**SUBJECT SUMMARY**

Fibonacci numbers are all about particular numbers, their sequence and their relationship. Leonardo Pisano (better know as Fibonacci) was a mathematician who was born in Italy around 1170 AD. He discovered a relationship of numbers known as the Fibonacci sequence in which each successive number is the sum of the two previous numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and so on.. These numbers have an unusual relationship where any given number is approximately 1.618 times the preceding number and any given number is approximately 0.618 times the following number. Fibonacci numbers and the golden ratio occur in nature astoundingly often, and can be strongly associated with many commonly occurring market patterns.

These Fibonacci relationships are applied to chart analysis to establish levels which will often indicate what will happen next. Traders use these levels to watch for a possible change in direction. The use of Fibonacci expansions is supported in any good charting software and generally they use the following expansion levels of a range: +61.8%, +161.8% and +323.6%. *The range expansion relationships are used to locate potential trend turning points.*

Among all the chart patterns that are used by traders, the triangle patterns are most commonly used.

The triangle patterns occur in different forms, such as symmetrical triangles, ascending triangles, descending triangles, and even wedges and pennants, which are classified as triangle patterns. While each has its own characteristic for entering a trade, the exits of the trades based on these patterns are very general and not very specific in nature.

Here we look at trading a triangle formation using Fibonacci, where we can define our entries, exits and stops very specifically. While this can be applied to all types of triangles, there are certain parameters that have to be met for applying this strategy.

*First and foremost for this strategy, we define our triangle with lines drawn on fractal bars only.*

Let us define what a fractal bar is. A fractal high bar forms, when the said bar has a higher high than the bar preceding it, and the bar subsequent to it. Similarly a fractal low is formed when the said bar has a lower low than the bar preceding it, and the bar subsequent to it.

The first diagram shows what a fractal bar would look like –

These fractal bars form the pivot points, from where price would usually be expected to turn.

Using these in our strategy, we define our first parameter.

*We define a triangle*__only when we have four fractal bars on the chart__While this may sound complicated, it is not very difficult to spot them on a chart.*– 2 up fractal bars with lower highs, and 2 down fractal bars with higher lows.*

The next diagram shows what our triangle should look like –

These 4 bars form the boundary of our triangle, and our strategy is effective only when we have this kind of triangle. It does not matter if it is an ascending or descending type, or a pennant or a wedge. *As soon as there are enough points to draw two lines with opposing slopes, we have a possible triangle trade in the making.*

Next we need to know the direction of the breakout from this triangle.

This gives us 3 touches on one line of the triangle, and 2 touches on the other line.*This happens when price breaks out of the triangle by penetrating any one line, and pauses / retraces without surpassing the last fractal.**We estimate that price should go in the direction where price has 3 touches.*Looking at our example above, we see that price penetrated the higher triangle line giving us 3 touches on the upper triangle line. This qualifies as our second condition.Next we need a value for calculating the Fibonacci ratios for the target. For this we calculate a price value which is the midpoint of the triangle.

*What we do is simply divide the triangle into two parts from where the triangle starts, to the apex of the triangle. Once we have this midpoint, we calculate the price difference between the upper and lower triangle line at this point.*

Now we have all our conditions in place, we shall use this example of a long trade to define our entry, exit and stop.

We saw that price paused after penetrating the higher triangle line in our chart. We place a buy order above the high of this bar since we estimate that prices should rise if this high is breached.*The entry should be placed above the high of the bar which penetrated the triangle line.*The upper and lower triangle lines should be extended forward to get the apex at their intersection. This is generally a very safe technical point for a stop, as price will rarely spike down to that level after the trend has started.*Our stop should be placed just below the apex of the triangle.*In this case, we take this value and add it to the entry to give us our first target. In a strong trending market this target is generally surpassed, with price reaching an extended target. This extended target is calculated by multiplying the midpoint value by the Fib ratio 1.618. In fact, this is the unique feature of this strategy that price will reverse or consolidate exactly at the extended target.*Our first target would be the price movement equivalent to the triangle midpoint we had calculated.*

We show another example of this strategy for a downtrend, and we can see the strategy is as effective.

Article as published in the __Guppytraders.com__ weekly newsletter, March 25th, 2006 edition.

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