Fibonacci Numbers

Celticheart Investor

A beginner's guide to trading and investing

Now this is one of my own personal favourite topics, not just because of its use as a technical analysis tool but because it absolutely fascinates me in the way that it appears so frequently in the natural world, such as in the branching of trees, the arrangement of leaves on a stem, the petals on a flower or the arrangement of a pine cone.

That of course is another blog altogether, so for now we will stick to its relevance in aiding us as a technical analysis tool.

Some think that Leonardo of Pisa (also known as Fibonacci) was the most talented western mathematician of the Middle Ages. Fibonacci is best known to us for spreading the ancient Hindu–Arabic numerical system in Europe, primarily through its publication in 1202 in his book Liber Abaci (Book of Calculation). You might want to think about why it is that, to this day, we still work mathematically from right to left in the Arabic manner. Without which we would have none of the mathematical tools available to us today, including computers which are so reliant on sequencing.

So lets look at the number sequence named after him the "Fibonacci numbers", (Also called Fib Numbers) which he did not in fact discover but simply used as an illustrative example in his book. The number sequence we now associate with Fibonacci was known to Indian mathematicians as long ago as the 6th century.

In the Fibonacci sequence of numbers, each number is the sum of the previous two numbers, starting with 0 and 1. This sequence begins 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987 and so forth.
 
The higher up in the sequence, the sum of the division of two consecutive numbers becomes closer to what Fibonacci called the Golden ratio which is approximately (1 : 1.618 or 0.618 : 1). 

e.g. 233/144 = 1.6180555 and 987/610 = 1.618033

The relevance to its use in technical analysis is that you will often find that a bullish rise will often retrace to a key Fib number and also the reverse is true,
a downtrend might correct itself and  rise to a key Fib number (not necessarily the next one in the sequence).

These are just some examples of how Fibonacci retracements in an uptrend look on the candlestick charts, along with the subsequent rises.
As with all things in charting the figures very rarely stop exactly on the fib numbers for reasons already mentioned above. The higher the number sequence the more accurate the golden ratio. 

Fibonacci numbers above all else seem to polarise opinion, with some people swearing by them and others dismissing them as nonsense. I would certainly not advocate using them as your sole means of measuring trends and directional change but, the frequency with which they appear makes me tend to take them seriously, at least as another useful technical analysis tool in your arsenal.

For a more detailed look at Fibonacci numbers check out the links below: 

http://www.tradingfives.com/articles/fibonacci_retracements.htm

http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibmaths.html

http://www.mi.sanu.ac.rs/vismath/lends/ch2.htm

Next Time: Parabolic SAR

A cautionary note, trading and investing in shares carries a level of risk, these blogs are only meant as a basic guideline to investing and trading, always do your own research and base your decisions on what you can afford to lose. This blog is not intended to provide financial advice as I am not qualified to do so, it is simply designed to provide information about how the markets work that might be of some help to private investors like myself.