ASX Charting Course

Chapter 39

The Fibonacci Series

The Fibonacci Series of numbers

Strange though it may seem but integrated within Elliot wave is the magic ratio of 0.618%. It is the most common retracement for any advancing leg or impulse wave.

The series is simply 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 … to infinity. It is propagated by adding the previous two numbers in the series. The ratio of any two adjacent numbers in the series approximates 1.618 or its inverse 0.618. The ratio between alternate numbers is either 2.618 or its inverse 0.382. Below is a table of interrelated properties.

2.618 - 1.618 = 1

1.618 - 0.618 = 1

1 - 0.618 = 0.382

2.618 * 0.382 = 1

2.618 * 0.618 = 1.618

1.618 * 0.618 = 1

0.618 * 0.618 = 0.382

1.618 * 1.618 = 2.618

The ratio occurs all over the place. It is the golden section, referred to by Plato. “Any length can be divided in such a way that the ratio between the smaller part and the larger part is equivalent to the ratio of the larger part to the whole. That ratio is 0.618.”

Whether it is the great pyramids of Gizeh or the logarithmic spiral of a snails shell or our own celestial Milky Way, the 0.618 ratio is common to all and exists repeatedly in the natural world. And so it is for commodity and stock price charts.

The simplest application is as a retracement. Assuming we’re retracing an obvious major impulse move, which could be a five wave structure. To apply the Fibonacci retracement ratios measure the extent of the advance and mark three horizontal retracement lines at 38.2%, 50% and 61.8% of the total move. It is surprising how often the market will retrace to these levels then turn and resume its trend.

A slightly more obtuse use of the ratio can be applied with Elliot theory when projecting the length of a wave three. Wave three is often a multiple of wave one by a factor of 0.618 or 1.618. In some cases even 2.618.