Section1 - Chapter 5 - The Fibonacci Sequence & Golden Ratio

Section1 - Chapter 5 - The Fibonacci Sequence & Golden Ratio - Presented by Rohan Sharma - The CMT Coach - Chartered Market Technician CMT Level 1 Study Material - CMT Level 1 Chapter Wise Short Notes - CMT Level 1 Course Content - CMT Level 1 2025 Exam Syllabus Visit Site : www.learn.ptaindia.com and www.ptaindia.com

1. Chapter 5 - The Fibonacci Sequence & Golden Ratio Section 1 – Theory and History of Technical Analysis Presented By : This Content is Copyright Reserved Rights Copyright 2025@PTAIndia

2. Agenda Learning Objective Statements: The Fibonacci Sequence and The Golden Ratio The Man The Numbers and Sequence The Golden Ratio The Fibonacci Sequence & The Golden Ratio Fibonacci Retracements Fibonacci Extensions Final Thoughts This Content is Copyright Reserved Rights Copyright 2025@PTAIndia

3. 🔄 Fibonacci Sequence & The Golden Ratio Fibonacci Sequence 1. Definition: A series of numbers where each number is the sum of the two preceding ones: o Formula: F(n)=F(n−1)+F(n−2)F(n) = F(n-1) + F(n-2)F(n)=F(n−1)+F(n−2) o Starting values: F(0)=0,F(1)=1F(0) = 0, F(1) = 1F(0)=0,F(1)=1 o Example: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34... 2. Applications: o Found in nature (spirals in flowers, pinecones, seashells). o Used in stock market analysis and technical trading. o Appears in computer science (e.g., search algorithms, data structures). o Found in art, music, and architecture. 3. Properties: o Each number is roughly 1.618 times the previous one (approaching the Golden Ratio). o The ratio between consecutive terms converges to Phi (ϕ) ≈ 1.618. o Can be used for recursive problem-solving in programming.

4. 🔄 Fibonacci Sequence & The Golden Ratio The Golden Ratio ( ϕ ≈ 1.618) 1. Definition: A mathematical constant derived from the Fibonacci sequence. o Formula: 2. Applications: o Found in art, architecture (e.g., Parthenon, Mona Lisa). o Used in photography for aesthetically pleasing compositions (rule of thirds). o Found in natural proportions (human body, galaxies, hurricanes). o Used in design, logos, and typography. This Content is Copyright Reserved Rights Copyright 2025@PTAIndia

5. 🔄 Fibonacci Sequence & The Golden Ratio Interpretation & Real-World Meaning • Mathematical Beauty: Fibonacci numbers and ϕ naturally emerge in many patterns. • Nature’s Design: Many living organisms grow in Fibonacci proportions (e.g., sunflower seed spirals, nautilus shells). • Aesthetic Balance: The Golden Ratio is often used in art, design, and architecture for pleasing proportions. • Financial Markets: Fibonacci retracement is used in stock trading to predict price levels. • Technology & Coding: Fibonacci algorithms help optimize recursive solutions in programming. This Content is Copyright Reserved Rights Copyright 2025@PTAIndia

6. 🔄 Fibonacci Sequence & The Golden Ratio Visual & Real-World Connections 1. Golden Spiral 🌀 o If you draw squares with Fibonacci-numbered sides (1x1, 2x2, 3x3, etc.) and connect their corners with an arc, you get a logarithmic spiral that follows the Golden Ratio. o Found in seashells, galaxies, hurricanes, and sunflower seed arrangements. 2. Architecture & Art 🎨 o The Parthenon, Leonardo da Vinci’s Vitruvian Man, and famous paintings like the Mona Lisa use ϕ for balanced proportions. 3. Finance & Stock Market 📈 o Fibonacci retracement levels (23.6%, 38.2%, 61.8%) help traders predict price corrections. 4. Human Body & DNA 🧬 o The ratio of various body parts (e.g., hand to forearm, face proportions) often approaches ϕ. o The double helix structure of DNA follows Fibonacci-related proportions. This Content is Copyright Reserved Rights Copyright 2025@PTAIndia

7. Fibonacci Retracements What Are Fibonacci Retracements? • A technical analysis tool used in trading to identify potential support and resistance levels. • Based on the idea that markets retrace predictable portions of a move before continuing in the original direction. • Derived from the Fibonacci sequence and Golden Ratio (ϕ ≈ 1.618). How They Work: • Traders use Fibonacci ratios to predict price pullbacks before a trend continues. • Common retracement levels: 23.6%, 38.2%, 50%, 61.8%, and 78.6%. • The most important levels are 38.2% and 61.8%, as price often reacts here. This Content is Copyright Reserved Rights Copyright 2025@PTAIndia

8. Cheat Sheet : Fibonacci Retracements Fibonacci Extensions (For Profit Targets) • 161.8%, 261.8%, 423.6% • Used to project price targets beyond the original move. This Content is Copyright Reserved Rights Copyright 2025@PTAIndia Fibonacci Level Meaning 23.6% Shallow retracement; minor bounce level 38.2% Moderate retracement; possible reversal 50.0% Psychological level (not Fibonacci-based) 61.8% Strong retracement; key level for trend continuation 78.6% Deep retracement; last line before trend failure 100% Full retracement; trend may reverse

9. Cheat Sheet : Fibonacci Retracements This Content is Copyright Reserved Rights Copyright 2025@PTAIndia

10. Fibonacci Retracements Interpretation & Real-World Use 1. Uptrend Example: o Price moves up, then retraces downward to 38.2% or 61.8% before continuing up. o Traders buy at these levels. 2. Downtrend Example: o Price moves down, then retraces upward to 38.2% or 61.8% before continuing down. o Traders sell at these levels. 3. Why It Works: o Markets move in waves, and traders psychologically react at Fibonacci levels. o Institutions often place buy/sell orders at these retracement points. 4. Combining With Other Tools: o Works best when combined with support/resistance levels, trendlines, and candlestick patterns. o Confluence of multiple signals increases reliability. This Content is Copyright Reserved Rights Copyright 2025@PTAIndia

11. Fibonacci Retracements Interpretation & Real-World Use 1. Uptrend Example: o Price moves up, then retraces downward to 38.2% or 61.8% before continuing up. o Traders buy at these levels. 2. Downtrend Example: o Price moves down, then retraces upward to 38.2% or 61.8% before continuing down. o Traders sell at these levels. 3. Why It Works: o Markets move in waves, and traders psychologically react at Fibonacci levels. o Institutions often place buy/sell orders at these retracement points. 4. Combining With Other Tools: o Works best when combined with support/resistance levels, trendlines, and candlestick patterns. o Confluence of multiple signals increases reliability. This Content is Copyright Reserved Rights Copyright 2025@PTAIndia

12. Fibonacci Extensions What Are Fibonacci Extensions? • A technical analysis tool used to predict future price targets in an extended trend. • Helps traders identify where price might move after a retracement ends. • Based on Fibonacci ratios derived from the Golden Ratio (ϕ ≈ 1.618). How They Work: • Fibonacci retracements identify pullback levels, while extensions project where price might go after resuming its trend. • Common extension levels: 127.2%, 161.8%, 200%, 261.8%, and 423.6%. • The 161.8% level is the most important, as price frequently reacts there. This Content is Copyright Reserved Rights Copyright 2025@PTAIndia

13. Fibonacci Extensions This Content is Copyright Reserved Rights Copyright 2025@PTAIndia Fibonacci Extension Level Meaning 127.2% Minor extension; early profit target 161.8% Strong extension; key price target 200% Full measured move; continuation signal 261.8% Aggressive extension; potential reversal 423.6% Extreme extension; overextended market How to Draw Fibonacci Extensions: Identify a strong trend move (impulse wave). Measure from swing low to swing high (in an uptrend) or swing high to swing low (in a downtrend). Apply Fibonacci extension levels from the retracement point . Use levels as potential profit targets or resistance zones .

14. Fibonacci Extensions This Content is Copyright Reserved Rights Copyright 2025@PTAIndia

15. Fibonacci Extensions Interpretation & Real-World Use 1. Uptrend Example: o Price moves up, retraces, then extends beyond the previous high. o Traders take profits at 161.8% or 261.8% extensions. 2. Downtrend Example: o Price drops, retraces, then extends below the previous low. o Traders set profit targets at extension levels. This Content is Copyright Reserved Rights Copyright 2025@PTAIndia

16. 📈 Fibonacci Extension Trading Strategy Step 1: Identify a Strong Trend Move (Impulse Wave) • Look for a clear uptrend or downtrend. • Example: Price moves from $100 to $150 (impulse wave). Step 2: Identify a Retracement (Pullback) • After the initial move, price pulls back (retraces) to a Fibonacci retracement level (38.2% or 61.8%). • Example: Price drops from $150 to $130. This Content is Copyright Reserved Rights Copyright 2025@PTAIndia

17. 📈 Fibonacci Extension Trading Strategy Step 3: Apply Fibonacci Extensions • Use the Fibonacci extension tool to measure from swing low to swing high, then project from the retracement level. • The key levels to watch: 127.2%, 161.8%, 200%, 261.8%. Step 4: Set Profit Targets at Extension Levels • Conservative Target: 127.2% extension (around $165) • Main Target: 161.8% extension (around $175) • Aggressive Target: 200% extension (around $190) Step 5: Confirm with Other Indicators • Check for candlestick patterns (e.g., bullish engulfing, reversal signals). • Use support/resistance levels to confirm targets. • Watch for RSI overbought/oversold conditions. This Content is Copyright Reserved Rights Copyright 2025@PTAIndia

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