What it means
The Fibonacci sequence starts 0, 1, 1, 2, 3, 5, 8, 13 and so on, with each number the sum of the previous two. Dividing a number by the next one in the sequence gives about 0.618, and dividing by the number two places ahead gives about 0.382.
These ratios are said to appear widely in nature and, according to chartists, in market behaviour. To use the lines, a trader identifies a swing low and a swing high.
In an uptrend the lines are drawn down from the high at each percentage of the rise, showing where the price could pull back to. In a downtrend the lines are drawn up from the low.
A price that stops near a line and then moves back with the trend is taken as confirmation, while a price that slices through several lines suggests the trend may be reversing. The 50% level is not strictly a Fibonacci ratio, but it is included because many traders watch half-way retracements.
The 61.8% line is often called the golden retracement. These lines are popular because they give a specific price to act on, for example a place to put an order or a stop-loss.
Their use also feeds on itself: when many traders put orders at the same levels, price can react there simply because of that crowd behaviour. Still, there is no strong proof that the ratios have special power.
Responsible traders combine the lines with other evidence such as moving averages, volume and earlier support levels. They also size positions so that a failed level costs only a small, defined amount.
Used in that way the lines are a planning aid, not a prediction. Software has made the lines easy to draw, which is part of their appeal and also part of the danger.
A beginner can place retracement levels on any chart in seconds and may be tempted to treat every coincidence as meaningful. Discipline in choosing swing points and in managing risk is more valuable than the lines themselves.
In practice
Real-world examples.
Example
A swing trader watches a technology share climb from $100 to $150. When it pulls back to $130.90, the 38.2% line, she buys with a stop-loss under $125.
Example
A forex analyst plots lines on a falling currency pair and notes the price has recovered to the 61.8% line. He treats this as a possible area to sell, because it is a deep retracement of the prior fall.
Example
A portfolio manager of a commodity fund uses the lines to time additions to an existing position. She waits for a pullback to the 50% line before adding, instead of buying after a rally.
Formula
Calculation
In an uptrend the retracement level is:
Level = High - Ratio x (High - Low)
A share rises from $100 to $150, a range of $50. The 23.6% level is $150 - 0.236 x $50 = $150 - $11.80 = $138.20. The 38.2% level is $150 - $19.10 = $130.90. The 50% level is $150 - $25 = $125, and the 61.8% level is $150 - $30.90 = $119.10. A trader might wait for a bounce near $130.90 or $125 and place a stop-loss below $119.10.Case study
Seen in the real world.
Copperfield Advisory is an illustrative, fictional investment boutique whose analysts were arguing about Fibonacci lines. One partner relied on them heavily, while another dismissed them as superstition.
They agreed to test the idea on two years of past data for ten liquid shares, recording how often price reversed within a small band around each retracement level. The results showed reversals near the lines about as often as near random price levels, though trades planned around the lines had clear stop points.
In this illustrative story the partners agreed to use the lines for risk planning, not for forecasting. The sceptic was satisfied that the firm was not claiming predictive power, and the believer was satisfied that the tool stayed in use.
Watch out
Common mistakes.
- Believing that price must reverse at a Fibonacci level, when the levels are only areas where traders pay attention.
- Drawing lines from minor wiggles instead of clear swing highs and lows, which produces levels that mean little.
- Calling 50% a Fibonacci ratio, when it is included by convention and is not derived from the sequence.
Questions
People also ask.
Which Fibonacci levels are most popular?
Traders mostly watch 38.2%, 50% and 61.8%, with 23.6% and 78.6% used less often.
Do Fibonacci lines work in all markets?
Traders apply them to shares, currencies, commodities and crypto assets, but their effectiveness is debated and they work best when combined with other signals.
What is the difference between retracement and extension?
Retracement lines show where a pullback might stop, while extension levels project where a move might travel beyond the previous high or low.
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