Fibonacci Retracements

A number sequence older than the stock market

Leonardo Pisano, better known as Fibonacci, published Liber Abaci in 1202. Kaufman tells the story: the book wasn't published until 1857 (translated centuries after Fibonacci's death), and the famous sequence emerged from a toy problem about rabbits:

Every month each pair produces a new pair, which, from the second month on become productive; deaths do not occur. — Liber Abaci, paraphrased in Kaufman

Solve the recurrence and you get:

Each term is the sum of the previous two. And the ratio between consecutive terms approaches a specific irrational number — the golden ratio:

The reciprocal is 0.618. Subtract from one and you get 0.382. Take the square root of 0.618 and you get 0.786. These are the ratios that show up on every Fib retracement tool on every charting platform.

Which ratios are actually Fibonacci?

Here's where the books disagree, instructively. Murphy takes a loose view — the early-series ratios (1/2 = 50%, 2/3 = 66%) are "Fibonacci by convergence" since all terms approach 0.618:

Many students of Elliott may be unaware that the famous 50% retracement is actually a Fibonacci ratio, as is the two-thirds retracement. — John Murphy

Kaufman disagrees, sharply. He says only 0.618 and 1.618 (and their direct power-derivatives like 0.786 = √0.618, 2.618 = 1.618²) are real Fibonacci. Everything else is convention:

Alternately, traders have used 0.382, the complement of 0.618, as a key retracement level; however, this is not a Fibonacci ratio. — Perry Kaufman, Trading Systems and Methods

The honest reading: 38.2% and 50% are not purely Fibonacci. They work — when they work — because three different traditions converge on the same zone:

All three rough in the same band — 33–67% retracement. Whether you call the 50% level "Fibonacci" or "Dow" or "Gann," traders draw a line there and react to it. The self-fulfilling element is real.

Murphy, in one of his sharpest lines:

The self-fulfilling prophecy is generally listed as a criticism of charting. It might be more appropriate to label it as a compliment.

Play with the levels

Toggle between Retracements and Extensions. The six retracement levels — 0 / 23.6 / 38.2 / 50 / 61.8 / 78.6 / 100 — are drawn across a hand-crafted rally from 100 to 161. Watch what the example does:

1. Initial pullback: price tags the 38.2% level (≈138.2) and bounces. "Shallow pullback in a strong trend" — Murphy's first zone.
2. Second pullback: price deepens to the 61.8% level (≈122.3) and holds. "Deep pullback in a still-valid trend."
3. Resumption: price rallies to the 161.8% extension (≈198.9) in extension mode.

Retracement depth as trend strength

Murphy's practical framing, which is more useful than any ratio mysticism:

In a strong trend, a minimum retracement is usually around 38%. In a weaker trend, the maximum percentage retracement is usually 62%.

And the structural cutoff:

Beyond 66%, the odds then favor a trend reversal rather than just a retracement. The move usually then retraces the entire 100%.

Rule-of-thumb ranges:

This framework is useful regardless of whether you believe the specific levels are "special." Retracement depth correlates with trend strength, and that correlation is independent of Fibonacci mysticism.

Extensions — targeting the next move

Once a retracement holds, traders project the extension to estimate where the next leg will end. The most-watched extensions:

• 127.2% — modest extension; often the first target
• 161.8% — the golden extension; classic target
• 261.8% — aggressive extension; rare

Computed as: swing_low + ratio × (swing_high − swing_low). In our example, the 161.8% extension lands at 198.9 — close to the actual high of 200.

Murphy doesn't call these "extensions" by name; he treats them under Elliott Wave theory. The wave-3 target is wave-1's length × 1.618 added to the bottom of wave 2. The wave-5 top is wave-1's length × 3.236 projected from wave 4. Same math, different vocabulary.

The honest critique

Now the part that most Fibonacci instruction skips. Nobody has cleanly tested whether price reacts at Fibonacci levels more often than at random levels. Not Murphy, not Kaufman, not even Bulkowski (and he tests everything). Bulkowski's verbatim verdict, the one sentence worth tattooing:

You might use Fibonacci retracements of 38%, 50%, or 62% as buying locations, but I don't think they'll give you an edge. — Thomas Bulkowski

Kaufman is blunter about the mechanism:

The obvious problem is that, if there are so many possible retracement levels, then the price is likely to stop at one of them, even if by chance.

And on the "more levels = more reactions" dynamic:

Adding more key levels increases the likelihood that prices will react at those levels, if only by chance.

Think about this. A default Fib retracement tool draws six lines (0, 23.6, 38.2, 50, 61.8, 100). Add 78.6%. Add the Gann 37.5% and 62.5%. Add round numbers. You now have ten lines across a range. Of course price reacts at one of them.

The only Bulkowski-tested pattern that uses Fibonacci ratios at all is the harmonic pattern family (AB=CD, Gartley). His data: "bearish AB=CD turns down at D only 32–38% of the time." Two-thirds of the time, the predicted Fibonacci reversal point doesn't even hold. That's the closest we have to an apples-to-apples test of Fibonacci reversal reliability, and it's mediocre.

Kaufman admits the unfalsifiable framing with unusual honesty:

Retracement rules have not been proved scientifically but they are accepted by most traders.

Fibonacci in nature — where reputable books start overselling

Kaufman catalogues the usual list: the Great Pyramid's proportions, the Parthenon, sunflower spirals (55 + 34 = 89), chambered nautilus logarithmic spirals, beehive genealogy, Leonardo da Vinci's Vitruvian Man. Then it keeps going: 5 fingers, 8 piano octave keys, 13 original US states, the 21-gun salute, the 33–36 day "emotional cycle," the Kondratieff 50–55-year wave.

To his credit, Kaufman himself hedges:

These examples are not meant to prove anything in the strict sense.

Treat the nature-mysticism content as historical color, not evidence. The Fib ratios show up in some plant geometry because certain recurrence relations are locally stable; the rest is pattern-matching on a large enough world that you'll find anything you look for.

Four things that actually matter

1. Retracement depth correlates with trend strength. This is true regardless of whether you believe the specific levels are special. Shallow pullbacks mean strong trends; deep pullbacks mean weaker ones. 78.6%+ means the trend is likely broken.
2. Use Fibonacci zones, not precise levels. Kaufman: "It is unrealistic to expect retracement levels to be reached exactly." Draw 38.2% as a ±1% zone, not a single price.
3. Self-fulfilling is not a bug. Enough traders watch these levels that reactions happen — and reactions are what you can trade. Murphy's framing is right.
4. Wait for confirmation at the level. Don't front-run the bounce. Wait for a candle close that reverses at the zone. Bulkowski's harmonic-pattern data — 62–68% fail at the predicted turn — is a sobering reminder.

What doesn't work

• Fibonacci on individual stocks. Kaufman: "index markets, such as the S&P 500, would also show 50% and 61.8% pullbacks, but individual stocks may not. Broad participation is a requirement." Fib needs crowd behavior, which thin stocks don't have.
• Fibonacci time targets read after the fact. Murphy's own warning: "Part of the problem is the variety of possible relationships. These relationships can always be found after the fact. It's not always clear which of the possible relationships are relevant to the current trend."
• Treating the level as a reversal signal without confirmation. Harmonic patterns (the one case Bulkowski tested) fail 62–68% of the time at the predicted Fibonacci turn.

Quick check

What you now know

• The Fibonacci sequence — each term the sum of the prior two — converges on the golden ratio φ ≈ 1.618. Reciprocal 0.618. Complement 0.382. Square root 0.786.
• Only 0.618, 1.618, 0.786, 2.618 are strict Fibonacci ratios (per Kaufman). 38.2% is the complement; 50% is Dow Theory; 66% is Gann eighths; they converge on the same zone.
• Murphy's depth framework is more useful than ratio mysticism: 23.6% = very strong trend, 38.2% = strong, 50% = moderate, 61.8% = deep but valid, 78.6%+ = trend likely broken.
• Extensions project beyond the swing high; 161.8% is the golden target.
• Bulkowski's verdict: "I don't think they'll give you an edge." The one Fibonacci-based pattern family he tested (harmonic patterns) fails 62–68% of the time at the predicted turn.
• Self-fulfilling is how this works. Enough traders watch the levels that reactions happen. That's tradeable; it's just not magic.
• Use zones, not lines; wait for confirmation; skip thin stocks. The levels are coordination phenomena, not physical laws.

Price Action unit complete. Next up: one of the remaining Indicator lessons (Stochastic or ATR) or into Volume & Order Flow.