Leonardo Pisano (nicknamed Fibonacci) was a 12th century Italian mathematician who introduced to the Western world what became known as the ‘Fibonacci sequence of numbers’. His work was based on ‘mathematical order’ found continuously in nature, an order consistently observed and considered too common to be random.
The Fibonacci series is an infinite sequence of numbers in which each number is the sum of the preceding two. ( 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144…). In the sequence the quotient of the adjacent terms (after the first few numbers) is always ~ 1.618, or its inverse .618 (known as the Golden Ratio). Subtracting this number from 1 equals .382, which is also the ratio of two numbers in the sequence with one number in between them, i.e. 34/89 = .382 (3 d.p.), 55/144 = 0.382 (3 d.p.) and so on.
Many traders use the Fibonacci series for trading decisions. Rather than using the raw numbers, which can be of little use, they typically use the ratios between the numbers in the series to determine various levels like retracements and extensions during trends, which can form important support and resistance levels. Amongst the popular Fibonacci studies utilized by traders are Fibonacci fans, retracements, expansions and time zones.
Fibonacci Fans are lines drawn on the price chart based on the Fibonacci sequence of numbers. To create the fan a user draws a trend-line between two points (typically important high and low), the fan is then drawn by dividing the vertical distance between the points by the key Fibonacci ratios of 38.2%, 50% and 61.8%. The resulting divisions form a point on the vertical distance to which the fan lines are projected from the start point of the trend-line. The Fans are used by traders to determine important support and resistance levels in the future in which to trade around.
Fibonacci retracements are used by traders to estimate reversal points during trends. Percentage retracement levels based on the Fibonacci numbers are plotted as horizontal lines over the price chart. These lines form the levels between two important price points to which a price may be expected to retrace. Traders will look to buy on retracements at a Fibonacci support level during up-trends and sell on a retracement at a Fibonacci resistance level during downtrends.
Fibonacci Expansions and Time Zones
Fibonacci expansions (or extensions) are used to project likely price targets for the next leg of an up-or downtrend. Percentage expansion levels are based on the significant Fibonacci numbers, which are plotted as horizontal lines above/below the previous trend move. These levels form important areas where price support or resistance may be encountered.
Fibonacci time zones are a series of vertical lines spaced in increments on the price chart based on the Fibonacci sequence of numbers (1,1,2,3,5,8,13,21...). These lines indicate areas in which major price movement may be expected. The time zone lines can also be used to determine time periods in which trend phases and patterns develop and complete.