When Paddy Power asked me for a Views and Opinions piece they didn’t say anything about skipping the Maths lesson. So apols if this is a little maths heavy, but I’ll try to get you to the ‘How might this improve my trading’ bit before your eyes glaze over.

So who the blazes was this fellow? Not some long dead Celtic warrior, (although to my untrained ear Fib O’Nacci sounds as though he could have been) nor Tony Soprano’s long lost cousin.

Fibonacci was an Italian mathematician from the 12th Century who became famous for spreading the Hindu-Arabic number system throughout Europe, and for a number sequence which (although he did not invent it) was named after him.

The Fibonacci Sequence or ‘Bonking Bunnies’.

Fibonacci was a strange chap (he was Italian after all)-to solve a mathematical problem he though of how fast rabbits might reproduce given the right conditions. I knew that ‘going at it like rabbits’ is popular phrase but I didn’t know that it could be used in Applied Maths. Anyway back to Fibo’s poser:

Stick a pair of rabbits in a field. Rabbits are fertile after one month, so that at the end of the second month a female can produce another pair. Suppose our rabbits don’t snuff it, aren’t caught by foxes, they escape the pot (and Glenn Close) and the female always produces one new pair every month from the second month. How many pairs will there be after a year?
1. At the end of the first month, they mate, but there is still one only 1 pair.
2. At the end of the second month the female produces a new pair, so now there are 2 pairs of rabbits in the field.
3. At the end of the third month, the original female produces a second pair, making 3 pairs in all in the field.
4. At the end of the fourth month, the original female has produced yet another new pair, the female born two months ago produces her first pair also, making 5 pairs.

The number of pairs of rabbits in the field at the start of each month is 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,144. So at the end of year there will be 144. Dirty little buggers!
This series of numbers is interesting (or as interesting as series of numbers get) because:
1. The sum of any two consecutive numbers equals the next higher number (8+13=21, 21+34=55). This is the Fibonacci sequence which also occurs in the number of petals on a flower, spirals in a sunflower, snowflakes etc
2. The ratio between any number and the next higher number approaches 0.618 after the first four calculations. Try it ….21/34 =0.618
3. The ratio between any number and the next lower number is approximately 1.618 (the inverse of 0.618). This is also known as THE GOLDEN RATIO.

The Golden Ratio
You’d be surprised how often the Golden Ratio crops up in the environment. The Ancient Greeks were fascinated by it - many of their temples were built using it. The proportions of the Pyramids are based on it, Leonardo da Vinci used it in his paintings, it appears in the double helix of the DNA molecule and … well .. you get the idea.

OK! Enough! It’s all very impressive but how do I use this in my trading?
Patience Grasshopper - I see you have not yet been blessed with Enlightenment! After a move in one direction, markets often retrace part of that move before continuing. Sometimes the retracement will be will be 61.8%, 50% or 38.2% (1 minus 0.618) of the original move. These retracement numbers can then act as potential support or possible resistance areas.

Tucked into the Paddy Power charting package is a handy little tool called Fibonacci Retracement which saves you the slog of calculating these numbers manually.

If you are using the Demo Account select Lines from the menu at the top of the window, then choose Fibonacci Retracement and then High /Low. Left click on a peak and, holding your left mouse button down, drag the mouse cursor down to a trough. When the cursor is on the trough release the mouse button. A ‘popup’ box should appear, with the retracement percentages of 38.2% 50% and 61.8% already entered. Just click on OK and the retracement lines will appear on your chart.

For the Real Account charts you just need to click on the button, at the top left of the chart window.
Then click once on the peak and again on the trough (or vice versa). Again the retracement lines will appear on your chart.
For an example I’m using the Dow charted on the Demo Account charting package.

The peak of the market in this example is at 14097 and the intermediate trough 13111, a distance of 986 points. From this we can calculate:

Stick on the retracement lines and the chart looks like this:

I’ve annotated these to make it a bit easier for you to see which is which.

Where did the Dow recover to? 13740 which is close enough for me.

Just to prove it works the opposite way too, take a look at the USD/CHF currency pair, which has been gaining ground during the recent market upheaval from just over 1.18 to 1.22. As risk appetite and stock markets have recovered over the last week, so the pair has lost some of its appeal. Look where initial support was-bang on the 38.2% retracement level of that 4 cent rally, whilst secondary support is at the 50% level.

Is this Fibowhatsit thing the Holy Grail of Trading?
Sadly it isn’t. Just like any other technical analysis tool it doesn’t work every time, but the beauty of a Fibonacci Retracement is that it can be applied to any timeframe and any asset class. Although it doesn’t always work out, plenty of traders are well aware of where potential Fibo support/resistance areas are, even if they don’t actually use them in their trading plan, so sometimes those support/resistance lines can become a ‘self fulfilling’ prophecy.
And finally, if I’ve managed to baffle you take a look at this site which also has a no-nonsense guide to Fibs. Although it doesn’t use exactly the same charting package most of the Fibonacci features are very similar.