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Fibonacci Retracement Levels: 23.6%, 38.2%, 50%, 61.8%, 78.6%

How Fibonacci retracement levels are calculated over 63- and 252-session swings, rally vs decline, and why they're a convention, not a forecast.

Reviewed · Sources at the end · How Vyreon measures
Vyreon's per-security reports are not live yet; this page describes what they will measure. Examples are illustrative.

Fibonacci retracement levels divide the distance between a recent high and low at fixed percentages: 23.6%, 38.2%, 50%, 61.8% and 78.6%. They mark how far a price has given back a previous rally or recovered from a previous decline. They are a charting convention; we know of no peer-reviewed evidence that prices respect them more than other levels.

Fibonacci Retracement Formula

Take the swing high (H) and swing low (L) and a ratio f (0.236, 0.382, 0.5, 0.618 or 0.786).

  • Retracing a rally (the high came after the low): level = H − f × (H − L)
  • Retracing a decline (the low came after the high): level = L + f × (H − L)

So after a rally, the 23.6% level is closest to the high; after a decline, it is closest to the low.

Illustrative example: a stock rallies from a low of 80 to a high of 120. The retracement levels are 110.56 (23.6%), 104.72 (38.2%), 100 (50%), 95.28 (61.8%) and 88.56 (78.6%).

Where The Ratios Come From

38.2% and 61.8% derive from the golden ratio (about 1.618), which appears in the Fibonacci sequence. 23.6% and 78.6% are related ratios. 50% is not a Fibonacci ratio at all, but it is included by convention.

How Vyreon Calculates It

Vyreon finds the highest high and the lowest low over two windows: the last 63 sessions (about three months) and the last 252 sessions (about one year), using daily bars adjusted for splits and dividends. Whichever came later sets the direction, reported as "retracing a rally" or "retracing a decline". Vyreon reports the swing high, swing low, direction and all five levels for each window.

Choosing swings by fixed windows makes the levels reproducible. Chartists who pick swing points by eye may draw different levels.

What Fibonacci Retracement Does Not Tell You

  • It is a convention. We know of no peer-reviewed evidence that it predicts prices, and no known mechanism links the ratios to prices.
  • With five levels across a range, any price inside the range is within about 12% of the range of a level or a swing point, which can make the levels look more meaningful in hindsight than they are.
  • They are not targets, support or resistance in any measured sense.

Related: pivot points · price channels · max drawdown · moving averages

Sources

  • Leonardo of Pisa (Fibonacci), Liber Abaci (1202): the Fibonacci sequence.
  • Euclid, Elements, Book VI: division in "extreme and mean ratio", the golden ratio.
  • John J. Murphy, Technical Analysis of the Financial Markets (New York Institute of Finance, 1999): Fibonacci retracements as a charting convention.

Fibonacci retracement is a market convention; we know of no peer-reviewed source establishing that prices respect its levels.