Fibonacci Sequence

Introduction

Welcome to the first part in a series of videos, designed to show you how you can use Fibonacci to improve your overall trading strategy.

My goal throughout this series is to build a solid foundational base, so you understand both the "how", along with the "why".

We'll start with exploring the origins of the popular Fibonacci Sequence, and connect the dots to how the sequence is used in trading. Much of this first part focuses on the 'theoretical' knowledge, with the goal of increasing your confidence in its baseline logic.

Once you have a firm grasp on these concepts, we will move on to practical application, including:

• Learning how to use different Fibonacci Tools
• How to build your own Fibonacci cluster zones
• How to use Fibonacci ratios to time your entries and exits for maximum profitability

By the end of this series, you should have a very clear understanding of how to use popular Fibonacci tools in your trading (and more importantly, WHEN to use them!).

Fibonacci Sequence: The Rabbit Riddle

Before we dive into how Fibonacci ratios revolutionized technical analysis, let's understand where this mathematical phenomenon came from. Leonardo Bonacci, better known as Fibonacci, was a 12th-century Italian mathematician whose work would fundamentally change how we understand patterns in nature, architecture, and yes (financial markets too).

While traveling through the Mediterranean as a young man, Fibonacci studied under Arab mathematicians and became fascinated with their numerical systems. Upon returning to Italy, he posed a seemingly simple mathematical puzzle that would become legendary:

"A certain man put a pair of rabbits in a place surrounded on all sides by a wall. How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begets a new pair which from the second month on becomes productive?"

To solve this puzzle, Fibonacci established some ground rules that reflect biological reality:

• You begin with one newborn male and one newborn female rabbit
• Rabbits reach reproductive maturity after one month
• Every mature pair produces exactly one new pair each month
• Each new pair consists of one male and one female
• No rabbits die during the year (optimal conditions)

What seems like a quirky math problem actually reveals one of nature's most fundamental patterns. Let's walk through the first five months to see how this mathematical sequence unfolds and why traders around the world now rely on these numbers every single day.

In Month 1, we have just the 1 pair of rabbits that we start with:

In Month 2, we have the original pair of rabbits, along with their first off-spring, for a total of 2 pairs of rabbits.

In Month 3, we have the original pair of rabbits, their latest offspring, and the offspring from Month 2. This leads us to have a total of 3 pairs of rabbits.

In Month 4, we have the original pair of rabbits, another set of offspring, the offspring from Month 2, the offspring from Month 3, and the offspring from Month 2's first set of offspring. This leads us to have a total of 5 pairs of rabbits.

In Month 5, we have the original pair of rabbits, another set of offspring, the offspring from Month 2, the offspring from Month 3, the offspring from Month 4, the offspring from Month 2's second set of offspring, the offspring from Month 2's first set of offspring, and the Month 3's first set of offspring. This leads us to have a total of 8 pairs of rabbits.

The number of rabbit pairs each month follows a distinct pattern: 1, 1, 2, 3, 5, 8... This is the Fibonacci Sequence.

The sequence follows a simple rule: each number is the sum of the two preceding numbers. Starting with 0 and 1, we get:

• 0 + 1 = 1
• 1 + 1 = 2
• 1 + 2 = 3
• 2 + 3 = 5
• 3 + 5 = 8
• 5 + 8 = 13
• And so on...

This gives us the complete sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377...

Here's what matters for traders: When you divide any number in the sequence by the one that follows it, the ratio approaches 0.618 as the numbers get larger. Divide a number by the one before it, and you get approximately 1.618. This is the Golden Ratio that appears throughout nature - from plant growth patterns to architectural proportions.

What Fibonacci couldn't have known in the 12th century is that these ratios would become fundamental tools for modern traders, helping identify key price levels where markets tend to pause, reverse, or accelerate. In the next section, we'll explore exactly how these ancient mathematical relationships translate into practical trading tools you can use every day in ThinkOrSwim.

Patterns and Ratios in Fibonacci Sequence

Now that we understand the mathematical foundation, let's explore how Wall Street transformed these ancient numbers into one of the most reliable tools in technical analysis. The transition from rabbit breeding to stock trading might seem like a leap, but the underlying principle is remarkably consistent: markets, like nature, tend to move in predictable patterns.

Professional traders focus on seven key Fibonacci ratios that have proven their worth across decades of market data: 0.236, 0.382, 0.500, 0.618, 0.786, 1.272, and 1.618. Each of these levels acts like a magnet for price action, attracting buyers and sellers at predictable intervals.

Notice how IWM respects multiple Fibonacci levels during its pullback. This isn't coincidence, it's the market's natural rhythm.

But where do these seemingly random percentages come from? The answer lies in the mathematical relationships within the Fibonacci sequence itself. Let me show you exactly how each ratio is calculated:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987...

These ratios work in trading for a simple reason: everyone uses them. Major banks, hedge funds, and trading algorithms all have these same levels programmed into their systems. When enough traders act on the same information, it becomes reality in the market.

The 38.2% retracement level is particularly interesting. Year after year, across different markets and timeframes, stocks tend to find support after pulling back roughly 38% from a recent high. This isn't magic or coincidence. It's simply where institutional buyers often start accumulating positions and where short sellers begin covering.

The more you observe these levels in action, the more you'll notice their consistency. A stock might bounce perfectly off the 61.8% level one day, then respect the 50% level on the next pullback. These patterns repeat because traders (both human and algorithmic) are programmed to react at these specific price points.

In Module 2, I'll walk you through the Fibonacci Retracement tool in ThinkOrSwim. You'll see exactly how to draw these levels on your charts and how to spot the best entry points when price approaches them. Once you understand how to use retracements properly, you'll start seeing profitable setups that most traders completely miss.