Technical Analysis · Intermediate · 5 min

Fibonacci retracements: tool or self-fulfilling prophecy?

You can draw Fibonacci retracement levels, explain why pullbacks so often seem to end near one, and summarize what research found.

Nature's ratio in charts?

The golden ratio, about 1.618, appears in sunflowers, shells and famous paintings. Many traders believe it also governs price charts, and draw Fibonacci levels on almost every move.

And often, the price seems to turn right at one of them. This lesson shows how the levels work, why they look so convincing, and what happens when researchers test them properly.

38.2, 50, 61.8

The Fibonacci sequence, named after the medieval mathematician Leonardo of Pisa, runs 1, 1, 2, 3, 5, 8, 13, 21… with each number the sum of the two before it. Dividing a number by the next one approaches 0.618, and that ratio is closely related to the golden ratio of about 1.618.

A Fibonacci retracement applies such ratios to a price move. After a rise, the levels show how much of the rise a pullback has given back:

38.2% of the move,
50%, which is not a Fibonacci ratio but is usually included,
61.8%, the most watched level.

Some traders add 23.6% and 78.6%.

In the fictional chart, a rise runs from 78.65 to 100.95, a move of 22.30. The 38.2% level is at 92.43, the 50% level at 89.80, the 61.8% level at 87.17. The pullback ends at 92.44 on candle 22, one cent from the 38.2% level. Then the price rises to 104.

That looks remarkable. But consider the geometry. Three levels between 38.2% and 61.8% cover the middle quarter of the move, and with 23.6% and 78.6% added, the levels are never far apart. Most pullbacks will end near one of them by chance, especially if "near" is generous.

Close to a level by chance

Researchers have tested this. Roy Batchelor and Richard Ramyar examined trends in the Dow Jones Industrial Average from 1914 to 2002 and tested whether the ratios between successive moves clustered around Fibonacci ratios. They found a few significant ratios, but no more than would be expected by chance given the number of tests.

A 2022 study by Tsinaslanidis, Guijarro and Voukelatos built an algorithm to find Fibonacci levels in three equity markets. Price bounces became more likely the wider the zones around the levels were drawn, which is what you would expect of any zone, and the authors did not present this as evidence of a profitable strategy.

There is one honest argument for Fibonacci levels: if many traders watch them and place orders there, they can matter for that reason alone, as Osler's work on round numbers suggests for other levels. That makes them partly self-fulfilling, not a law of nature.

Common mistakes

Counting the hits, forgetting the misses. With five levels, one is usually close.
Choosing the swing points after the fact. Different start and end points give different levels.
Treating 61.8% as magic. Research finds no special power.
Ignoring other reasons. A level that is also old support matters for that reason too.

The takeaway

Fibonacci retracements mark parts of a move. With several levels close together, some always look right. Research finds no special power.

Check yourself

Quick quiz

4 questions. Instant feedback, nothing is saved.

1Tap the candle where the pullback ended.

Tap the chart.

Candle 22 reached 92.44, one cent from the 38.2% retracement at 92.43. It looks impressive, but read on.
2A move runs from 80 to 100. Where is the 61.8% retracement?

100 − 0.618 × 20 = 87.64. The 38.2% level would be 92.36 and the 50% level 90.
3What did Batchelor and Ramyar find when they tested Dow Jones trends for Fibonacci ratios?

Testing 1914 to 2002, they found no evidence that trends turn at Fibonacci ratios more often than chance would produce.
4Why might Fibonacci levels still matter sometimes?

If enough people act at a level, it can matter for that reason alone, like round numbers. That is different from a natural law.

of 4 correct.

Sources

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