XM News: Confluence of the Fibonacci Numbers on a Currency Pair

Fibonacci is shrouded in mystery, which adds to the intrigue of the mythology that surrounds it. However, in terms of market applicability, the simple version is that Fibonacci retracement levels provide potential areas for support and/or resistance to develop; and because market participants may use these levels in their analysis and, as a result, because these prices have a potential impact on price behavior, this can be an excellent addition to the FX trader's repertoire of support and resistance analysis.

Origins

Leonardo Fibonacci, an Italian mathematician, is credited with discovering the Fibonacci sequence in the 13th century, thus the name 'Fibonacci.' While his book Liber Abaci popularized the Fibonacci sequence in the Western world, traces may be discovered in Indian mathematics dating back to 200 BC. The steps are straightforward: The next value is calculated by adding two integers together. So 1+1 equals 2, 1+2 equals 3, 2+3 equals 5, 5+3 equals 8, and so on. The first 22 Fibonacci sequence values are listed below:

13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711

When we look at the connection of the numbers in the sequence to each other, things start to become interesting. If we take a figure and divide it by the previous value, we obtain something similar to 161.8 percent. So, after we get out of the first part of the series, each number in the sequence is 161.8 percent bigger than the previous value (after the value of 89). This is the Golden Ratio of 161.8%.

• 17711/10946 = 1.61803

• 10946/6765 = 1.61803

• 6765/4181 = 1.61803

• 6765/4181 = 1.61803

What astonished Fibonacci over a thousand years ago, and what shocked a thousand years before that, is how prevalent this ratio and sequence are in the world around us. Fibonacci used the mating cycle of rabbits as an example in Liber Abaci, demonstrating how rabbit populations in isolation would expand according to the numerical sequence of 1, 1, 2, 3, 5, 8, 13, and so on. However, this is just the tip of the iceberg; the number of flower petals will often follow the following sequence: Lilies have three petals, buttercups have five, chicory has twenty-one, and daisies have 34. To provide for optimum sunlight, each petal is set. at 618 per turn. The Fibonacci sequence may be seen in tree branches in the way trunks split and branches develop. In a geometric spiral pattern, shells, storms, and even human faces conform to the Golden ratio.

Looking down at your right arm right now, you can see that you have eight fingers, five on each hand, three bones in each finger, two bones in each thumb, and one thumb on each hand. Oh, and the ratio between your forearm and hand — that, too, is presumably governed by the Golden ratio.

Market Applicability

While many graduate-level mathematics students are preoccupied with the application of Fibonacci in nature, traders have more immediate concerns: applying the subject to financial markets. Fibonacci, in its most frequent form, employs the golden ratio in support and resistance analysis. So, plot a substantial rise, draw a line at 61.8 percent of that move, and we have an area to keep an eye on for a likely pullback to find support. The reciprocal of.618 is.382, so we have another figure to deal with at the 38.2% level.

On the chart below, we're looking at the EUR/USD lifetime move, from the low in 2000 to the high in 2009. We start at the beginning of the move and draw the retracement to the top, and we can see the retracement at 1.3056 38.2 percent of the way down. At 1.1212, we can also observe the 61.8 percent retracement of this trend. Take note of how this level aided in the formation of resistance in the pair for 15 of the 30 months after its introduction in January of 2015. As the EUR/USD dropped like a rock in expectation of ECB QE coming online in a few short months, we found support at this level on the way down in January of 2015; however, we then had eight continuous months of resistance at or around this critical 61.8 percent retracement level.

EUR/USD Monthly: 15 of 30 Months with 61.8 percent Resistance

3 Months of Support, Retracement

The EUR/USD has been on a roller coaster ride over the last several months. Following a somewhat frightening dip surrounding the U.S. Presidential Election leading up to the start of 2017 (seen in red below), the pair put in an aggressive turnaround as bulls ran rampant. However, as prices were in the process of reversing from the previous negative mode into a more bullish one, the 38.2 percent retracement of the post-Election rise gave some support (seen in green) before the 61.8 percent retracement provided some resistance (indicated with purple). After prices broke above those highs and went wild, resistance has started to form near the 161.8% extension of that advance (orange box).

EUR/USD Daily: Fib Applied to recent move in EUR/USD, 161.8 Extension Providing Resistance

Going a Step Further

Levels discovered around 61.8 and 38.2 percent retracements may be useful for traders, as seen by large swings of different shapes and sizes. This may be used for both short-term and long-term charts, although as is typically the case in technical analysis, longer-term studies tend to be a little more consistent due to the bigger number of viewpoints over a longer assessment time.

However, we can take it a step further using Fibonacci analysis. We already mentioned. True, 382 is the reciprocal of.618, however, this isn't the entire significance of.382. If we pick any number in the series after the first set of numbers and divide it by the value two places further down in the sequence, we get.382 or 38.2 percent.

• 13/34 =.382

• 21/55 =.3818 – rounded to.382

• 34/89 =.382

• 55/144 =.3819

But we can take it a step further by dividing a value in the sequence by a value three places later to get a consistent result of 23.6.

• 21/89 =.2359

• 13/55 =.2363

• 55/233 =.2361

• 34/144 =.2361

• 55/233 =.2361

This provides us with another retracement number of 23.6 percent to deal with. So we now have the 23.6, 38.2, and 61.8 percent retracement levels to use in our search for support and/or resistance.

We're not done yet: there's still room for improvement. With retracement levels of 23.6, 38.2, and 61.8 percent, the research will be fairly uneven, with two values in one half of the retracement and just one in the other. This has prompted market players to go beyond the box, as many will simply take the reciprocal of 23.6 and use it as a level as well. This would be the 76.4 percent retracement, which has no genuine Fibonacci significance. But.786 is a fascinating number to deal with since it is the square root of.618, and it may be a potentially more appealing stand-in for.764.

This gives us four values across the chart, and in reality, many traders may apply a mid-line at 50%, which has no genuine Fibonacci value; nevertheless, that observation is much less relevant to traders than the fact that other traders and analysts have it on their chart and may react to it.

This offers us five figures to deal with when analyzing trading data using Fibonacci retracements: 23.6, 38.2, 50, 61.8, and 78.6. (or 76.4).

Putting Everything Together

As previously stated, the goal of this research is not to predict what will occur in the future. No analysis, whether based on Fibonacci, Astrology or Psychological levels, can provide that. The usefulness of identifying support and resistance lies in the capacity to control risks with trading setups. If prices are heading up, that's great; if the uptrend breaks down, you may exit with a little loss, all in the name of limiting the damage when markets eventually come around. But if that uptrend continues, you'll be in a terrific position to manage a winning position.

The key to using Fibonacci retracements is to identify a viable significant move and then let market action lead to how each level should be treated. On the AUD/USD daily chart below, we can see a Fibonacci retracement applied to a recent negative move. 2015 high is drawn down to the 2016 low in orange, and we've used red and blue boxes to emphasize a couple of the most noticeable instances of resistance or support that have arisen as a result of these intervals.

While the following chart is far from ideal in that it does not show every point of support or resistance, it does show quite a few. As we described in our last post, the possibility of confluence might include levels from many kinds of analysis, such as psychological whole numbers.

On the AUD/USD chart below, we used the same Fibonacci retracement as previously and added levels for psychological levels at.7000,7500, and.8000, as well as a price action swing indicated by a green box. While we don't capture every top or bottom, we do catch a lot of them with these basic kinds of analysis. And the barrier that persisted in the pair at the 61.8 percent retracement is confluent with the.7750 psychological level, which is likely why bulls struggled to break past it.

Daily AUD/USD: Confluence of Support and Resistance

Price action may be used to find out how to trade with each of these possible support or resistance inflections depending on the context of that market's state at a certain moment in time when traders have this system of support and resistance in their analytical quiver.