FIBONACCI NUMBERS

Fibonacci retracement is a very popular tool among technical traders and is based on the key numbers identified by mathematician Leonardo Fibonacci in the 13th century. However, Fibonacci’s sequence of numbers is not as important as the mathematical relationships, expressed as ratios, between the numbers in the series. In technical analysis, Fibonacci retracement is created by taking two extreme points (usually a major peak and trough) on a stock chart and dividing the vertical distance by the key Fibonacci ratios

The key Fibonacci ratios are: 23.6%, 38.2%, 50%, 61.8% and 100%.

Once these levels are identified, horizontal lines are drawn and used to identify possible support and resistance levels. Before we can understand why these ratios were chosen, we need to have a better understanding of the Fibonacci number series. The Fibonacci sequence of numbers is as follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc. Each term in this sequence is simply the sum of the two preceding terms, and on it goes until the sequence reaches infinity. One of the remarkable characteristics of this numerical sequence is that each number is approximately 1.618 times greater than the preceding number. This common relationship between every number in the series is the foundation of the common ratios used in retracement studies.

The four studies are;

1. Fibonacci Retracements (most common)
2. Fibonacci Arcs
3. Fibonacci Fans
4. Fibonacci Time Zones

The key Fibonacci ratio of 61.8% – also referred to as “the golden ratio” or “the golden mean” – is found by dividing one number in the series by the number that follows it. For example: 8/13 = .6153, and 55/89 = .6179.

The 38.2% ratio is found by dividing one number in the series by the number that is found two places to the right. For example: 55/144 = .3819.

The 23.6% ratio is found by dividing one number in the series by the number that is three places to the right. For example: 8/34 = .2352.

For reasons that are unclear, these ratios seem to play an important role in the financial market, just as they do in nature, and can be used to determine critical points that cause an asset’s price to reverse. The direction of the prior trend is likely to continue once the price of the asset has retraced to one of the ratios listed above.

Fibonacci and the Golden Ratio

There is a special ratio that can be used to describe the proportions of everything from nature’s smallest building blocks, such as atoms, to the most advanced patterns in the universe, such as unimaginably large celestial bodies. Nature relies on this innate proportion to maintain balance, but the financial markets also seem to conform to this ‘golden ratio’. Here we take a look at some technical analysis tools that have been developed to take advantage of it.