Fibonacci Retracement Levels

What Are Fibonacci Retracement Levels?

Fibonacci retracement levels—stemming from the Fibonacci sequence—are horizontal lines that indicate where support and resistance are likely to occur.

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. The indicator will then create the levels between those two points.

Suppose the price of a stock rises $10 and then drops $2.36. In that case, it has retraced 23.6%, which is a Fibonacci number. Fibonacci numbers are found throughout nature. Therefore, many traders believe that these numbers also have relevance in financial markets.

Fibonacci retracement levels were named after Italian mathemetician Leonardo Pisano Bigollo, who was famously known as Leonardo Fibonacci.  However, Fibonacci did not create the Fibonacci sequence. Fibonacci, instead, introduced these numbers to western Europe after learning about them from Indian merchants. Fibonacci retracement levels were formulated in Ancient India between 450 and 200 BCE.

Key Takeaways

  • Fibonacci retracement levels connect any two points that the trader views as relevant, typically a high point and a low point.
  • The percentage levels provided are areas where the price could stall or reverse.
  • The most commonly used ratios include 23.6%, 38.2%, 50%, 61.8%, and 78.6%.
  • These levels should not be relied on exclusively, so it is dangerous to assume the price will reverse after hitting a specific Fibonacci level.
  • Fibonacci numbers and sequencing were first used by Indian mathematicians centuries before Leonardo Fibonacci.

Numbers First Formulated in Ancient India

Despite its name, the Fibonacci sequence was not developed by its namesake. Instead, centuries before Leonardo Fibonacci shared it with western Europe, it was developed and used by Indian mathematicians.

Most notably, Indian mathematician Acarya Virahanka is known to have developed Fibonacci numbers and the method of their sequencing around 600 AD. Following Virahanka's discovery, other subsequent generations of Indian mathematicians—Gopala, Hemacandra, and Narayana Pandita—referenced the numbers and method. Pandita expanded its use by drawing a correlation between the Fibonacci numbers and multinomial coefficients.

It is estimated that Fibonacci numbers existed in Indian society as early as 200 AD.

The Formula for Fibonacci Retracement Levels

Fibonacci retracement levels do not have formulas. When these indicators are applied to a chart, the user chooses two points. Once those two points are chosen, the lines are drawn at percentages of that move.

Suppose the price rises from $10 to $15, and these two price levels are the points used to draw the retracement indicator. Then, the 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).


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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.

However, the origin of the Fibonacci numbers is fascinating. They are based on something called the Golden Ratio. Start a sequence of numbers with zero and one. Then, keep adding the prior two numbers to get 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 indefinitely.

The Fibonacci retracement levels are all derived from this number string. After the sequence gets going, dividing one number by the next number yields 0.618, or 61.8%. Divide a number by the second number to its right, and the result is 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.

The Golden Ratio, known as the divine proportion, can be found in various spaces, from geometry to human DNA.

Interestingly, the Golden Ratio of 0.618 or 1.618 is found in sunflowers, galaxy formations, shells, historical artifacts, and architecture.

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. Then, it starts to go up again. Since the bounce occurred at a Fibonacci level during an uptrend, the trader decides to buy. The trader might set a stop loss at the 61.8% level, as a return below that level could indicate that the rally has failed.

Fibonacci levels also arise in other ways within technical analysis. For example, they are prevalent in Gartley patterns and Elliott Wave theory. After a significant price movement up or down, these forms of technical analysis find that reversals tend to occur close to certain Fibonacci levels.

Market trends are more accurately identified when other analysis tools are used with the Fibonacci approach.

Fibonacci retracement levels are static, unlike moving averages. The static nature of the price levels allows for quick and easy identification. That helps 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 reversal or a break.

Fibonacci Retracements vs. Fibonacci Extensions

While Fibonacci retracements apply percentages to a pullback, Fibonacci extensions apply percentages to a move 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 might 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 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 traders struggle to know which one will be useful at any particular time. When it doesn't work out, it can always be claimed that the trader should have been looking at another Fibonacci retracement level instead.

Why are Fibonacci Retracements Important?

In technical analysis, Fibonacci retracement levels indicate key areas where a stock may reverse or stall. Common ratios include 23.6%, 38.2%, and 50%, among others. Usually, these will occur between a high and low point for a security, designed to predict the future direction of its price movement.

What Are the Fibonacci Ratios?

The Fibonacci ratios are derived from the Fibonacci sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, and so on. Here, each number is equal to the sum of the two preceding numbers. Fibonacci ratios are informed by mathematical relationships found in this formula. As a result, they produce the following ratios 23.6%, 38.2%, 50% 61.8%, 78.6%, 100%, 161.8%, 261.8%, and 423.6%. Although 50% is not a pure Fibonacci ratio, it is still used as a support and resistance indicator. 

How Do You Apply Fibonacci Retracement Levels in a Chart?

As one of the most common technical trading strategies, a trader could use a Fibonacci retracement level to indicate where he would enter a trade. For instance, if the trader notices that after significant momentum, a stock has declined 38.2%. As the stock begins to face an upward trend, he decides to enter the trade. Because the stock reached a Fibonacci level, it is deemed a good time to buy, with the trader speculating that the stock will then retrace, or recover its recent losses.

How Do You Draw a Fibonacci Retracement?

Fibonacci retracements are trend lines drawn between two significant points, usually between absolute lows and absolute highs, plotted on a chart. Intersecting horizontal lines are placed at the Fibonacci levels.

The Bottom Line

Fibonacci retracements are useful tools that help traders identify support and resistance levels. With the information gathered, they can place orders, identify stop-loss levels, and set price targets. Although useful, traders often use other indicators to make more accurate assessments of trends and make better trading decisions.

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  1. The Free Press Journal. "How the Fibonacci sequence has an Indian connection."