Fibonacci retracements and extensions

• The significance of Fibonacci numbers in the world around us
• Fibonacci numbers in trading: retracements and extensions
• Considerations worth taking into account while using Fibonacci in trading strategy

Mathematics defines the Fibonacci numbers and the sequence they form as a chain of numbers where each number is the sum of the two preceding ones. The Fibonacci sequence looks as follows:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and goes on indefinitely.

Even these numbers are named by Leonardo of Pisa (known as Fibonacci), who introduced these into western mathematics in his book 1202 “Liber Abaci”, the first time these numbers were mentioned is as early as 200 BC. The first known mention was made in an Indian mathematics book by Pingala, an ancient Indian poet and mathematician, where he enumerated possible patterns of Sanskrit poetry formed from syllables of two lengths.

The quotient between each successive pair of Fibonacci numbers approximates 1.618, or its inverse 0.618. This proportion is known as the golden ratio, the golden mean, ɸ, divine proportion and by other names.

Examples of Fibonacci numbers and their sequences are often spotted in nature.

• In a pineapple fruit, where 8 spiral lines go one way, while 5 or 13 the other way.
• In sunflowers, the spirals you see in the center are generated from this sequence ﹣ there are two series of curves winding in opposite directions, starting at the center and stretching out to the petals.

In roman cauliflower, the peaked florets are arranged in beautiful Fibonacci spirals, 8 and 13 in this case.

What seems really interesting, it turns out that in most of the plants, leaves and stems develop from a centrally placed cell cluster (called meristem) ﹣each of these developments grows in other direction and the angle of that direction is constant ﹣approximately 137,5 degree. This angle is called ‘golden angle’ and it is impossible to be described as a vulgar fraction. Interestingly though, its complement to 360 angle is 5/8 of full angle, more precisely 8/13 and even more precise, 13/21 and so forth. Looks familiar?

It is not really certain whether these patterns and ratios came to art naturally or by design, but the presence of Fibonacci in art is very common.

Some musicologics tend to notice the Fibonacci sequence in the art of music. Those relationships are typically noticed in the rhythm, but they are also quite apparent when it comes to shapes of musical instruments.

The golden ratio can be found throughout the violin by dividing lengths of specific parts of the instrument. Some believe this might be the reason why the violin sounds so beautiful.

As for always handcrafted violins, the golden mean that comes from the Fibonacci sequence is also used for saxophone mouthpieces, and even in the acoustic design of some cathedrals.

It is also noticeable in probably the most familiar musical instrument in the world: the full octave of the classical piano keyboard, which consists of 13 notes, places keys of C major chord in the Fibonacci sequence.

In paintings, the golden ratio is observed very often as well, predominantly in composition.

One of the biggest masterpieces of all time, 'Gioconda' (Mona Lisa) by Leonardo da Vinci, makes use of it as a frame for the subject’s pose on this Italian Renaissance masterpiece. With master Leonardo, this is not a coincidence, most certainly.

With the argument is that if these numbers apply everywhere in nature, there’s no reason why they can’t be applied to patterns on a chart. Chartists then convert these numbers to percentages. So, 0.618 becomes 61.8%.0.5 becomes 50% and so on. Traders who use the Fibonacci tool believe that price is drawn to the different levels of the Fibonacci sequence as if by a law of nature.

The Fib, as traders often call it, assumes the asset you are thinking of trading is in a trend, either up or down. As a tool it doesn’t provide reliable information if the market is ranging or consolidating. Once we’ve pulled up a chart that shows a strong trend, we look for major swing lows and swing highs.

A swing high will have a recent high with two lower highs on the left and right of the high itself, while a swing low is a recent low with at least two higher lows on either side of the low itself.

Now let’s take an example of how you might use the Fibonacci retracement tool on an OANDA platform.

Just below you have a chart for EUR/USD showing the base pair (EUR) beginning to break down against the Dollar. First, we select the Fib tool from the tools section on your chart. Once you’ve selected the Fib, you then click on the point of the most recent major swing high and drag the mouse down to the most recent major swing low. You’ll see the Fib maps out retracement levels between these two points; it’s these levels that represent potential areas of support and resistance and, therefore, of interest to a trader looking for entries and exits.

On this hourly EUR/USD chart, we can see the start of a possible downtrend from the high. The price action slipped below the 0.236 retracement, but found some support around the 0.382 retracement before retesting the 0.236 level above and failing at the next level of resistance.

Many traders use Fibonacci retracements as a guide for setting their stop loss. For example, if you were to enter a buy trade at the start of an upward trend, you could place your stop loss just below the origin of the swing low. Once the reversal trend gets going, you can move your stop loss up a few pips below the next Fibonacci retracement, repeating the process until the trend begins to exhaust itself.

If you were shorting a currency pair that was in a downward trend, you would apply the opposite technique, placing your stop loss just above each successive resistance level as indicated by the Fibonacci retracement tool.

This tool is slightly different from the Fibonacci retracement tool as it depends on connecting three different points on a trend in order for it to be useful, whereas the Fibonacci retracement requires only two points.

Let’s take an example. First, locate the Fibonacci extension tool - it’s in the same section as the Fib retracement tool if you’re using the TradingView platform.

Start by clicking on the bottom of the candle at the start of the impulse (or swing low in the example below), drag your mouse up to the end of that impulse where you click and draw down to the end of the retracement. The Fibonacci extension tool will spread out as you can see on the image below, giving you FIbonacci extension levels. We can then use these levels as potential profit targets.

If you look at the chart below, you can see the Fibonacci extension tool provides you with a variety of levels which could be seen to give you price points for taking profit. What you tend to find is the earlier levels are more accurate, but as the trend continues up, at least in this case, the candles start to move in a sideways fashion, closing in between the levels.

You might reasonably ask yourself, how do I know which Fibonacci Extension level to set my profit target at? The following factors could be of help:

Consider the market environment. Has there been a strong breakout, for example? The stronger the trend the more likely the upper extensions could prove useful to you.

You could test for confluence by drawing in major support and resistance levels to see if your Fib extension levels coincided with your Fib-derived price point for a take profit. You could also check to see where these levels are in relation to key moving averages, such as the 50 MA.

Unlike other indicators that draw from actual price data, both Fibonacci tools work outside of any real market data. Many traders will tell you that the Fibonacci tool works only in as much that so many traders use the Fibonacci retracement tool, their decisions based on readings from the Fibonacci retracement tool could influence the movement of the markets, creating a sort of self-fulfilling prophecy.

• Fibonacci ratios are common in everyday life, and are seen in galaxy formations, snail shells and the formation of petals. This is why many traders believe these common ratios also apply to the action of price in the financial markets
• Traders use the Fibonacci retracement and extension tools to mark out levels on a chart where price can be expected to pause and reverse, and are best used in a trending market
• To use the Fibonacci retracement tool, you typically connect the swing low to the swing high (or the reverse in a bearish trend) to reveal the ratios found in the FIbonacci sequence together with a halfway point: 23.6%, 38.2%, 50%, 61.8%, and 78.6%
• The Fibonacci extension tool works by connecting the first point of an impulse wave to the first pivot to the downside (or upside in a bearish trend) and then to the swing high
• Common Fibonacci extension levels are 61.8%, 100%, 161.8%, 200%, and 261.8%
• Both retracement and extension levels can serve as areas of support and resistance but traders should consider the environment of the market, such as momentum and seasonality, before relying on them exclusively for favorable results

If you want to be a good leverage trader, you need good trading education. Explore the variety of training materials available in our learning section, such as our free webinars, workshops and how-to videos. Once you’ve opened an account, live or demo, you can put your knowledge into practice.

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