Fibonacci Studies

Fibonacci studies involve a collection of technical analysis tools that utilize Fibonacci numbers and ratios, which reflect the geometric principles of nature and human behavior, in the context of financial markets.

A diverse group of traders employs Fibonacci numbers and ratios to identify potential market turning points.

The Fibonacci series was first presented by the Italian mathematician Leonardo Pisano Bogollo, commonly known as Fibonacci (son of Bonacci), in his 1202 manuscript, Liber Abaci.

This series is generated by summing the two preceding numbers, starting with 0 and 1 as the initial numbers.

With 0 and 1 as the first two numbers, the third number in the series is the sum of these two (0 + 1), resulting in 1.

The fourth number is derived from the second and third numbers in the series, which is 1 + 1, and this pattern continues.

The initial numbers in the series are as follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, … ∞

As the series progresses towards infinity, mathematical relationships emerge as ratios between the numbers.

For instance, the ratio of consecutive numbers tends to converge towards 1.618034, known as the golden ratio, golden section, or golden mean, represented by the uppercase Greek letter Phi (Φ) in mathematics. This ratio is calculated by dividing a number in the series by the one that precedes it: 233 ÷ 144 = 1.618055.

The inverse of this ratio is 0.618034, denoted by the lowercase Greek letter phi (φ). This is found by dividing a number in the series by the one that follows it: 144 ÷ 233 = 0.618025.

Generally, these ratios are utilized to forecast support and resistance levels based on the relationships among Fibonacci numbers. The most commonly used Fibonacci ratios include:

• 0.618 (61.8%): A Fibonacci number divided by the subsequent number is approximately 0.618.
• 0.382 (38.2%): A Fibonacci number divided by the number two positions later is approximately 0.3820.
• 0.2360 (23.60%): A Fibonacci number divided by the number three positions later is approximately 0.2360.
• 0.764 (76.4%): This is calculated by adding the difference between 38.2% and 23.6% to 61.8%, i.e., 76.4% = 61.8% + (38.2% – 23.6%).
• 0.5 (50%): This represents the midpoint of the main trend, being the average of 38.2% and 61.8%.
• 0.0 (0%): This marks the beginning of a market movement.
• 1.0 (100%): This signifies the end of a market movement.

To grasp Fibonacci studies, it is essential to understand the concepts of support and resistance.

Support: These are the troughs (or lows) where buying interest is strong enough to surpass selling pressure, causing the decline to halt and the price to rise again.

Resistance: These are the peaks (or highs) that indicate a price level or area above the market where selling pressure exceeds buying pressure.