Ch6. Fibonacci and Wave Theory

The Fibonacci Sequence and the Golden Ratio

In Leonardo Fibonacci’s sequence (0, 1, 1, 2, 3, 5, 8, 13, 21…), the ratio of each number to the one before it converges on the golden ratio: 1.618.

Key Fibonacci ratios:
0.236 (23.6%)
0.382 (38.2%)
0.500 (50.0%)  ← Not mathematically Fibonacci, but widely used in practice
0.618 (61.8%)  ← Reciprocal of the golden ratio ★★★
0.786 (78.6%)

Extension ratios:
1.272, 1.618, 2.618

Fibonacci Retracements

Used to forecast how far a move will retrace before resuming its trend:

How to apply in an uptrend:
1. Identify the swing low (A) and swing high (B)
2. Plot Fibonacci levels across the A–B range
3. 38.2%, 50%, and 61.8% become potential support zones

Buying strategy:
38.2% retracement → shallow pullback (strong trend)
61.8% retracement → deep pullback (weakening trend)
→ A break below 61.8% signals a possible trend reversal

Fibonacci Extensions — Setting Price Targets

Calculating an upside target:
A (swing low) → B (swing high) → C (retracement low)
Target = C + (A→B price range × 1.618)

Example:
A = $10.00, B = $15.00, C = $12.50
A→B range = $5.00
Target = $12.50 + ($5.00 × 1.618) = $20.59

Elliott Wave Theory

Ralph Elliott (1938) identified recurring patterns in market price action:

Basic structure:
5 impulse waves (upward) + 3 corrective waves (downward) = one complete cycle

Impulse waves (motive):
Wave 1: Initial rally (recognized by only a few)
Wave 2: Retracement (cannot retrace 100% of Wave 1)
Wave 3: Strongest and longest wave ★ (cannot be the shortest impulse wave)
Wave 4: Retracement (cannot overlap Wave 1's price territory)
Wave 5: Final push higher (momentum fading)

Corrective waves (A-B-C):
Wave A: First leg down
Wave B: Counter-rally (a trap for longs)
Wave C: Strong second leg down

Wave Counting Rules

Hard rules (cannot be violated):
1. Wave 2 cannot retrace below the start of Wave 1
2. Wave 3 cannot be the shortest of the three impulse waves (1, 3, 5)
3. Wave 4 cannot overlap into Wave 1's price territory

Guidelines (tendencies):
- Wave 3 is typically the longest and strongest
- Alternation principle: Waves 2 and 4 tend to take different forms
  (one simple, one complex)

Combining Fibonacci and Elliott Wave in Practice

Projecting a Wave 3 target:
→ Wave 1 low + (Wave 1 range × 1.618)
→ Wave 3 commonly extends to the 161.8% level of Wave 1

Entry strategy:
→ Wait for the 5-wave impulse to complete
→ Ride out the A-B-C correction
→ Enter long when Wave C ends (the next impulse cycle begins)
→ Strongest entry when Wave C terminates near the 61.8% Fibonacci support

Core Fibonacci levels: 38.2%, 50%, 61.8% (support/resistance for retracements) Breaking below 61.8% = warning of a potential trend reversal Elliott Wave hard rules: Wave 2 cannot undercut Wave 1 start; Wave 3 is never the shortest; Wave 4 cannot enter Wave 1 territory Wave 3 target = Wave 1 low + (Wave 1 range × 1.618)