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Contents

## 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 Hindu-Arabic 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 trend-trading strategy. In this scenario, traders observe a retracement taking place within a trend and try to make low-risk 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.

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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.

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 five-minute 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 Fibonacci-based 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:

## 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 counter-trend 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 (1170-1250), 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.

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 3-9 months. Focus will be on moderate retracements (38.2-50%) 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 mid-July 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 September-October, 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 two-day 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 counter-trend bounce. Corrections and counter-trend bounces often retrace a portion of the prior move. While short 23.6% retracements do occur, the 38.2-61.8% 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.

## How to use Fibonacci Retracements

The Fibonacci retracements pattern can be useful for swing traders to identify reversals on a stock chart. On this page we will look at the Fibonacci sequence and show some examples of how you can identify this pattern.

Fibonacci numbers were developed by Leonardo Fibonacci and it is simply a series of numbers that when you add the previous two numbers you come up with the next number in the sequence. Here is an example:

1, 2, 3, 5, 8, 13, 21, 34, 55

See how when you add 1 and 2 you get 3? Now add 2 and 3 and you get 5, and so on. So how does this sequence help you as a swing trader?

Well, the relationship between these numbers is what gives us the common Fibonacci retracements pattern in technical analysis.

## Fibonacci retracements pattern

Stocks will often pull back or retrace a percentage of the previous move before reversing. These Fibonacci retracements often occur at three levels: 38.2%, 50%, and 61.8%. Actually, the 50% level really does not have anything to do with Fibonacci, but traders use this level because of the tendency of stocks to reverse after retracing half of the previous move. Here is an example using a graphic explaining the retracement pattern:

This picture shows a graphical representation of the reversal points for stocks in an uptrend. The pattern is reversed for stocks that are in down trends.

After a stock makes a move to the upside (A), it can then retrace a part of that move (B), before moving on again in the desired direction (C). These retracements or pullbacks are what you as a swing trader want to watch for when initiating long or short positions.

Once the stock begins to pull back (retrace), then you can plot these retracement levels on a chart to look for signs of a reversal. You do not automatically buy the stock just because it is at a common retracement level! Wait, and look for candlestick patterns to develop at the 38.2% area. If you do not see any signs of a reversal, then it may go down to the 50% area. Look for a reversal there. You do not know if or when the stock will reverse at a Fibonacci level! You just mark these areas on a chart and wait for signal to go long or short.

## How to draw a fib grid

So how do we identify Fibonacci patterns on a chart. Easy, we draw a Fibonacci grid (fib grid) using swing points. Here is an example:

Draw the fib grid from the swing point high and the swing point low of a swing. Your charting software should come with this feature. It is a standard option on most charting packages. If not, you can calculate it manually by using this formula:

Calculate the range from the swing point high to the swing point low.

Now multiply the range times a Fibonacci ratio: 38.2% (0.382), 50% (0.500), and 61.8% (0.618).

Finally, subtract that number from the swing point high. That will give you your Fibonacci levels.

This chart shows an actual trade that I made. HS pulled back into the TAZ and then formed a bullish engulfing candle right at the 50% level. That gave me the signal to go long. Nice trade!

## Is it useful?

Well. maybe. sometimes.

Most of the time, when you draw a fib grid on a chart, you will notice that the grid lines up with support and resistance areas that you would see anyway without drawing the lines in! So you really do not need to draw the lines in. Instead, you can just look at a chart and estimate where the levels are.

Look again at the chart above of HS. If you didn’t draw the Fibonacci retracement lines in, you can still tell just by looking at the chart that the stock has retraced 50% of the previous move.

If drawing the lines in helps you to better visualize the fib levels, then by all means use it! The choice is up to you.

## Fibonacci eBook

Check out this Fibonacci eBook. It was written by Wayne Gorman who has 25 years experience in trading, forecasting, and portfolio management. He also worked for Citibank and Westpac Banking Corporation.

This 90 page e-book goes into detail on Fibonacci time relationships, retracements, extensions, clusters, etc. There is also a big emphasis on Elliott Wave theory in this eBook. Some of it can get complicated but you’ll definitely be an expert on Fibonacci by the time you finish reading this!

So there you have it. Hopefully, this page gave you a good idea of how Fibonacci works. At least now you can start plotting fib grids and looking at retracement levels the next time you consider a trade.

Price is king. Wait for signs of a reversal before you initiate a trade!

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