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How to Use the Magic Numbers Retracement Theory

The “magic numbers” theory about how retracements should form is based on the Fibonacci sequence of numbers. This theory says that a retracement is most likely to stop at one of a series of numbers, with an emphasis on 38 percent or 62 percent of the original move.

A 13th-century Italian mathematician named Fibonacci discovered a self-replicating sequence of numbers with curious properties. It starts with 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and so on to infinity. The numbers in this sequence have these properties:

  • The sum of two adjacent numbers in the sequence forms the next higher number in the sequence.

  • The ratio of any two consecutive numbers approximates 1.618 or its inverse, 0.618 (after the first few numbers).

Nature offers many examples of these ratios: daisy petals, ferns, sunflowers, seashells, hurricanes, whirlpools, and atomic particles in a bubble chamber. And many of man’s works purportedly embody the Fibonacci ratios, as well: the pyramids in Egypt, the Parthenon in Greece, and Cézanne’s choice of canvas shape (although some mathematicians dispute some or all of these examples).

Scientists say that to attribute human behavior to any single number sequence is ludicrous or, at least, not plausible.

A stock trader named Ralph Nelson Elliott believed that man’s behavior, including his behavior when trading in the stock market, revealed similar characteristics as the Fibonacci sequence and could therefore be charted to predict future behavior:

  • Elliott observed that securities prices appear in a wavelike form on charts, hence the name of his forecasting method, Elliott Wave.

  • Elliott wrote that the Fibonacci sequence provides the mathematical underpinnings of the wave principle.

  • Elliott Wave adherents expanded Elliott’s use of the Fibonacci sequence and often use Fibonacci levels, with special attention to 38 percent and 62 percent (but also including 23.6 percent, 50 percent, and 100 percent of the high-low span), to predict the extent of retracements.

    Technically, 50 percent isn’t a Fibonacci number. It’s customary to include it, though, possibly because of Gann’s influence.

To make life difficult, some traders who like the Fibonacci sequence aren’t strict adherents of the Elliot Wave principle, and some Elliot Wave traders don’t necessarily believe that price moves will stick to Fibonacci numbers.

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