Leonardo Fibonacci is widely considered to be the most influential Western mathematician of the Middle Ages. In 1202, he became famous for the so-called Book of Calculations, which is credited for spreading the Hindu-Arabic numeral system in Europe. The book also contained a numerical sequence as an example that would eventually be named after him as the Fibonacci sequence.
The Fibonacci sequence is defined by a recurrence relation whereby Fn = Fn –1 + Fn – 2, or in other words, the current digit is the sum of the two before it. For example, the first part of the sequence is 1, 1, 2, 3, 5, 8. Dividing a number of by its immediate predecessor yields the so-called golden ratio of approximately 1.618. For example, 8 divided by five is 1.600 and 5 divided by 3 is 1.666.
In this article, we will take a look at the uncanny significance of the Fibonacci sequence and golden ratio, as well as how the numbers play a role in the financial markets [see also 25 Stocks Day Traders Love].
Fibonacci & Golden Ratio
The Fibonacci sequence and golden ratio appear many times throughout science and nature. In 1854, Adolf Zeising described a universal law that contained “the ground-principle of all formative strivings for beauty and completeness in the realms of both nature and art, and which permeates, as a paramount spiritual ideal, all structures, forms, and proportions, which cosmic or individual.”
If that sounds a little over-the-top, consider the following examples of the golden ratio’s prevalence in everyday life:
- The spirals on sunflowers, pineapples, or cauliflowers add up to numbers in the Fibonacci sequence (although quite a way down the line).
- Honeybee colonies contain family trees that follow the Fibonacci sequence since drones hatch from unfertilized eggs and all females have two parents.
- The human body has one nose, two eyes, three limb segments, five fingers, and other proportions that amount to Fibonacci numbers.
Different derivations of the Fibonacci numbers are also prevalent in both mathematics and science. For example, the inverse of 1.618 (0.618 or 61.8%) is a ratio that accurate describes moves within the financial markets, along with other derivations like 38.2%, 50%, 23.6%, 161.8%, 423%, and so forth. These are all calculated by dividing a number by various positions in the Fibonacci sequence.
Fibonacci Studies in Finance
The Fibonacci sequence has grown to play a major role in the financial markets given its uncanny prevalence, particularly among short-term traders. Over time, many different tools evolved to evaluate Fibonacci relationship in terms of price movements and time periods. Traders can use these tools in conjunction with other forms of analysis to improve their odds of a successful trade.
Fibonacci retracements are the most popular Fibonacci-based indicator given their ease and practicality. By identifying a low-to-high or high-to-low price movement, traders can calculate the likely areas of support or resistance based on key Fibonacci levels like 38.2%, 50%, and 61.8%. These support or resistance levels tend to see the greatest incidence of reversals across multiple timeframes.
In Figure 1, Fibonacci retracements were able to accurately predict price declines following moves higher. The stock price rebounded from almost exactly the 50% and 61.8% retracement levels after retracing lower. Successfully using Fibonacci retracements requires that traders realize that these levels are simply price points that are likely to see rebounds rather than absolute guarantees of a rebound.
Fibonacci fans derived from Fibonacci retracements by connecting the point of origin with the various Fibonacci retracement levels at the peak price to create diagonal trend lines, as can be seen in Figure 2 below. While Fibonacci fans aren’t quite as popular as retracements, traders use them to identify potential areas of support or resistance that could see reversals in price.
In Figure 2, Fibonacci fans accurately predicted areas of support and resistance that traders should have been watching. The stock rebounded from both the 50% and 61.8% Fibonacci fan trend lines and met some resistance at the 38.2% fan trend lines. As with Fibonacci retracements, traders should use these trend lines as likely areas of support and resistance rather than definitive signs of a reversal.
Fibonacci arcs are half circles that are derived from Fibonacci retracements, created by drawing circles that intercept key retracement levels, as seen in Figure 3 below. By adding a time element to the equation, traders use Fibonacci arcs to predict when price movements will occur as well as areas of support and resistance. Price movements tend to occur between these levels using them as support or resistance.
In Figure 3, Fibonacci arcs accurately predict the timing and support levels for an uptrend after a retracement took place. The stock rebounded from the middle arc and moved higher using the line as a key support level. In addition, a brief rebound was seen when the price rebounded for a second time off of the third arc before moving lower once again to its 50-day moving average.
The Fibonacci sequence and golden ratio can be used to create a virtually limitless number of technical indicators. While the three indicators mentioned above are the most popular among traders, other indicators like Fibonacci Time Zones exist to help traders use the ratio to make various predictions. The accuracy of these indicators varies, which means they shouldn’t be used alone in technical analysis.
The Bottom Line
Leonardo Fibonacci became famous for publishing the Book of Calculations, but his namesake sequence could have even bigger implications. Using the principles of the golden ratio, traders have developed a series of technical indicators designed to forecast areas of support and resistance as well as identify reversals, including Fibonacci retracements, fans, and arcs, among others.
While these tools have an uncanny ability to predict reversals, traders should realize that they are only likely areas of support or resistance and not definitive reversals. Traders can improve the odds of success by combining Fibonacci studies with other technical indicators, chart patterns, and technical analysis tools. In the end, Fibonacci is just another valuable tool in a well-rounded trader’s toolbox.
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