Fibonacci Retracement and Extension Levels Explained

The Fibonacci sequence is a series of numbers, beginning with "0, 1," in which each subsequent number is equal to the sum of the two preceding numbers:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, etc.

This series was described long before Fibonacci's time, but what matters most to traders are the ratios derived from dividing the numbers, not the numbers themselves. For example, 13/8 = 1.625. As you move up the sequence, the ratio approaches 1.618—the figure famously known as the golden ratio that was studied by mathematicians as far back as Greek geometer Euclid, who described it in his Elements treatise around 300 BCE.

For traders, other ratios—like the inverse of the golden ratio, or 0.618—have potential analytical value. Beginning in the early 20th century, technical analysts began studying how these ratios might relate to market behavior.

In the 1930s, Ralph Nelson Elliott developed the Elliott Wave Theory, which identifies long-term market trends and uses Fibonacci levels to describe the relationship between these "waves." His analysis found that market trends tend to follow a pattern of five waves in the trend's direction, followed by three corrective waves.

Elliott's work applied ratios derived from the Fibonacci sequence, including 23.6%, 38.2%, 61.8%, 78.6%, and 161.8%. The 38.2% is derived by dividing any number in the Fibonacci series by the number two places to its right (e.g., 21/55), and 23.6% is derived by dividing any number by the number three places to its right. The inverse of the golden ratio, 61.8%, is obtained by dividing any number by the next number in the sequence (e.g., 55/89). The 50% and 100% levels aren't derived from the Fibonacci sequence, but many traders consider them psychologically significant.

All of these levels can help technical traders identify potential areas of support, resistance, and retracement. When a stock moves off its peak or trough, traders want to gauge where it might go next. Traders can use the thinkorswim^® platform to apply these Fibonacci levels to a chart to indicate where support and resistance may emerge.

Because the Fibonacci retracement tool can help traders identify potential support and resistance, it may provide insight into when to enter or exit a trade. Here's how to apply this tool on thinkorswim:

1. Select Charts.
2. Enter a ticker symbol and select a time frame.
3. Retracement levels may be analyzed from either a high or low price point. To start with a high, place the cursor at a high price point, right-click, and select Add a drawing.
4. From the menu of icons, select % (Fibonacci Retracements).
5. Place the cursor on the high or low point, click once, move to the next high or low point to the right, and click again. The tool automatically calculates the corresponding Fibonacci percentage and price levels.

Another Fibonacci tool is the extension level. While Fibonacci retracements help traders track moves within an existing trading range, Fibonacci extensions help traders identify potential new support and resistance when a security rallies to a new all-time high or falls to a new low. At these new price levels, historical support and resistance no longer apply because the stock is trading outside of prior ranges.

The extensions tool can help a trader estimate what the new support and resistance may be. One approach is to use Fibonacci extensions to identify potential areas to consider taking profits by extending the series beyond 100% with commonly cited extension levels including 127.2%, 161.8%, 200%, and 261.8%, and 423.6%.

Creating Fibonacci extensions starts with selecting three recent prices: a recent significant high, a recent significant low, and the end of the retracement against a recent move. The tool then helps identify potential support, resistance, and price target levels. Here's how to apply this tool on thinkorswim:

1. Select Charts.
2. Enter a ticker symbol.
3. Place the cursor at the first price point to analyze, then right-click, and select Add a drawing.
4. From the menu of icons, select the Fibonacci Extensions tool, represented by a percentage symbol with two zigzag lines.

Fibonacci retracements and extensions may offer traders an idea of where a security's price could be moving next. And the more traders who use the technique, the more psychological significance these seemingly esoteric levels may hold. The thinkorswim platform makes it straightforward to explore different Fibonacci approaches when analyzing historical price action and considering risks and opportunities that may lie ahead.