Direct answer
A worked example of a Fibonacci Fan shows, step by step, how to draw the Fan’s lines using Fibonacci ratios applied to the vertical distance between two chosen price anchors. Because Fibonacci Fans depend on selected anchors (and on how they are plotted), the example is a geometry exercise: it helps you understand how the lines are constructed, but it does not by itself guarantee any future market behavior.
Mechanism or definition
A Fibonacci Fan is a chart-drawing method built from:
- Two anchor points: an earlier swing low and a later swing high (or the reverse).
- A starting point for each Fan line: one anchor (the “base” point).
- A set of Fibonacci ratios: commonly 0.382, 0.5, 0.618, and 1.0 (some charting tools also include others).
The core construction is based on the distance between anchors. Let:
- Base price = P0
- Top (or second anchor) price = P1
- Vertical move = D = P1 − P0
For a Fan line corresponding to a ratio r, the method uses a level (a derived price) at:
- Derived price = P0 + r·D (when the second anchor is above the base)
Then the charting tool draws straight lines (often represented as rays) from the base time/price location toward the chart area using the derived price level(s), spreading across the horizontal axis.
Evidence or example
Here is a transparent numerical worked example with explicit assumptions.
Assumptions:
- We are plotting on a single chart where vertical movement is measured in price units.
- We choose anchors that form an upward swing.
- We use ratios r ∈ {0.382, 0.5, 0.618, 1.0}.
- We ignore spreads, commissions, and real-time pricing because the goal is construction, not trading outcomes.
Example inputs:
- Base anchor (earlier low) price: P0 = 100
- Second anchor (later high) price: P1 = 115
- Vertical move: D = P1 − P0 = 115 − 100 = 15
Compute derived price levels:
- For r = 0.382: 100 + 0.382·15 = 100 + 5.73 = 105.73
- For r = 0.5: 100 + 0.5·15 = 100 + 7.5 = 107.50
- For r = 0.618: 100 + 0.618·15 = 100 + 9.27 = 109.27
- For r = 1.0: 100 + 1.0·15 = 100 + 15 = 115.00
Interpretation of the geometry:
- The Fan lines are created by taking rays from the base anchor’s time/price location toward the chart using these derived price levels as targets.
- If your charting platform labels the same ratios, you should be able to reproduce the same derived price numbers from the same P0 and P1.
Cross-check you can do independently:
- If you change only the anchors to new values P0’ and P1’, recompute D’ = P1’ − P0’ and multiply by the same r values. Any Fan derived from the same ratio set should shift consistently because every derived level depends only on P0, P1, and r.
Limitations and risks
At least one material limitation is anchor sensitivity. Because the Fan is built from two chosen swing points, different anchor selections can produce noticeably different rays and derived levels, even if the Fibonacci ratios are the same. This means the method is not uniquely determined by “the market” alone; it is partially determined by how the chart’s swings are identified.
Other limitations and failure modes:
- Ratio set differences: different tools or educators may use slightly different ratio collections, so the drawn rays may not match.
- Scale and measurement conventions: price units, chart scaling, and the exact implementation of rays versus curves can affect how lines visually line up.
- Limited causal meaning: the Fan is a geometric mapping of chosen anchors; historical alignment does not establish that the same behavior will occur later.
- Context dependence: the method does not incorporate costs, liquidity, execution, or jurisdictional constraints that affect real results.
Verification or next question
If you want to verify your understanding, repeat the worked example using your own anchors (pick two prices, compute D, multiply by each r, and list the derived levels). Then compare your computed levels to the labels your charting tool shows when you select the same anchor points and the same ratio settings.