Trading systems: is it possible to design a mechanical trading system from the harmonic square ? Here is the answer … The use of support and resistance is one of the most commonly used tools in technical analysis, as it provides the investor with technical points before price touches them. Their use is extended to determine market entry points but also to liquidate positions (target to be reached or maximum amount of money to be lost). Most of the time, these levels are calculated by using mathematical formulas enabling the generation of several levels based on past price evolution. As examples for these formulas we have the Fibonacci sequence or the Gann angles. The current article will be dedicated to one of these techniques, Murrey´s mathematical system but also other trading systems can be created from scratch.

Murrey´s Mathematics and trading systems
The following system was developed by T. Henning Murrey in his book “Murrey Math Trading System for All Traded Markets”. This system is basically a method looking for harmonic price patterns. Once one of these patterns is found, a group of supports and resistances is generated in relation to the figure´s most significant points.
Let´s start with an explanation of the pattern we are looking for: Murrey´s intention with his system is ranslating the study of musical rhythm to sequences analysis in the price. To do so, he generates a figure on the price chart in order to represent the eight note succession in the musical scale (which is known as an octave).
The figure in question is a square divided in eight parts of equal size so that the octave is represented. The target of all this to generate barriers in the price forecasting.
In the following section, we are going to explain the building up process of the harmonic square. Later on, we will explain how to interpret the price reaction on each level (or note, following up with the symphonic similitude) and the consequences issued from this result.

Construction of the Harmonic Square: is it possible to transform it in trading systems ?
In this article you will find the algorithm developed for the construction of the harmonic square in Visual Chart 5. Nevertheless, we are going to try to explain briefly the creation process of this figure. The sequence to be followed is described next:

Step 1: Locating the extreme points.

In function of a certain period of bars to be studied, we look for the higher and lower price of this period.
Step 2: Determining the corresponding fractal.

Once the highest point has been found, we need to find the position it occupies inside the rhythmic scale suggested by Murrey and translate this value to the corresponding point. The scales list can be found in the previously mentioned programming code.

Step 3: Calculating the displacing range.

The following step will be calculating the displacing range between the higher and lower value. This size must be specified at the scale of the value obtained in point 2.

Step 4: Determining the base and height of the square.

Once we have the previous elements at our disposal, we will proceed to the calculation of the base and height of the square. This process requires a series of mathematical calculations and as their explanation can be a bit boring, so we will avoid this explanation. For those, interested in the process, it can be found in the programming algorithm.

Step 5: Dividing the square in octaves.

After having extracted the base and height of the square, the following step will be dividing the figure in eight parts of equal size with which we will be able to represent the size of the octave. The process is simple as it essentially consists of dividing the height into eight proportional segments.

Once we have the lines forming the Murrey square, we can draw them over the chart. In Figure 1 you can see how a 64 bar compression is represented.

If we take a closer look to the example, the square has been calculated in these trading systems by using the higher and lower prices between points A and B. The indicator designed for Visual Chart 5 runs a study starting up in point B back through 64 previous bars and draws the figure for this interval. In the chart of the IBEX future we notice the representations of the figure coloured in green. The square is crossed by a series of lines, following the specifications given by Murrey. As a consequence, a series of crossovers are formed and these crossovers are forming, according to the author, the key points of the figure. These points will be the source for the creation of supports and resistances to be studied.
This representation is merely artistic but it doesn´t help identifying the source of the different levels. In order to distinguish them from each other, each level receives a name going from “8/8P” to “0/8P”, as we can see in the drawing. These levels will be drawn over the 64 subsequent bars after the appearance of the harmonic square so that it corresponds to the influence period. After 64 new bars, we calculate a new square again, generating the following extreme values and repeat the process again.

The result will be a sequence of levels being calculated every 64 bars (or whichever period we estimate adequate).

The price contact with each of these points has a different lesson as we will explain further on.

Analysis of Support and Resistance Levels in Murrey trading Systems

As we have stated earlier on, the extension of the main lines of the harmonic square will be the most helpful element for our price behaviour study. Murrey provides each of the lines with a different weight so that each line has higher or lower influence than the others.
In Figure 2 you can see the lines Murrey Math applied to a 15-minute chart of the German Bund. This will help us in monitoring the price reaction on each of the levels.
Let´s study the characteristics of each group:

• Lines 0/8P and 8/8P

These two lines are the extreme levels of the square. Both are support and resistance key levels and as a consequence very difficult levels to overcome. Its price auctions outside the square both levels will work in the opposite sense, in fact, line 0/8P will turn into a strong resistance level and 8/8P a strong support level. In Figure 2, these lines are drawn in red. Point C and point I represent this situation. In point C, the price touches several times the level 8/8P, and even though finally the level is broken, its interest as a strong resistance point is evident. The price reaction in point I is even more interesting: price breaks out of the level, but is attracted back two days later by the strength of this support.

• Lines 1/8P and 7/8P

These new lines are also quite relevant. They are normally the most studied levels. If price auctions above/belowthese levels it will probably reach the levels 0/8P y 8/8P respectively. However, if price gets closer to them but does not overcome them, a strong movement in the opposite direction can be expected. In Figure 2, these lines are coloured in Green and are wider. In point A we notice how
price bounces by reaching the level 7/8P. Theoretically, in order to have a rebound, this level should not be overcome, however, in this case it is. This fact leads us to think that a margin of error factor of X points is to be used before developing the trading management. However point G is a perfect example of a price bounce after touching 7/8P. Point B and point F are breakout examples deriving from a price extension towards lines 8/8P and 0/8P respectively. This can be considered a proper level but we shall no forget the error margin previously mentioned.

• Lines 2/8P and 6/8P

These levels are considered of less importance by the author in the discussion of his trading sytems even though price can change its direction when reaching them. In Figure 2, these lines are grey coloured but we have not considered them relevant. However if we take a closer look at the chart, price reactions occur at these levels. An example can be studied at the beginning of April just after the turn- around in point A.

• Lines 3/8P and 5/8P

The author in his explanation regarding his trading systems describes these two points as the limits in price bracketing movements. Therefore, we can consider that, while price moves inside the channel limits of these two levels, the underlying asset is in a congestion zone (non-trending). Likewise, the breakout of this channel can involve a new distributions process. In Figure 2, these lines are coloured in violet. In the example, the lateral movements are not significant and consequently price does not remain time enough inside this range. An example of this could be found in May 20th, after the reversion in points G.

• Line 4/8P

This line also acquires special relevance as it is considered as in important resistance zone during the distribution process started up in the zones 0/8P or 8/8P. A reversion movement is to be expected when price gets close to this level (providing the fact that the movement has started in previously mentioned levels).

An example of the above situation occurs in point E. After price fails from line 8/8P, a retracement takes place when reaching the level 4/8P. It is interesting to observe that in the reversion movement, price stops again in the level 5/8P, movement that could have resume in to a bracketing market if price had not bounce again in the lower extreme of the congestion zone (level 3/8P). However, the bearish movement is stronger and extends the range towards the lower extreme of the square (level 0/8P). It is clear that is not strightforward to design a trading system on this approach but it is possible for sure.

Conclusions on Murray’s Trading systems

One of the most interesting aspects when analysing the price reaction on the lines of the harmonic squares is to take into account that the generation of the pattern is a consequence of the previous phase of the price movement. However, we are reminded that the harmonic square is based on the study of the music octave thus theoretically there should not be a direct relation between the generation of the model and its consequence in market price movement. However, we note that the use of patterns is often seen in nature and is not necessarily based in scientific hypotheses, but is instead related to human behaviour, and is common in technical analysis. So that you can start programming a bunch of trading systems from this very basic approach.

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Emilio Tomasini is Chief Editor of the Italian edition of TRADERS’ MAGAZINE (www.traders-mag.it), the leading monthly publication in Europe for trading and investment, and since 1999 he organizes the TRADERS’ CUP the most important real money European trading competition (www.traders-cup.it). His personal weekly free newsletter L’Indipendente di Borsa (www.indipendentediborsa.it) is one of the most reputable Italian financial media and counts more than 100.000 readers. His website in English is www.emiliotomasini.com

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