# Fibonacci Retracements

A long time ago, this Italian mathematician called Fibonacci, or Leonardo of Pisa, got credit for discovering a sequence of numbers which he used in a book to demonstrate the reproduction rate of rabbits. Actually, the sequence was known to the Indians in the sixth century, they just didn’t want to let on about it, knowing that it could be useful to traders in the Western world much later! Earlier still, the Greeks also knew about the actual numbers used, and they called the ultimate value (1.618054, or the inverse 0.618054) the Golden Ratio.

This is a number which is echoed in all nature, the spirals in a sunflower head, florets in a pineapple, etc. The fact is that the ratio is the most pleasing to the eye, and in the realm of useless information, you should know that this ratio was used by the Danish mathematician Piet Hein to design efficient roundabouts in Stockholm.

CTC (cut the crap), we use it to make lines on the chart at predetermined ratios, which then tend to be significant or turning points for retracements, etc. Whether this is because other traders expect this, and therefore make it happen, or whether it is a mysterious force of nature that applies to the Stock Market, is still hotly debated – we just observe the effect and try to use it to beat the market. After all, we’ve already established that trading is all about the psychology of other traders.

You can read several trading books, and get several different opinions about where to use Fibonacci lines. This is just a reflection of the fact that the ratios occur in many places. The actual numbers that are used for price retracements are 0.236, 0.382, 0.500, 0.618, 0.764, and when they are used for price extension the numbers are zero, 0.382, 0.618, 1.000, 1.382, and 1.618. Whole books have been written about the uses of Fibonacci lines in trading, but I’ll just mention a few.

The Fibonacci retracement is created by taking two extreme points on a chart – usually a major peak and trough – and dividing the vertical distance by the key Fibonacci ratios of 23.6%, 38.2%, 50%, 61.8% and 100%. The lines you make can be from the bottom of the historic lows – a short term low with higher lows on each side – to the top – that’s the high point with two lower highs on each side. If you click and drag with the tool, you will get the lines drawn at the right locations, and it uses the first set of numbers given above. If you look at previous retracements, you will probably see that some of them line up with the fibonacci retracement lines, and they generally mark where you would expect to see periods of consolidation, and will give you some confidence in projecting forward. The expectation is that if the market retraces from the high, it will find some support at one of these levels, because traders will be buying in the hope and expectation that the market goes back up.

The price extension numbers are generally meant to show where you can take profits on a long trade in an uptrend. The zero would be at the low point that you are hoping to go up from, and the 0.382 would be lined up with the previous high. The ex-tensions above the previous high point would give levels at which you might find the in-creasing price peaks out.

You may hear the name Fibonacci in connection with some other trading tools. You can use the ratios with not just retracements and extensions, but also with arc and fan shapes.