Fibonacci Series, Golden Ratio, and Market Applications

The Fibonacci Series

The Fibonacci Series was created by Leonardo Fibonacci, often cited as the greatest European mathematician of the Middle Ages, who introduced the Hindu Arabic numeric system to Europe.

The series begins:

  1. 1
  2. 2
  3. 3
  4. 5
  5. 8
  6. 13
  7. 21
  8. 34
  9. 55
  10. 89
  11. 144
  12. 233
  13. 377

Series Rule: Each number is the sum of its previous two numbers (e.g., 13 + 21 = 34).

Key Fibonacci Ratios

The core significance of the series lies in the ratios derived by dividing adjacent numbers. These ratios are connected by the constant number 0.618.

Primary Ratios (Retracements)

  • 0.618 (The Golden Ratio): Found by dividing any number by the number immediately following it (e.g., 89 / 144 = 0.618).
  • 0.382: Found by dividing any number by a number two places after it (skipping one number, e.g., 144 / 377 = 0.382).
  • 0.236: Found by dividing any number by a number three places after it (skipping two numbers, e.g., 89 / 377 = 0.236).

Inverse Ratios (Extensions)

The inverse calculations reveal additional important ratios, maintaining the 0.618 relationship (e.g., 1.618 / 2.618 = 0.618).

  • 1.618: Found by dividing any number by the number immediately preceding it (e.g., 377 / 233 = 1.618).
  • 2.618: Found by skipping one number backward (e.g., 377 / 144 = 2.618).
  • 4.236: Found by skipping two numbers backward (e.g., 377 / 89 = 4.236).

The Golden Ratio (Phi)

The number 0.618 is the Golden Ratio, denoted by the Greek letter Phi. Pythagoras stated that on any given line segment, there is a unique point (not in the middle) that divides the line such that the ratio of the smaller segment (B) to the larger segment (A) is equal to the ratio of the larger segment (A) to the whole line (A+B). This number is 0.618.

The Golden Rectangle and Spiral

The Golden Ratio is used to construct the Golden Rectangle. If a rectangle has sides where the ratio of the short side to the long side is 0.618, it is considered a golden rectangle.

By continuously drawing diagonals across nested golden rectangles, a Golden Spiral is created. This spiral expands by the number Phi every quarter turn.

Phi in the Natural World

The Golden Spiral and Golden Rectangle appear ubiquitously in nature, reflecting the universality of Phi:

  • Botany: The growth patterns of tree branches and roots follow Fibonacci numbers.
  • Anatomy: Human bodies considered symmetrical or "perfect" are based on Phi (e.g., the ratio of the height from the floor to the belly button versus the height from the belly button to the head is 1.618).
  • Biology: Our DNA is made up of golden rectangles (21 by 34 angstroms).
  • Fluid Dynamics: Water flowing down a drain often follows the shape of a golden spiral.
  • Cosmos: Galaxies follow the shape of a golden spiral.
  • Weather: Hurricanes, viewed from satellites, often exhibit the shape of a golden spiral.

Applying Fibonacci to Supports and Resistances

It has been observed that prices in financial markets tend to find supports and resistances at the key Fibonacci ratios. All drawing must proceed from left to right.

In an Uptrend

Finding Potential Supports (Retracements)

Draw Fibonacci from the all-time low (ATL) to the all-time high (ATH).

  • Use the 23.6% level
  • Use the 38.2% level
  • Use the 61.8% level

Finding Potential Resistances (Extensions)

Draw Fibonacci from the all-time high (ATH) to the last bottom.

  • Use the 161.8% level
  • Use the 261.8% level
  • Use the 423.6% level

In a Downtrend

Finding Potential Resistances (Retracements)

Draw Fibonacci from the all-time high (ATH) to the all-time low (ATL).

  • Use the 23.6% level
  • Use the 38.2% level
  • Use the 61.8% level

Finding Potential Supports (Extensions)

Draw Fibonacci from the all-time low (ATL) to the last top.

  • Use the 161.8% level
  • Use the 261.8% level
  • Use the 423.6% level

Detailed Summary

The provided text offers an in-depth explanation of the Fibonacci Series, the Golden Ratio (Phi, 0.618), and their practical application in analyzing financial markets. The Fibonacci Series, introduced by Leonardo Fibonacci, is generated by adding the two preceding numbers (e.g., 2+3=5). Key ratios (0.618, 0.382, 0.236) derived from the series are fundamental to the Golden Ratio, a universal constant found ubiquitously in nature (e.g., galaxies, DNA structure, botany, and human anatomy). In financial analysis, these ratios are used as retracements (0.236, 0.382, 0.618) to identify potential supports in uptrends and resistances in downtrends, and as extensions (1.618, 2.618, 4.236) to determine future resistances in uptrends and supports in downtrends.

Key Takeaways

  • The Fibonacci Series, created by Leonardo Fibonacci, is generated by summing the two previous numbers in the sequence (e.g., 1, 2, 3, 5, 8...).
  • The series is crucial for deriving key ratios linked by the constant 0.618.
  • The Golden Ratio (Phi) is 0.618, found by dividing a number in the series by the number immediately following it.
  • Primary Ratios (Retracements) are 0.618, 0.382, and 0.236.
  • Inverse Ratios (Extensions) are 1.618, 2.618, and 4.236.
  • Phi governs the geometry of the Golden Rectangle and Golden Spiral, which appear widely in natural phenomena (e.g., hurricanes, DNA, galaxy shapes).
  • In financial markets, Fibonacci ratios are used to predict potential supports and resistances.
  • For Retracements (finding support in an uptrend or resistance in a downtrend), drawing is done from the low (ATL) to the high (ATH), focusing on 23.6%, 38.2%, and 61.8%.
  • For Extensions (finding resistance in an uptrend or support in a downtrend), ratios like 161.8%, 261.8%, and 423.6% are utilized, based on specific drawing methods relative to the trend direction.