0.382  233 ÷ 89 = 2.618  89 ÷ 377 = 0.236  377 ÷ 89 = 4.236 
144 ÷ 377 = 0.382  377 ÷ 144 = 2.618  144 ÷ 610 = 0.236  610 ÷ 144 = 4.236 
As you can see, we could get many different numbers by just taking numbers within the Fibonacci sequence and developing a divisory pattern within the sequence. However, this is not the only way to come up with Fibonacci ratios. Once we have the numbers from dividing, we can then take the square roots of each of those numbers to get more numbers. See the chart below for some examples of those values.
FIBONACCI RATIO  OPERATION  RESULT 

0.236  Square root of 0.236  0.486 
0.382  Square root of 0.382  0.618 
0.618  Square root of 0.618  0.786 
1.618  Square root of 1.618  1.272 
2.618  Square root of 2.618  1.618 
4.236  Square root of 4.236  2.058 
What about 50%?
While the 50% ratio is often used in Fibonacci analysis, it is not a Fibonacci ratio. Some say that the 50% level is a Gann ratio, created by W.D. Gann in the early 1900’s. Others call the 50% level an inverse of a “sacred ratio.” Just like the Fibonacci ratios, many people will either take the inverse or square root of the “sacred ratios” to form more values. Some examples can be found in the table below.
SACRED RATIO  OPERATION  RESULT  INVERSE OF SACRED RATIO 

1  Square root of 1  1  1 
2  Square root of 2  1.414  0.5 
3  Square root of 3  1.732  0.333 
4  Square root of 4  2  2.236 
5  Square root of 5  0.25  0.2 
Whatever the source, the 50% ratio seems to be a rather important and relevant level when trading, so often times it is included in Fibonacci analysis as if it were a Fibonacci ratio. Some of the other numbers included in the table have been mistaken as Fibonacci ratios as well, but obviously are not.
How Fibonacci retracement works
In trading, these ratios are also known as retracement levels. Traders wait for prices to approach these Fibonacci levels and act according to their strategy. Usually, they look for a reversal signal on these widely watched retracement levels before opening their positions. The most commonly used of the three levels is the 0.618 – the inverse of the golden ratio (1.618), denoted in mathematics by the Greek letter .
How to draw Fibonacci retracement levels
Drawing Fibonacci retracement levels is a simple threestep process:In an uptrend:
 Step 1 – Identify the direction of the market: uptrend
 Step 2 – Attach the Fibonacci retracement tool on the bottom and drag it to the right, all the way to the top
 Step 3 – Monitor the three potential support levels: 0.236, 0.382 and 0.618
In a downtrend:
 Step 1 – Identify the direction of the market: downtrend
 Step 2 – Attach the Fibonacci retracement tool on the top and drag it to the right, all the way to the bottom
 Step 3 – Monitor the three potential resistance levels: 0.236, 0.382 and 0.618
Of course, it is more reliable to look for a confluence of signals (i.e. more reasons to take action on a position). Don’t fall into the trap of assuming that just because the price reached a Fibonacci level the market will automatically reverse.
Combine Fibonacci levels with Japanese Candlestick patterns, Oscillators and Indicators for a stronger signal. As you can see in the chart below, the “Three White Soldiers” pattern is confirmed by the fact that prices are trading above the Moving Average line, and additionally that the MACD (Moving Average/Convergence Divergence) is above the zero line.
Trading using Fibonacci retracements
Every trader, especially beginners, dreams of mastering the Fibonacci theory. A lot of traders use it to identify potential support and resistance levels on a price chart which suggests reversal is likely. Many enter the market just because the price has reached one of the Fibonacci ratios on the chart. That is not enough! It is better to look for more signals before entering the market, such as reversal Japanese Candlestick formations or Oscillators crossing the base line or even a Moving Average confirming your decision. Language



















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