Fibonacci in Financial Markets

Fibonacci summary:

• Fibonacci is a popular way to identify support and resistance levels across financial markets. In this article I use a live example on EUR/USD.
• The root of Fibonacci analysis is the mathematical sequence of the Fibonacci sequence, which I touch on below.
• The aim of this article is trading analysis, so I’ve attempted to keep the math and background relatively light and the analytical application as front-and-center, which begins with the section for Fibonacci Application in Financial Markets.

Support and resistance is an important concept in trading analysis and while its firmly in the field of technical analysis, a little bit of knowledge around the concept could be helpful for those focusing on fundamental analysis, as well. Namely, in its ability to help manage risk, as support and resistance can offer ‘lines-in-the-sand’ with which traders can define their exposure or positioning, using actual market data to assist with both decision making and risk management.

Within the field of support and resistance are several different analytical mediums, and while none are perfect some will seem better suited than others for certain approaches. Fibonacci analysis has seen significant growth as online trading has taken over and likely one reason behind this is individual investors and traders’ ability to work with dynamic charts, offering tools and indicators with which they can apply to their own analysis.

Fibonacci isn’t something that’s relegated just to financial markets, it has a wide presence throughout the worth with which we live. Fibonacci is often attributed to Leonardo Fibonacci, an Italian mathematician born around A.D. 1170 and originally known as Leonardo of Pisa. He published a book in 1202 that was a textbook to teach tradesman how to do mathematical calculations, and this introduced the Fibonacci sequence to the Western world.

But the Fibonacci sequence has origins dating back to at least 200 BC in Indian mathematics and at its core it’s simply a mathematical sequence of numbers that builds on top of itself, by adding the two numbers prior. You can start with one and one, and then move on, as such:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1,597, etc.

Why Does Fibonacci Matter to non-Mathematicians?

Fibonacci shows in numerous ways across the world around us, and this was noted all the way back to the Western world’s introduction of the concept. The mating cycle of rabbits is often cited, as this was one of the examples offered by Leonardo of Pisa in his 1202 book, Liber Abaci. But the Fibonacci sequence can also be seen in many fruits and vegetables, or seed heads or pinecones displaying spiral patterns that, when counted, express Fibonacci numbers.

Take a sunflower, for instance: You’ll observe patterns curving left and right and if you count those spirals, your total will be a Fibonacci number. If you divide those spirals into those pointing left and those pointing right, you’ll get two consecutive Fibonacci numbers. This also applies to pineapples, pinecones and cauliflower.

But that’s not where the application to trading and financial markets comes in, for that, we must take the Fibonacci sequence to the next step, with the Golden Ratio and its related derivatives.

Fibonacci Sequencing in a Sunflower

The Golden Ratio

Within the Fibonacci sequence is a relationship between the numbers themselves known as the Golden Ratio. Once we get to ‘233’ in the sequence, dividing the number by the prior number in the sequence always delivers a value of 1.618. And the larger it goes, the closer the value is to 1.618, or the golden ratio.

This is important because from that ratio, we can begin to establish relationships elsewhere, and this is where the Fibonacci application to financial markets is borne.

Fibonacci Application in Financial Markets

From the Fibonacci sequence, and from the golden ratio, we can begin to find usable information for application on the chart. Automatically 161.8% is of interest as this is the golden ratio, and this can be used to devise ‘Fibonacci extensions’ or ‘Fibonacci projections.’

But we can take the sequencing of Fibonacci a step further, and if we divide a number in the sequence by the number following it, we get 61.8%. So, 55 divided by 89 gives us .6179 or 144 divided by 233 gives us .61803. This relationship will hold throughout the sequence, and this is similarly considered to be an important part of the sequence.

So, the trader can activate the Fibonacci retracement tool from their charting package, starting the annotation at the beginning of the trend and then drawing it to the end of the move. The tool will then apply the percentages or ‘retracements’ within the major move. The big level of .618 or 61.8% becomes an area to investigate for possible support or resistance.

We can then take the ratio of numbers in the sequence a step further. If we divide a number by the number two digits later (so skipping a number in the sequence), we’ll always arrive at 38.2%. So, 55 divided by 144 is .3819, or .382, or 38.2%. Or, 89 divided by 233 is .3819 or, .382 or, expressed otherwise, 38.2%.

From this, we can get a basis for applying a Fibonacci retracement, by noting a significant major move – with a high and low that has yet to be violated, and then apply the retracement to the start and end of the move. Retracement levels will then be applied at the 38.2% and 61.8% intervals.

EUR/USD Weekly Chart

Chart prepared by James Stanley, EUR/USD on Tradingview

Fibonacci a Step Further

Going along the lines of what we looked at above to arrive at the 38.2% ratio, we can take this a step further and divide a number in the sequence by the number three digits later. So, 34 divided by 144 is .2361, or 23.6%. Or, 233 divided by 977 is .23607, or .236 simplified, which equals 23.6%.

This gives us another digit which we can use on our Fibonacci tool with a 23.6% retracement.

So, just from the ratios produced by dividing a number in the sequence by the number following it, or two or three numbers following it, we get three important intervals of 23.6%, 38.2% and 61.8%.

Applying this to the chart will seem imbalanced, and there’s a couple of additional numbers that will often come into play when Fibonacci is applied to a trading chart.

The .786 or 78.6% retracement is quite common, as this is the square root of .618. But some charting packages will instead use 76.4 which is simply the inverse of 23.6 (1 - .236 = .764).

And lastly for the common levels, 50% is often found as a default level in Fibonacci retracement tools. This is not a Fibonacci level in any way at all, it’s merely a half-way point of the move being analyzed but nonetheless, it can come up as a support or resistance level to some degree of frequency, so many traders will choose to keep it on.

Once these levels are applied, the chart will look like this, with ‘1’ at the start of the move and ‘0’ at the end, with retracement levels at 23.6%, 38.2%, 50%, 61.8% and 76.4% or 78.6% (or both).

EUR/USD Weekly Chart

Chart prepared by James Stanley, EUR/USD on Tradingview

Fibonacci Retracement Levels as Basic Support and Resistance

In its most simple form, the above chart can be utilized by traders looking to incorporate Fibonacci retracement levels as support or resistance. The move being analyzed is the major move in EUR/USD from 2021-2022, and since the trend had finished in late-2022, there have been multiple important inflections.

The 2023 high in EUR/USD formed right around the 61.8% retracement. And then for the first half of 2024, the low had formed right around the 38.2% retracement, which ended up coming into play as resistance in December before sellers pushed an aggressive sell-off into the end of the year.

The 50% retracement at 1.0943 played a role, as well, helping to set resistance in both March and July of 2024, before seeing sellers defend the price in November as they held a lower-high ahead of the downturn in the pair.

The 23.6% retracement plots at 1.0200, and so far for 2025, that’s helping to mark the low for the year.

EUR/USD Weekly Chart

 Chart prepared by James Stanley, EUR/USD on Tradingview

Fibonacci Confluence

If there’s one reason for buyers or sellers to stand in to set a higher or a low, then two reasons could be better, right?

This speaks to confluence when there’s multiple reasons for a support or resistance level to play and from the above weekly chart in EUR/USD there’s an interesting relationship that we can begin to establish.

We have the dominant, major move that spanned from 2021 through 2022; but from those lows a bounce developed into early-2023 and that, too, is a major move with a high and low that hasn’t yet been violated; so, another major move.

We can also draw a Fibonacci retracement around that move which I’ve done in red on the below chart. That bounce was an almost perfect 61.8% retracement of the prior sell-off, with only one pip of difference between the retracement level (1.12748) and the 2023 swing high (1.12758).

But perhaps more interestingly is the confluence that can be seen between the two retracements, where the 61.8% retracement of the bounce plots at the same 1.0200 price that the 23.6% retracement of the dominant move plots.

Or the 50% marker of the bounce move plots at the same 1.0611 level which is the 38.2% retracement of the longer-term major move.

The fact that these levels align so near or, in this case, right at each other adds an element of confluence to each price, giving greater potential for each level to function as a support or resistance levels.

EUR/USD Weekly Chart

Chart prepared by James Stanley, EUR/USD on Tradingview

Fibonacci For Trading Strategy

So first and foremost, from the above charts we can look to operate with support and resistance on a shorter time frame. Since we’re using the weekly chart above, we can go down to the daily chart to look for daily highs or lows, reactions at those specific prices on the Fibonacci retracement, from which we can then investigate swings.

The 1.0200 support hit, for instance, marked the swing higher as a morning star formation had built. There was a similar backdrop back in April of last year when the 38.2% retracement (of the dominant move and the bounce move) helped to set support as a morning star formation built into a bounce.

And then there were episodes in November and December when that same price held the highs, indicated with daily wicks highlighting a bearish response.

Going back to 2023, there’s a number of these inflections that have taken place and I’ve marked a handful on the below chart, with red for resistance inflections and blue for support, with the logic being a wick on the daily intersecting with that Fibonacci retracement level opening the door for a counter-swing in the pair.

EUR/USD Daily Chart

Chart prepared by James Stanley, EUR/USD on Tradingview

Fibonacci For Shorter Terms

When I was learning Fibonacci for trading purposes much of the instruction seemed to be based on shorter terms, and as I gained experience and naturally gravitated towards longer-term horizons, the above analysis seemed to suit me more optimally. But – that doesn’t mean that Fibonacci analysis doesn’t have a usage on shorter time frames for traders that are looking for intra-day approaches.

So, from the above example there was a major move taking place from the December high around the 1.0611 level, which is the 38.2% retracement on both major moves – and down to the current 2025 low at 1.0200 which is the 23.6% retracement of the longer-term move and the 61.8% retracement of the shorter-term bounce move.

Well, that’s a major move that hasn’t yet seen the high or low violated, so a Fibonacci retracement can be applied. I’ve marked the move itself with a light green background, but it’s the inflections themselves that are most interesting, and I’ve highlighted those with a darker shade of green.

Shortly after the bounce from 1.0200, the 38.2% retracement of the shorter-term move was in-play at 1.0350, initially showing as resistance, and then as support.

The rally from that led to a run up to the 61.8% retracement at 1.0457, which led to a pullback to the 50% mark of 1.0404 (which was confluent with the 50% retracement of the bounce move). Notice the underside wicks on that four-hour chart, highlighting bullish defense of the level after the pullback.

From the pullback another bullish run appeared, and this time it was the 76.4% and 78.6% retracements that were holding the highs. The 78.6% level was a perfect match of the swing-high at 1.0533, before sellers came back in the picture.

At that point, sellers started to take back over, and that led to a dip to a lower-low, and the bounce from that held lower-high resistance at the 61.8% retracement at 1.0457.

After a precipitous sell-off at month-end and around the February open, support held above the 1.0200 level, and the bounce from that again started to work within the confines of Fibonacci structure, with 1.0350 showing initial resistance followed by 1.0284 as higher-low support.

EUR/USD Four-Hour Chart

Chart prepared by James Stanley, EUR/USD on Tradingview

Fibonacci in Financial Markets Summarized

Through the above example in EUR/USD I showed just a few of the ways that Fibonacci can be incorporated into a trading strategy and an approach. And to be sure, there are more, as many traders will apply Fibonacci retracements to even shorter time frames. But the point of this was not to demand any specific usage of the Fibonacci sequence or Fibonacci retracements, but rather to open the door to a wide field of study that can allow traders to make it their own.

Regardless of the analytical methods being used, the future will remain as uncertain to a large degree, and this is relevant for both technical and fundamental analysis.

As a trader, you will never control the future. You can only hope to control your own actions in the present. And while the past may be a decent guide for how we can build our expectations for the future, it will not be perfect – and this is why risk management is a necessity for traders looking to navigate an uncertain future.

I teach this in the Trader’s Course, of which the first three sections are available to anyone interested, and you can start that from the ‘start lesson’ button for those modules at the following page.

The Trader’s Course

The reason that support and resistance are valuable for traders is the potential for asymmetry, as ways to try to risk $1 in the aim of making $2, or $3. Not all support or resistance will hold, and we saw that across a few examples above. But some will, and in those cases, traders can find themselves in the position to benefit more than they had to risk.

Fibonacci can be one of the more interesting ways of tracking and locating support and resistance levels as I hope this article has explained.

--- written by James Stanley, Senior Strategist