Fibonacci Retracement
Fibonacci retracement is a technical analysis tool that plots horizontal price levels at specific percentage ratios derived from the Fibonacci number sequence — most commonly 23.6%, 38.2%, 50%, 61.8%, and 78.6% — to identify historically significant price zones within a prior price swing.
The Fibonacci sequence, discovered by medieval mathematician Leonardo of Pisa (known as Fibonacci), is a series of numbers in which each number is the sum of the two preceding ones: 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on. As the sequence progresses, the ratio of any number to the next approaches approximately 0.618 — the 'golden ratio' — while the ratio to the number two positions ahead approaches approximately 0.382. These ratios form the mathematical basis for the Fibonacci retracement levels used in technical analysis.
To apply a Fibonacci retracement, a technical analyst identifies a significant price swing — from a notable low to a notable high (or vice versa) — and plots horizontal lines at the Fibonacci percentage levels within that range. For example, if a stock moved from $40 to $60 (a $20 range), a 38.2% retracement level would be at $60 - ($20 × 0.382) = $52.36, and the 61.8% retracement level would be at $60 - ($20 × 0.618) = $47.64.
Technical analysts study these levels as potential historical zones of support or resistance. The rationale is that in historical market data, corrections within established trends have frequently paused or reversed near these mathematically defined ratios, a phenomenon some attribute to market participants collectively watching the same levels. Whether this reflects genuine market psychology or simply the tendency to find patterns in historical data remains debated.
The 50% level is commonly included in Fibonacci retracement tools even though it is not a pure Fibonacci ratio, reflecting the historically observed significance of price moves that retrace exactly half of a prior swing. The 61.8% level — the golden ratio — is frequently described in technical literature as the most significant retracement level.
Fibonacci retracement levels, like all technical analysis tools, are descriptive of historical price data. The presence of price activity near a Fibonacci level in past data does not establish that future price action will respect the same levels. Confirmation from other technical tools, broader market context, and fundamental analysis are all relevant considerations for investors examining historical chart patterns.