What is Fibonacci Retracement and Where Do Its Ratios Come From?

A Fibonacci retracement is a popular tool among technical traders and is based on the key numbers identified by mathematician Leonardo Fibonacci in the 13th 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. Before we can understand why these ratios were chosen, we need to have a better understanding of 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.

For reasons that are unclear, these 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. 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 Fibonacci retracement can be used. 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% and 61.8% levels. The 50% retracement level is not really a Fibonacci ratio, but it is used because of the overwhelming tendency for an asset to continue in a certain direction once it completes a 50% retracement.

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 stop-loss orders or target prices, and even act as a primary mechanism in a countertrend trading strategy. However, there are some conceptual and technical disadvantages that traders should be aware of when using a Fibonacci retracement.

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 self-fulfilling prophecy. If traders are all watching and using the same levels or 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 is 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. For this reason, the Fibonacci retracement requires other indicators or technical signals.

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.