# Fibonacci Levels for Trading – Freaky Maths

The first thing to understand is where these Fibonacci levels come from, so back to school for some Basic facts: 1.  The Fibonacci number sequence is where it all begins. The sequence begins with 1 and 1 and then each subsequent number is the sum of the previous two. The image below shows this clearly. 2.  The Golden Ratio is formed by dividing the consecutive pairs of number in the sequence to infinity as below.  As you will see as the calculations continue the results converge towards the Golden Ratio 1.618 and is classed as a constant and sometimes called the Devine Proportion.  Also note that the inverse or reciprocal of 1.618 is 0.618.  The Golden ratio 1.618 occurs in mathematics, design and in nature.In trading there are many different strategies and uses Fibonacci levels so I will concentrate on the main levels that I use in my strategies and that are most commonly used throughout the trading world.  The main ratio’s I use are 0.382, 0.50, 0.618, 0.786, 1.00, 1.27 and 1.618.  I also use 0.236 but alway round that to 0.25 as I mainly use it as minimum point of a pull back as you will see further in this article.  All these Fibonacci Levels are related mathematically to the main Golden Ratio as below, the Freaky Maths Bit:

1.0 – 0.618 = 0.382

0.618 x 0.618 = 0.382

0.618 – 0.382 = 0.236

0.382 x 0.618 = 0.236

Square root of 0.618 = 0.786

0.618 is the reciprocal of 1.618

Square root of 1.618 = 1.272

0.786 x 1.272 = 1

There are more and many more ratio’s but I think you get the Freaky.

Example 1.  In this example I discuss the Fibonacci Levels used in my “With Trend” Strategy trading the Elliott 5th Wave.  The Following was a Trade Setup for a Short Trade on the Harley Davidson Stock on a Daily time frame.  The overall Trend for this stock at the Time was Bearish and the recent Bullish Wave 4 Pull back was coming to an end  The main rules that I use with Fibonacci Levels in this scenario is that the Wave 4 Pull Back, whether for a Long Or Short trade setup, should pull back between The 0.25 and the 0.618 Fibonacci Levels taken from a retracement between the Wave 2 extreme and the Wave 3 extreme. (As I mentioned earlier I have rounded up the 0.236 Fibonacci ratio to 0.25 as a safety margin on these pull backs).  You can see on the Chart below the the Wave 4 did in fact pull back in that zone but more importantly found support at the 0.382 Fibonacci retracement level.  This same same 0.382 level also acted as support after the gap down. (click on the chart to enlarge then click the back space in your browser to return to the article) It is important to note that on many Pull Backs that have occurred after a long swing from one “Over” zone of the stochastic to the other, the Fibonacci Levels I discussed above can be used as indications of resistance or support levels.  In the Chart above you can see the Wave 2 was in the Over Bought Zone and then the Wave 3 was in the Over Sold Zone.  This is why we take the extremes of these movements to draw a Fibonacci retracement to identify potential Support and resistance levels and for me I also have the zone in which the Pull back should complete and turn back around to the overall direction.  To see how this trade finished up you can read my Full Trade Diary for this Trade HERE. 