Fibonacci Retracement

Technical Indicators - Fibonacci lines

Leonardo Fibonacci was an Italian mathematician, born in Pisa about 1170. He introduced the Hindu-Arabic decimal system of numbers that we use today to Europe, along with a number sequence now known as the Fibonacci sequence. This was not his discovery however, the sequence was known to Indian mathematicians as far back as the 6th century.

In the sequence, each number is the sum of the previous two, so we get the following:  1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 etc. (he started with a 1, modern mathematicians use 0). Each number is about 1.618 times the preceding number, and 1.618 is known as the 'golden ratio', or divine proportion, as it can be found in many places - the proportions of the human face, plant structures, geometry, musical form, and architecture, to give just a few examples.

It's magical properties have also been applied to the world of technical trading. We can examine just how, starting with Fibonacci retracements.

Retracements are used to identify lines of support and resistance, or possible trend reversals. A line is drawn between the desired highest and lowest points on a chart, and the Fibonacci levels, expressed as a percentage (50% is not a Fibonacci number, but it's used anyway because it's thought of as a common retracement level), appear as a series of support and resistance lines. In the example below we've had a long rise in prices which has pulled back, as you can see, to precisely the 50% mark before bouncing up again. A 50% retracement is seen as moderate, and a 61.8% as golden (in synch with the golden ratio). A bounce at this level could indicate  a strong move up again.

You can apply the same thing in reverse - a long decline followed by an up move (see below).

Traders who use Fibonacci monitor the levels and may act on the signals they derive from doing so. You might think of them as reversal alert levels.

A second variation of Fibonacci is the fan. The principle is the same, and in the example below the leftmost line has been drawn from a low to a high point. Potential areas of support are indicated by the lines fanning out to the right, at 38.2%, 50% and 61.8% respectively.  You can see that there's been a bounce off the 38.2% level. Again, you can use the fan in reverse on a downward trend to identify potential lines of resistance.

 

The next variation is the Fibonacci Arc. The innermost arc below is 38.2%, the one below is 50%, and the outermost 61.8%. You get an added element of time with arcs, because a 20 day rise in prices will produce wider arcs than a shorter 10 day price rise. 

Fibonacci extensions are again identifying support and resistance levels, and can be used by traders as possible points to take profit from a trade. In the example below I've drawn a line from low to high of a period of uptrend. The three lines above represent target levels at 61.8%, 100% and 138.2%.  This is a retrospective example really, you can see where there were significant resistance levels at 61.8% and 100%. The final extension line remains to be hit. 

 The last Fibonacci variant I'll deal with is the Fibonacci time zone. These are vertical lines extending from an initial high or low point on a chart (see no. 1 below). They indicate points of possible price reversal. Each number represents a period of days, and you can see how the Fibonacci sequence is being used by adding the sum of the previous two numbers to find the next time zone. Again, this is a retrospective example.

 

Darren Winters