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Strategies for Trading Fibonacci Retracements
Leonardo Pisano, nicknamed Fibonacci, was an Italian mathematician born in Pisa in the year 1170. His father Guglielmo Bonaccio worked at a trading post in Bugia, now called Béjaïa, a Mediterranean port in northeastern Algeria. As a young man, Fibonacci studied mathematics in Bugia, and during his extensive travels, he learned about the advantages of the HinduArabic numeral system.
In 1202, after returning to Italy, Fibonacci documented what he had learned in the “Liber Abaci” (“Book of Abacus“). In the “Liber Abaci,” Fibonacci described the numerical series that is now named after him. In the Fibonacci sequence of numbers, after 0 and 1, each number is the sum of the two prior numbers. Hence, the sequence is as follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610 and so on, extending to infinity. Each number is approximately 1.618 times greater than the preceding number.
Key Takeaways
 In the Fibonacci sequence of numbers, after 0 and 1, each number is the sum of the two prior numbers.
 In the context of trading, the numbers used in Fibonacci retracements are not numbers in Fibonacci’s sequence; instead, they are derived from mathematical relationships between numbers in the sequence.
 Fibonacci retracement levels are depicted by taking high and low points on a chart and marking the key Fibonacci ratios horizontally to produce a grid; these horizontal lines are used to identify possible price reversal points.
This value–1.618–is called Phi or the Golden Ratio. The inverse of 1.618 is 0.618. The Golden Ratio mysteriously appears frequently in the natural world, architecture, fine art, and biology. For example, the ratio has been observed in the Parthenon, in Leonardo da Vinci’s painting the Mona Lisa, sunflowers, rose petals, mollusk shells, tree branches, human faces, ancient Greek vases, and even the spiral galaxies of outer space.
Fibonacci Levels Used in the Financial Markets
In the context of trading, the numbers used in Fibonacci retracements are not numbers in Fibonacci’s sequence; instead, they are derived from mathematical relationships between numbers in the sequence. The basis of the “golden” Fibonacci ratio of 61.8% comes from dividing a number in the Fibonacci series by the number that follows it.
For example, 89/144 = 0.6180. The 38.2% ratio is derived from dividing a number in the Fibonacci series by the number two places to the right. For example: 89/233 = 0.3819. The 23.6% ratio is derived from dividing a number in the Fibonacci series by the number three places to the right. For example: 89/377 = 0.2360.
Fibonacci retracement levels are depicted by taking high and low points on a chart and marking the key Fibonacci ratios of 23.6%, 38.2%, and 61.8% horizontally to produce a grid. These horizontal lines are used to identify possible price reversal points.
The 50% retracement level is normally included in the grid of Fibonacci levels that can be drawn using charting software. While the 50% retracement level is not based on a Fibonacci number, it is widely viewed as an important potential reversal level, notably recognized in Dow Theory and also in the work of W.D. Gann.
Fibonacci Retracement Levels as Trading Strategy
Fibonacci retracements are often used as part of a trendtrading strategy. In this scenario, traders observe a retracement taking place within a trend and try to make lowrisk entries in the direction of the initial trend using Fibonacci levels. Traders using this strategy anticipate that a price has a high probability of bouncing from the Fibonacci levels back in the direction of the initial trend.
For example, on the EUR/USD daily chart below, we can see that a major downtrend began in May 2020 (point A). The price then bottomed in June (point B) and retraced upward to approximately the 38.2% Fibonacci retracement level of the down move (point C).
Figure 1: EUR/USD Daily Chart Fibonacci retracement. Chart Courtesy of TradingView.
In this case, the 38.2% level would have been an excellent place to enter a short position in order to capitalize on the continuation of the downtrend that started in May. There is no doubt that many traders were also watching the 50% retracement level and the 61.8% retracement level, but in this case, the market was not bullish enough to reach those points. Instead, EUR/USD turned lower, resuming the downtrend movement and taking out the prior low in a fairly fluid movement.

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The likelihood of a reversal increases if there is a confluence of technical signals when the price reaches a Fibonacci level. Other popular technical indicators that are used in conjunction with Fibonacci levels include candlestick patterns, trendlines, volume, momentum oscillators, and moving averages. A greater number of confirming indicators in play equates to a more robust reversal signal.
Fibonacci retracements are used on a variety of financial instruments, including stocks, commodities, and foreign currency exchanges. They are also used on multiple timeframes. However, as with other technical indicators, the predictive value is proportional to the time frame used, with greater weight given to longer timeframes. For example, a 38.2% retracement on a weekly chart is a far more important technical level than a 38.2% retracement on a fiveminute chart.
Using Fibonacci Extensions
While Fibonacci retracement levels can be used to forecast potential areas of support or resistance where traders can enter the market in hopes of catching the resumption of an initial trend, Fibonacci extensions can complement this strategy by giving traders Fibonaccibased profit targets. Fibonacci extensions consist of levels drawn beyond the standard 100% level and can be used by traders to project areas that make good potential exits for their trades in the direction of the trend. The major Fibonacci extension levels are 161.8%, 261.8% and 423.6%.
Let’s take a look at an example here, using the same EUR/USD daily chart:
Fibonacci Retracements
Table of Contents
Fibonacci Retracements
Introduction
Fibonacci Retracements are ratios used to identify potential reversal levels. These ratios are found in the Fibonacci sequence. The most popular Fibonacci Retracements are 61.8% and 38.2%. Note that 38.2% is often rounded to 38% and 61.8 is rounded to 62%. After an advance, chartists apply Fibonacci ratios to define retracement levels and forecast the extent of a correction or pullback. Fibonacci Retracements can also be applied after a decline to forecast the length of a countertrend bounce. These retracements can be combined with other indicators and price patterns to create an overall strategy.
The Sequence and Ratios
This article is not designed to delve too deep into the mathematical properties behind the Fibonacci sequence and Golden Ratio. There are plenty of other sources for this detail. A few basics, however, will provide the necessary background for the most popular numbers. Leonardo Pisano Bogollo (11701250), an Italian mathematician from Pisa, is credited with introducing the Fibonacci sequence to the West. It is as follows:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610……
The sequence extends to infinity and contains many unique mathematical properties.
1.618 refers to the Golden Ratio or Golden Mean, also called Phi. The inverse of 1.618 is .618. These ratios can be found throughout nature, architecture, art, and biology. In his book, Elliott Wave Principle, Robert Prechter quotes William Hoffer from the December 1975 issue of Smithsonian Magazine:
….the proportion of .618034 to 1 is the mathematical basis for the shape of playing cards and the Parthenon, sunflowers and snail shells, Greek vases and the spiral galaxies of outer space. The Greeks based much of their art and architecture upon this proportion. They called it the golden mean.
Alert Zones
Retracement levels alert traders or investors of a potential trend reversal, resistance area or support area. Retracements are based on the prior move. A bounce is expected to retrace a portion of the prior decline, while a correction is expected to retrace a portion of the prior advance. Once a pullback starts, chartists can identify specific Fibonacci retracement levels for monitoring. As the correction approaches these retracements, chartists should become more alert for a potential bullish reversal. Chart 1 shows Home Depot retracing around 50% of its prior advance.
The inverse applies to a bounce or corrective advance after a decline. Once a bounce begins, chartists can identify specific Fibonacci retracement levels for monitoring. As the correction approaches these retracements, chartists should become more alert for a potential bearish reversal. Chart 2 shows 3M (MMM) retracing around 50% of its prior decline.
Keep in mind that these retracement levels are not hard reversal points. Instead, they serve as alert zones for a potential reversal. It is at this point that traders should employ other aspects of technical analysis to identify or confirm a reversal. These may include candlesticks, price patterns, momentum oscillators or moving averages.
Common Retracements
The Fibonacci Retracements Tool at StockCharts shows four common retracements: 23.6%, 38.2%, 50%, and 61.8%. From the Fibonacci section above, it is clear that 23.6%, 38.2%, and 61.8% stem from ratios found within the Fibonacci sequence. The 50% retracement is not based on a Fibonacci number. Instead, this number stems from Dow Theory’s assertion that the Averages often retrace half their prior move.
Based on depth, we can consider a 23.6% retracement to be relatively shallow. Such retracements would be appropriate for flags or short pullbacks. Retracements in the 38.2%50% range would be considered moderate. Even though deeper, the 61.8% retracement can be referred to as the golden retracement. It is, after all, based on the Golden Ratio.
Shallow retracements occur, but catching these requires a closer watch and quicker trigger finger. The examples below use daily charts covering 39 months. Focus will be on moderate retracements (38.250%) and golden retracements (61.8%). In addition, these examples will show how to combine retracements with other indicators to confirm a reversal.
Moderate Retracements
Chart 3 shows Target (TGT) with a correction that retraced 38% of the prior advance. This decline also formed a falling wedge, which is typical for corrective moves. The combination raised the reversal alert. Chaikin Money Flow turned positive as the stock surged in late June, but this first reversal attempt failed. Yes, there will be failures. The second reversal in midJuly was successful. Notice that TGT gapped up, broke the wedge trend line and Chaikin Money Flow turned positive (green line).
Chart 4 shows Petsmart (PETM) with a moderate 38% retracement and other signals coming together. After declining in SeptemberOctober, the stock bounced back to around 28 in November. In addition to the 38% retracement, notice that broken support turned into resistance in this area. The combination served as an alert for a potential reversal. Williams %R was trading above 20% and overbought as well. Subsequent signals affirmed the reversal. First, Williams %R moved back below 20%. Second, PETM formed a rising flag and broke flag support with a sharp decline the second week of December.
Golden Retracements
Chart 4 shows Pfizer (PFE) bottoming near the 62% retracement level. Prior to this successful bounce, there was a failed bounce near the 50% retracement. The successful reversal occurred with a hammer on high volume and followed through with a breakout a few days later.
Chart 5 shows JP Morgan (JPM) topping near the 62% retracement level. The surge to the 62% retracement was quite strong, but resistance suddenly appeared with a reversal confirmation coming from MACD (5,35,5). The red candlestick and gap down affirmed resistance near the 62% retracement. There was a twoday bounce back above 44.5, but this bounce quickly failed as MACD moved below its signal line (red dotted line).
Conclusion
Fibonacci retracements are often used to identify the end of a correction or a countertrend bounce. Corrections and countertrend bounces often retrace a portion of the prior move. While short 23.6% retracements do occur, the 38.261.8% zone covers the most possibilities (with 50% in the middle). This zone may seem big, but it is just a reversal alert zone. Other technical signals are needed to confirm a reversal. Reversals can be confirmed with candlesticks, momentum indicators, volume or chart patterns. In fact, the more confirming factors, the more robust the signal.
Using with SharpCharts
You can use our ChartNotes annotation tool to add Fibonacci Retracement Lines to your charts. Below, you’ll find an example of a chart annotated with Fibonacci Retracement Lines.
To learn more about how to add this annotation to your charts, check out our Support Center article on ChartNotes’ Line Study Tools.
What Is Fibonacci Retracement and Where Do Its Ratios Come From?
A Fibonacci retracement is a popular tool among technical traders. It is based on the key numbers identified by mathematician Leonardo Fibonacci in the 13 th century. Fibonacci’s sequence of numbers is not as important as the mathematical relationships, expressed as ratios, between the numbers in the series.
In technical analysis, a Fibonacci retracement is created by taking two extreme points (usually a major peak and trough) on a stock chart and dividing the vertical distance by the key Fibonacci ratios of 23.6%, 38.2%, 50%, 61.8%, and 100%. Once these levels are identified, horizontal lines are drawn and used to identify possible support and resistance levels.
Key Takeaways
 A Fibonacci retracement is a popular tool that traders can use to identify support and resistance levels, and place stoploss orders or target prices.
 A Fibonacci retracement is created by taking two extreme points on a stock chart and dividing the vertical distance by the key Fibonacci ratios of 23.6%, 38.2%, 50%, 61.8%, and 100%.
 Fibonacci retracements suffer from the same drawbacks as other universal trading tools, so they are best used in conjunction with other indicators.
Fibonacci Retracement
How the Fibonacci Sequence Works
Before we can understand why these ratios were chosen, let’s review the Fibonacci number series.
The Fibonacci sequence of numbers is as follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc. Each term in this sequence is simply the sum of the two preceding terms, and the sequence continues infinitely. One of the remarkable characteristics of this numerical sequence is that each number is approximately 1.618 times greater than the preceding number. This common relationship between every number in the series is the foundation of the common ratios used in retracement studies.
The key Fibonacci ratio of 61.8% is found by dividing one number in the series by the number that follows it. For example, 21 divided by 34 equals 0.6176 and 55 divided by 89 equals 0.6179.
The 38.2% ratio is found by dividing one number in the series by the number that is found two places to the right. For example, 55 divided by 144 equals 0.3819.
The 23.6% ratio is found by dividing one number in the series by the number that is three places to the right. For example, 8 divided by 34 equals 0.2352.
Fibonacci Retracement and Predicting Stock Prices
For reasons that are unclear, these Fibonacci ratios seem to play an important role in the stock market, just as they do in nature, and can be used to determine critical points that cause an asset’s price to reverse.
Fibonacci retracements are the most widely used of all the Fibonacci trading tools. This is partially due to their relative simplicity and partially due to their applicability to almost any trading instrument. They can be used to identify and confirm support and resistance levels, place stoploss orders or target prices, and even act as a primary mechanism in a countertrend trading strategy.
Fibonacci retracement levels use horizontal lines to indicate where possible support and resistance levels are. Each level is associated with one of the above ratios or percentages, indicating the percentage is how much of a prior move the price has retraced. The direction of the prior trend is likely to continue once the price of the asset has retraced to one of the ratios listed above.
The following chart illustrates how a Fibonacci retracement appears. Most modern trading platforms contain a tool that automatically draws in the horizontal lines. Notice how the price changes direction as it approaches the support/resistance levels.
In addition to the ratios described above, many traders also like using the 50% level.
The 50% retracement level is not really a Fibonacci ratio, but traders often like it because of the overwhelming tendency for an asset to continue in a certain direction once it completes a 50% retracement.
Fibonacci Retracement Pros and Cons
Despite the popularity of Fibonacci retracements, the tools have some conceptual and technical disadvantages that traders should be aware of when using them.
The use of the Fibonacci retracement is subjective. Different traders may use this technical indicator in different ways. Those traders who are profitable using the Fibonacci retracement verify its effectiveness; those who lose money say it is unreliable. Some argue technical analysis is a case of a selffulfilling prophecy. If traders are all watching and using the same levels or the same technical indicators, the price action may reflect that fact.
The underlying principle of any Fibonacci tool is a numeric anomaly that is not grounded in any logical proof. The ratios, integers, sequences, and formulas derived from the Fibonacci sequence are only the product of a mathematical irregularity. This is not inherently wrong, but it can be uncomfortable for traders who want to understand the rationale behind a trading strategy.
Furthermore, a Fibonacci retracement strategy can only point to possible corrections, reversals, and countertrend bounces. This system struggles to confirm any other indicators and doesn’t provide easily identifiable strong or weak signals.
The Bottom Line
Fibonacci trading tools suffer from the same problems as other universal trading strategies, such as the Elliott Wave theory. That said, many traders find uses for Fibonacci retracements and have found success using them to place transactions within greater price trends.
Fibonacci retracement can become even more powerful when used in conjunction with other indicators or technical signals. Investopedia Academy’s Technical Analysis course covers these indicators as well as how to transform patterns into actionable trading plans.

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