Fibonacci retracement
Where the 38.2%, 50% and 61.8% levels come from, how the tool is anchored, why the anchor choice decides the levels, and what the evidence supports.
Key points
- The levels are percentages of a move you select: 23.6%, 38.2%, 50%, 61.8% and 78.6% of the distance between two anchors.
- They come from ratios in the Fibonacci sequence, except 50%, which is simply half and has no Fibonacci basis at all.
- The anchors are chosen by the person drawing, so two people can produce different levels on the same chart.
How the levels are constructed
A retracement measures how far a price has given back a prior move. Pick a low and a high, and the tool divides the distance between them at fixed percentages, drawing a horizontal line at each.
A share that rose from $100 to $200 has a 61.8% retracement at $138.20, because it has given back 61.8% of the $100 move. Nothing about the level is predictive on its face: it is arithmetic on two points somebody selected.
The drawing tool on the price chart anchors to the data rather than to the screen, so the levels stay attached to the same two prices and dates when the chart is zoomed or panned.
| Level | Origin | On a $100 to $200 move |
|---|---|---|
| 23.6% | A Fibonacci ratio, one term divided by the term three places on | $176.40 |
| 38.2% | A Fibonacci ratio, one term divided by the term two places on | $161.80 |
| 50% | Not a Fibonacci ratio; simply half the move | $150.00 |
| 61.8% | The inverse of the golden ratio | $138.20 |
| 78.6% | The square root of 61.8% | $121.40 |
Where the ratios come from
The Fibonacci sequence adds each pair of terms to make the next: 1, 1, 2, 3, 5, 8, 13, 21 and onward. The ratio between consecutive terms converges on 1.618, the golden ratio, and its inverse is 0.618. Dividing a term by the one two places later approaches 0.382, and three places later 0.236.
Those three numbers are the Fibonacci content of the tool. The 50% level, which is the one traders reference most, is not from the sequence at all, and 78.6% is the square root of 61.8% rather than a ratio of terms.
The mathematics is exact. What it does not supply is any reason a share price should respect these particular fractions, and that gap is the whole argument about the tool.
Why the anchors decide everything
The levels are entirely determined by the two points chosen. Anchor to the intraday high and low and you get one set; anchor to the closing high and low over the same period and you get another. Choose a different swing altogether and the lines move again.
This is where most of the disagreement about retracements actually lives. Two people looking at the same chart can produce different levels and each can then find the price respecting theirs, because on a chart with enough lines on it something is always nearby.
The discipline that makes the tool defensible is choosing the anchors before looking for confirmation, and keeping them: a level redrawn after the fact describes the past rather than framing the future.
Does Fibonacci retracement work?
There is no established evidence that these ratios have predictive power in markets, and the numbers themselves are not derived from anything about how prices form.
The argument usually made in their favour is reflexive: enough participants watch the same levels that orders cluster near them, which can produce the behaviour the tool describes. That is a claim about crowding rather than about geometry, and it applies most where the levels are most widely watched.
The more defensible use is as a framing device. A retracement divides a move into zones and gives a reference point for what has been given back, and reading it as one input beside volume, the trend and what the company has reported is different from reading it as a forecast.
Common mistakes
Redrawing the anchors until a level lines up with what the price has already done.
Treating 50% as a Fibonacci level. It is half, and it is on the tool by convention.
Adding so many levels that some line is always close to the price, which makes the tool unfalsifiable.
Mixing intraday and closing extremes between the two anchors, so the measured move is not a move that happened.
Using a retracement on a price driven by an event, where the level says nothing about what has changed in the business.
Educational information about how these figures are constructed. Not investment advice, and not a recommendation to buy or sell any security.
