Fibonacci series

A number progression in which each successive number is the sum of the two immediately preceding it: 1, 2, 3, 5, 8, 13, 21, 34, 55, and so on.

As the series progresses, the ratio of a number in the series divided by the immediately preceding number approaches 1.618, a number that is attributed significance by many traders because of it appearance in natural phenomena (the progression a shell’s spiral, for example), as well as in art and architecture (including the dimensions of the Parthenon and the Great Pyramid). The inverse, 0.618 (0.62), has a similar significance.

Some traders use fairly complex variations of Fibonacci numbers to generate price forecasts, but a basic approach is to use ratios derived from the series to calculate likely price targets.

For example, if a stock broke out of a trading range and rallied from 25 to 55, potential retracement levels could be calculated by multiplying the distance of the move (30 points) by Fibonacci ratios say, 0.382, 0.50, and 0.618 and then subtracting the results from the high of the price move. In this case, retracement levels of 43.60 [55 - (30*.38)], 40 [55 - (30*.50)], and 36.40 [55 - (30*.62)] would result.

Similarly, after a trading range breakout and an up move of 10 points, a Fibonacci follower might project the size of the next leg up in terms of a Fibonacci ratio –– e.g., 1.382 times the first move, or 13.82 points in this case.

The most commonly used ratios are 0.382, 0.50, 0.618, 0.786, 1.00, 1.382, and 1.618. Depending on circumstances, other ratios, such as 0.236 and 2.618, are used.