What are Fibonacci Numbers/Lines

The Fibonacci numbers and lines are technical indicators using a mathematical sequence developed by the Italian mathematician Leonardo Fibonacci. These sequence of numbers, starting with zero and one, are created by adding the previous two numbers. For example, the early part of the sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, and 144.

BREAKING DOWN Fibonacci Numbers/Lines

The Fibonacci numbers are significant because of the so-called golden ratio of 1.618. In the Fibonacci sequence, any given number is approximately 1.618 times the preceding number. This golden ratio is ubiquitous in nature where it describes everything from the number of veins in a leaf to the magnetic resonance of spins in cobalt niobate crystals.

Fibonacci Numbers/Lines in Finance

Many traders believe that the Fibonacci numbers and golden ratio play an important role in finance. In particular, many traders are focused on three percentages based on the golden ratio, including 38.2%, 50%, and 61.8%. These ratios are created by dividing the next highest number (e.g. 89/55 = 0.618 and 13/34 = 0.382). Using this technique, traders can calculate percentages as high or low as needed.

These percentages are applied using many different techniques:

  1. Fibonacci Retracements - These are horizontal lines on a chart that indicate areas of support and resistance.
  2. Fibonacci Arcs - These are compass-like movements stemming from a high or low that represent areas of support and resistance.
  3. Fibonacci Fans - These are diagonal lines created using a high and a low that represent areas of support and resistance.
  4. Fibonacci Time Zones - These are vertical lines into the future designed to predict when major price movements will occur.
Example of Fibonacci Retracements

Fibonacci retracements are the most common form of technical analysis based on Fibonacci numbers, which can be seen in the example chart above. The usage of the Fibonacci studies is somewhat subjective since the trader must use highs and lows of their choice. When building trading systems, traders may choose to select a high and a low during a set period of time.

Many traders use Fibonacci numbers and lines in conjunction with other forms of technical analysis. For example, traders may look for conformation of a breakout from a Fibonacci retracement by looking at on-balance volume or the relative strength index (RSI). These studies may also be used in conjunction with chart pattern analysis, such as ascending triangles or flags to calculate take-profit or stop-loss points along the way.