Fibonacci Retracement

What the levels are

A swing is a move from a low to a high (an up swing) or from a high to a low (a down swing). A retracement is the part of that move that price gives back afterwards. Fibonacci retracement is a way of measuring that give-back as a fraction of the swing and marking the common fractions as lines on the chart.

The ratios come from the Fibonacci sequence, where each number is the sum of the two before it: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89. Divide a number by the one after it and the result settles near 0.618. Divide it by the number two places on and you get near 0.382. Divide by the number three places on and you get near 0.236. The 0.786 level is the square root of 0.618. The 50 percent line is not from the sequence at all. It is there because half of a move is an easy thing to look at.

Why would a market respect these numbers? There is no accepted mechanism. The usual explanation is that many traders watch the same lines, so orders gather near them. That is a story about attention, and it is not proven here. Treat the levels as places some people look, and measure whether they matter for the rule you are testing.

How the levels are drawn

Pick a swing low and a swing high. The distance between them is the range. Each level is the high minus the range times the ratio, for an up swing that is pulling back down.

Some charting tools also draw extensions beyond the swing, such as 127.2 and 161.8 percent, to mark where a move that continues might reach. They use the same range, just ratios above 1.

A worked example with made-up numbers

Take a made-up up swing from a low of 100 to a high of 110. The range is 10. The 38.2 percent level is 110 - 10 x 0.382 = 106.180, shown as 106.18. The table gives all five. The right-hand column shows the same levels if the swing low had been drawn from an earlier wick at 99.

Every level moves when the low moves by one point, and the move is largest for the shallow ratios. All numbers are made up, calculated by us on 31 Oct 2026, exact. Neither drawing is the right one. Both are defensible swings, and a bot has to be told which to use.

How the levels fail

• The swing is a choice. Which low and which high count? A wick or a close? The last visible swing or a larger one? Two people draw different lines on the same chart, and each can point to a pullback that "respected" theirs.
• Many lines, many chances. With five levels on a 10-point swing, a pullback of normal size will pass close to at least one of them. A line that was "hit" is easy to find after the fact. That is how a convention starts to look like a law.
• Price can go straight through. A deep pullback passes every level and keeps going. The levels do not say where a move stops, only where it could.
• No fixed rule for the end. If price falls through 61.8 percent, do you switch to 78.6 percent? At some point the swing itself has failed. Each answer is another setting.
• Selection after the fact. Tuning which ratios, which swings and what tolerance to the past is overfitting. A set that fits last year can fail this year.

How a bot encodes "price near a level"

A bot cannot look at a chart. It needs a rule in numbers. A typical version has three parts.

• Find the swing. For example, the highest high and lowest low of the last N bars, or a swing-point rule such as the highest high with M lower highs on each side. N and M are settings.
• Compute the levels. The formula above, for chosen ratios.
• Test the distance. "Near" means the absolute difference between price and a level is at or below a tolerance. The tolerance may be in points, in percent, or in multiples of the average true range (ATR, the average size of a bar over recent bars).

Now the fragile part. Take the made-up closes in the picture, 15 bars starting at the high of 110. With the five levels fixed, a bar counts as near a level at a tolerance of 0.1 points 3 times, at 0.3 points 7 times and at 0.6 points 12 times. The prices did not change, only one setting did. Shift the swing low from 100 to 99 with the 0.3 tolerance and the count becomes 6. A backtest of this rule would give different trades for each of these, and each looks reasonable. That is also why a single good backtest tells you little: see how to backtest.

There is also a timing problem. A swing high is only known to be a high after price has turned down from it. A bot that finds the swing using bars it could not yet have seen is committing look-ahead bias. Charts redrawn in hindsight make this very easy to do by accident.

Using it with other tools

Traders often combine a retracement level with something else, such as a moving average, a round number or an oscillator like the RSI indicator. Levels from different tools that sit close together are called confluence. The idea is that more reasons at one price mean more orders there. For a bot, every extra condition is another setting to fit. The VWAP indicator, Bollinger bands and an EMA crossover are common partners, and each adds its own parameters. When a level coincides with a breakout level, see also false breakout and breakout trading.

How to check a rule that uses retracement levels

Write down every setting before you test: the swing rule, the ratios, the tolerance, the entry, the exit and the stop. Run it on real data across rising, falling and flat periods, with spread, fees and slippage included. Count the trades, the average result per trade and the worst losing run. Then vary each setting a little. If a small change in tolerance flips the result, as in the example above, the rule has fitted noise. Keep a final stretch of data untouched and test on it once. Size any test position with a tool such as the position size calculator, so a bad run is survivable.

What this does not tell you

It does not say that price stops at any level, how often it does, or whether any rule built on the levels is worth running. The swing, the prices and the counts on this page are made up to show the arithmetic and the fragility. This page is education, not a signal.