This sequence has since been studied extensively, not only because of the number sequence, but more significantly, because of the ratio between two consecutive numbers. 

If you divide one Fibonacci number by the previous Fibonacci number, the result is close to the value of 1.618. The further along the sequence you move, the closer the ratio between two consecutive numbers is to this value. 

This ratio is what the ancient Greeks called the "golden ratio" and much of their architecture incorporates this ratio - for example the front façade of the Parthenon is a rectangle with sides in the ratio of 1 to 1.618. The Greeks were so interested in this number that they represented it by the Greek letter Phi.

Another significant ratio within Fibonacci numbers is the ratio from dividing one number by the following number. This gives the ratio of 0.618, the inverse of the "golden ratio"

Further studies have been made of the ratios using alternate numbers - one number divided by the number 2 along in the sequence. This gives the ratio of 2.618 or the inverse ratio 0.38196.

By now you are probably starting to think - what has any of this got to do with trading? Some people say "not very much". Others believe that the Fibonacci ratios can be used to determine the point that a trending market will retrace to. 

Most traders agree that when a market or stock is trending, it tends to bounce along a bit, moving up, then back, then up a bit further and so on until it reaches its final high point (that is, when the market is trending upwards). The most common retracement points are 50%, 33% and 67%. 

However, supporters of Fibonacci believe that the Fibonacci ratios are a more accurate reflection of where the market will move to. So they replace the two thirds with 62% (the 0.618 ratio) and 38% (the 0.3819 ratio). If the Fibonacci retracement tool is applied to a market, it can be seen where the market is likely to move to, which can assist traders to determined future price movements.

Take a look at the following chart, which is a Commonwealth Bank daily bar chart with a Fibonacci retracement tool applied. You can see that as the market trends upwards, the price retraces several times back to the 38% Fibonacci line. Point A on the chart shows where the price tops out in early December. This then runs down and tests the 38% line twice (points B and C) before there is enough selling pressure to push through this support level. The price then continues to move down and tests the 50 % line where it manages to close for 3 days only below the 50% line (Point D) before it retraces again .

We can see that it fails to get anywhere near the tops above $32.00 (Point E) and when the price turns down again the previous support at 38% and 50% is easily taken out. 

So, what does this mean? Skeptics argue that this is coincidental, and that if you look at enough charts, you'll eventually see that the same ratios occurring. However, this belief hasn't stopped Fibonacci Retracements becoming one of the more popular analysis tools used by technical analysts today, based on the number of times historically that the markets have retraced to these levels. 

Fibonacci Retracements are typically used to identify potential support and resistance points within a particular share or market. Additional indicators would then be used to determine whether this was support and resistance or a reversal in the trend.

Experiment with the Fibonacci Retracement tool and see for yourself how this centuries old number sequence can be applied to the modern markets.

Aaron Lynch is a product specialist with The HUBB Organisation Ltd. He is extensively involved in client training and product enhancement.

If you've done any study of technical analysis, there's a fair chance you would have come across tools related to Fibonacci numbers. But what exactly are these numbers and just how do they apply to technical analysis.

Fibonacci numbers are a sequence of numbers that have been studied across a number of mathematical disciplines. The sequence was first studied by 13th century Italian mathematician, Fibonacci who posed the following question:

"How many pairs of rabbits will be produced in a year, beginning with a single pair, if in every month a pair bears a new pair which becomes productive from the second month."

The result was a sequence of numbers where each number is the sum of the previous two numbers, as shown here:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233,…