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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 Retracement Definition & Levels
What is a Fibonacci Retracement?
A Fibonacci retracement is a term used in technical analysis that refers to areas of support or resistance. Fibonacci retracement levels use horizontal lines to indicate where possible support and resistance levels are. Each level is associated with a percentage. The percentage is how much of a prior move the price has retraced. The Fibonacci retracement levels are 23.6%, 38.2%, 61.8% and 78.6%. While not officially a Fibonacci ratio, 50% is also used.
The indicator is useful because it can be drawn between any two significant price points, such as a high and a low, and then the indicator will create the levels between those two points.
If the price rises $10, and then drops $2.36, it has retraced 23.6%, which is a Fibonacci number. Fibonacci numbers are found throughout nature, and therefore many traders believe that these numbers also have relevance in the financial markets.
Key Takeaways
 The indicator connects any two points that the trader views at relevant, typically a high and low point.
 Once the indicator has been drawn on the chart, the levels are fixed and will not change. The percentage levels provided are areas where the price could stall or reverse.
 Levels should not be relied on exclusively. For example, it is dangerous to assume the price will reverse after hitting a specific Fibonacci level. It may, but it also may not.
 Fibonacci retracement levels are most frequently used to provide potential areas of interest. If a trader wants to buy, they watch for the price to stall at a Fibonacci level and then bounce off that level before buying.
 The most commonly used ratios include 23.6%, 38.2%, 50%, 61.8% and 78.6%. These represent how much of a prior move the price has corrected or retraced.
The Formulas for Fibonacci Retracement Levels Are:
The indicator itself doesn’t have any formulas. When the indicator is applied to a chart the user chooses two points. Once those two points are chosen, the lines are drawn at percentages of that move.
If the price rises from $10 to $15, and these two prices levels are the points used to draw the retracement indicator, then 23.6% level will be at $13.82 ($15 – ($5 x 0.236)) = $13.82. The 50% level will be at $12.50 ($15 – ($5 x 0.5)) = $12.50.
How to Calculate Fibonacci Retracement Levels
As discussed above, there is nothing to calculate when it comes to Fibonacci retracement levels. They are simply percentages of whatever price range is chosen.
You may wonder where these numbers come from, though. They are based on something called the Golden Ratio.
If you start a sequence of numbers with zero and one, and then keep adding the prior two numbers, you end up with a number string like this:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987. with the string continuing on indefinitely.
The Fibonacci retracement levels are all derived from this number string. Excluding the first few numbers, as the sequence gets going, if you divide one number by the next number you get 0.618, or 61.8%. Divide a number by the second number to its right and you get 0.382 or 38.2%. All the ratios, except for 50% since it is not an official Fibonacci number, are based on some mathematical calculation involving this number string.
Interestingly, the Golden Ratio of 0.618 or 1.618 is found in sunflowers, galaxy formations, shells, historical artifacts and architecture.
Fibonacci Retracement
What Do Fibonacci Retracement Levels Tell You?
Fibonacci retracements can be used to place entry orders, determine stop loss levels, or set price targets. For example, a trader may see a stock moving higher. After a move up it retraces to the 61.8%% level, and then starts to bounce again. Since the bounce occurred at a Fibonacci level, and the longer trend is up, the trader decides to buy. They could set a stop loss at the 78.6% level, or the 100% level (where the move started).
Fibonacci levels are used in other forms technical analysis as well. For example, they are prevalent in Gartley patterns and Elliott Wave theory. After a significant price movement up or down, when the price retraces (which it always does), these forms of technical analysis find the retracements will tend to reverse near certain Fibonacci levels.
Fibonacci retracement levels are static prices that do not change, unlike moving averages. The static nature of the price levels allows for quick and easy identification. This allows traders and investors to anticipate and react prudently when the price levels are tested. These levels are inflection points where some type of price action is expected, either a rejection or a break.
The Difference Between Fibonacci Retracements and Fibonacci Extensions
While Fibonacci retracements apply percentages to a pullback, Fibonacci extensions apply percentages to a move back in the trending direction. For example, a stock goes from $5 to $10, and then back to $7.50. The move from $10 to $7.50 is a retracement. If the price starts rallying again and goes to $16, that is an extension.
Limitations of Using Fibonacci Retracement Levels
While the retracement levels indicate where the price could potentially find support or resistance, there are no assurances the price will actually stop there. This is why other confirmation signals are often used, such as the price actually starting to bounce off the level.
The other argument against Fibonacci retracement levels is that there are so many of them that the price is likely to reverse near one of them quite often. The problem is that in advance traders struggle to know which one will be useful on the current retracement they are analyzing.
How to Use Fibonacci Retracement to Enter a Trade
The first thing you should know about the Fibonacci tool is that it works best when the forex market is trending.
The idea is to go long (or buy) on a retracement at a Fibonacci support level when the market is trending up, and to go short (or sell) on a retracement at a Fibonacci resistance level when the market is trending down.
Fibonacci retracement levels are considered a predictive technical indicator since they attempt to identify where price may be in the future.
The theory is that after price begins a new trend direction, the price will retrace or return part way back to a previous price level before resuming in the direction of its trend.
Finding Fibonacci Retracement Levels
Then, for downtrends, click on the Swing High and drag the cursor to the most recent Swing Low.
For uptrends, do the opposite. Click on the Swing Low and drag the cursor to the most recent Swing High.
Now, let’s take a look at some examples on how to apply Fibonacci retracements levels to the currency markets.
Uptrend
This is a daily chart of AUD/USD.
Here we plotted the Fibonacci retracement levels by clicking on the Swing Low at .6955 on April 20 and dragging the cursor to the Swing High at .8264 on June 3.
Tada! The software magically shows you the retracement levels.
As you can see from the chart, the Fibonacci retracement levels were .7955 (23.6%), .7764 (38.2%), .7609 (50.0%), .7454 (61.8%), and .7263 (76.4%).
Now, the expectation is that if AUD/USD retraces from the recent high, it will find support at one of those Fibonacci retracement levels because traders will be placing buy orders at these levels as price pulls back.
Now, let’s look at what happened after the Swing High occurred.
Price pulled back right through the 23.6% level and continued to shoot down over the next couple of weeks.
Later on, around July 14, the market resumed its upward move and eventually broke through the swing high.
Clearly, buying at the 38.2% Fibonacci level would have been a profitable longterm trade!
Downtrend
Now, let’s see how we would use the Fibonacci retracement tool during a downtrend. Below is a 4hour chart of EUR/USD.
As you can see, we found our Swing High at 1.4195 on January 25 and our Swing Low at 1.3854 a few days later on February 1.
The retracement levels are 1.3933 (23.6%), 1.3983 (38.2%), 1.4023 (50.0%), 1.4064 (61.8%) and 1.4114 (76.4%).
The expectation for a downtrend is that if price retraces from this low, it could possibly encounter resistance at one of the Fibonacci levels because traders who want to play the downtrend at better prices may be ready with sell orders there.
Let’s take a look at what happened next.
Yowza, isn’t that a thing of beauty?!
The market did try to rally, stalled below the 38.2% level for a bit before testing the 50.0% level.
In these two examples, we see that price found some temporary forex support or resistance at Fibonacci retracement levels.
Because of all the people who use the Fibonacci tool, those levels become selffulfilling support and resistance levels.
If enough market participants believe that a retracement will occur near a Fibonacci retracement level and are waiting to open a position when the price reaches that level, then all those pending orders could impact the market price.
One thing you should take note of is that price won’t always bounce from these levels. They should be looked at as areas of interest, or as Cyclopip likes to call them, “KILL ZONES!” We’ll teach you more about that later on.
For now, there’s something you should always remember about using the Fibonacci tool and it’s that they are not always simple to use!
If they were that simple, traders would always place their orders at Fibonacci retracement levels and the markets would trend forever.
In the next lesson, we’ll show you what can happen when Fibonacci retracement levels FAIL.
Fibonacci Retracement Levels in Day Trading
Tool to Help Isolate When Pullbacks Could End
Moves in a trending direction are called impulses, and moves against a trend are called pullbacks. Fibonacci retracement levels highlight areas where a pullback can reverse and head back in the trending direction, making them helpful in confirming trendtrading entry points.
Origins of Fibonacci Levels
Fibonacci levels are derived from a number series that Italian mathematician Leonardo of Pisa—also known as Fibonacci—introduced to the west during the 13th century. The sequence starts like this:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89.
Each new number is the sum of the two numbers before it. As the sequence progresses, each number is approximately 61.8% of the next number, approximately 38.2% of the following number, and approximately 23.6% of the number after that. Subtract 23.6 from 100, and the result is 76.4.
These are Fibonacci retracement levels: 76.4, 61.8, 38.2, and 23.6.
The Relevance of the Sequence
What Fibonacci and scholars before him discovered is that this sequence is prevalent in nature in spiral shapes such as seashells, flowers, and even constellations. As a spiral grows outward, it does so at roughly the same rate as the percentages derived from the Fibonacci ratios.
Some believe these ratios extend beyond just shapes in nature and actually predict human behavior. The thinking is that people start to become uncomfortable with trends that cause changes to happen too rapidly and adjust their behavior to slow or reverse the trend.
According to this theory, if someone started out with $100 in his wallet, he would begin to slow his spending—or stop altogether—once he has spent about $61.80 and has only about $38.20 remaining.
How to Use Fibonacci Retracement Levels
When a stock is trending very strongly in one direction, the belief is that the pullback will amount to one of the percentages included within the Fibonacci retracement levels: 23.6, 38.2, 61.8, or 76.4. Some models also include 50%.
For example, if a stock jumps from $10 to $11, the pullback should be expected to be approximately 23 cents, 38 cents, 50 cents, 62 cents, or 76 cents. Early or late in trends, when a price is still gaining or losing steam, it is more typical to see retracements of a higher percentage.
In this image, you’ll notice that between 61.8% and 38.2% there are two downward trends. This is an example of a Fibonacci retracement. The theory states that is a usual circumstance for stocks to trend in this manner because it is inherent in behavior to follow the sequence.
If your day trading strategy provides a shortsell signal in that price region, the Fibonacci level helps confirm the signal. The Fibonacci levels also point out price areas where you should be on high alert for trading opportunities.
Using a Fibonacci retracement tool is subjective. There are multiple price swings during a trading day, so not everyone will be connecting the same two points. The two points you connect may not be the two points others connect.
To compensate for this, draw retracement levels on all significant price waves, noting where there is a cluster of Fibonacci levels. This may indicate a price area of high importance.
Retracement Warnings
While useful, Fibonacci levels will not always pinpoint exact market turning points. They provide an estimated entry area but not an exact entry point. There is no guarantee the price will stop and reverse at a particular Fibonacci level, or at any of them.
If the price retraces 100% of the last price wave, the trend may be in question. If you use the Fibonacci retracement tool on very small price moves, it may not provide much insight. The levels will be so close together that almost every price level appears important.
Fibonacci retracements provide some areas of interest to watch on pullbacks. They can act as confirmation if you get a trade signal in the area of a Fibonacci level. Play around with Fibonacci retracement levels and apply them to your charts, and incorporate them if you find they help your trading.
Fibonacci Retracement Trading Strategy In Python
Fibonacci trading tools are used for determining support/resistance levels or to identify price targets. It is the presence of Fibonacci series in nature which attracted technical analysts’ attention to use Fibonacci for trading. Fibonacci numbers work like magic in finding key levels in any widely traded security. In this article, I will explain one of the famous Fibonacci trading strategy: retracement to identify support level.
Fibonacci sequence
The Fibonacci sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610……
It extends to infinity and can be summarized using below formula:
What are some interesting facts about the Fibonacci sequence?
Similarly, divide any number in the sequence by the next number; the ratio is always approximately 0.618.
0.618 expressed in percentage is 61.8%.
The square root of 0.618 is 0.786 (78.6%).
Similar consistency is found when any number in the sequence is divided by a number two places right to it.
0.382 expressed in percentage is 38.2%
Also, there is consistency when any number in the sequence is divided by a number three places right to it.
0.236 expressed in percentage terms is 23.6%.
The ratios 23.6%, 38.2%, 61.8%, and 78.6% are known as the Fibonacci ratios.
Fibonacci retracement trading strategy
We can arrive at $230 by using a simple math
Total up move = $250 – $200 = $50
38.2% of up move = 38.2% * 50 = $19.1
Retracement forecast = $250 – $19.1 = $230.9
Any price level below $230 provides a good opportunity for the traders to enter into new positions in the direction of the trend. Likewise, we can calculate for 23.6%, 61.8% and the other Fibonacci ratios.
How to find Fibonacci retracement levels?
Let’s take an example of Exxon Mobil to understand the Fibonacci retracement construction
As seen from the graph, there is substantial upward movement in the price from September 2020 to end of October 2020. In this case, the minimum price is $76 and maximum price is $84. The $8 is the total up move.
The retracement levels for Fibonacci ratios of 23.6%, 38.2% and 61.8% are calculated as follows:
Output:
The first retracement level at 23.6% is $82.10, the second retracement level at 38.6% is $80.90, and the next retracement level at 61.8% is $79.05. During midNovember, the Exxon Mobil stock price went down to $80.40, (falling below 38.6% retracement level) and then continued the upward movement.
How to use the Fibonacci retracement trading strategy?
This Fibonacci retracement trading strategy is more effective over a longer time interval and like any indicator, using the strategy with other technical indicators such as RSI, MACD, and candlestick patterns can improve the probability of success.
Good luck with Fibo nacci trading
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Disclaimer: All investments and trading in the stock market involve risk. Any decisions to place trades in the financial markets, including trading in stock or options or other financial instruments is a personal decision that should only be made after thorough research, including a personal risk and financial assessment and the engagement of professional assistance to the extent you believe necessary. The trading strategies or related information mentioned in this article is for informational purposes only.

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