THE SYMBOLs METHOD

to the Symbol's Method - 2

THE SYMBOL'S METHOD - 3

1.1.3 - TECHNIQUES OF HAMILTON’S DIAGRAM.

Hamilton, to implement his technique parted directly from graphs of equities quotations, in which the price (quotation) is in the Y axis and time is in the X axis, that is, the classic graphs of the evolution of quotations in time.

Figure 2 bis

The first question which Hamilton asked himself was: Which is it that makes the graph goes up or down...?

And the answer was: ABSTRACT FORCES, as they manage to drive the graph upwards: PUSHING UP FORCES, or downwards: PULLING DOWN FORCES.

In that time, the majority was convinced that without the intervention of forces nothing moves, as the General Theory of Relativity, which appeared in 1915, speaks of curved spaces instead of forces. Despite all the astronomic tests to verify the curvature of light done in 1919, General Theory of Relativity could not be verified in the laboratory until 1960, by means of the Mössbauer effect (Rudolf Ludwig Mössbauer was awarded the Nobel Prize in 1961) and therefore, in the twenties it could only be said that if a graph was moving it was because forces, abstract of course, acted upon it as they were supposed to directly push or pull any graph to rise or to fall.

In the case which Hamilton was occupied with, graphs of the Stock , which were the real forces hiding behind the abstract forces driving those graphs ? To Hamilton there was no doubt, the forces were two: the FORCE of DEMAND and the FORCE of SUPPLY, and with these two he set up the following premises:

(1) If demand increases and supply remains constant, quotation goes up.
(2) If demand increases and supply withdraws, equity quotation goes further up.
(3) If demand remains constant and supply increases, quotation goes down.
(4) If demand withdraws and supply increases, quotation goes further down.
(5) If both demand and supply remain equal and constant, quotation repeats.
(6) If demand and supply increase in parallel, quotation repeats.
(7) If demand and supply withdraw in parallel, quotation repeats.
(8) If demand remains constant and supply withdraws, quotation rises.
(9) If demand withdraws and supply remains constant, quotation falls.

In which are observed 3 rises, 3 falls and 3 repetitions posing important qualitative differences. Indeed:

If premises (1) and (8) are produced, in both cases quotation goes up, but the two rises have different qualities, as the rise under premise (1) is consistent (healthy according to Hamilton) and rise under premise (8) is non consistent, (unhealthy according to Hamilton).

For Hamilton the reason of the prior paragraph was even common sense, because the type (1) rise, is as a relay race. Participants pass the baton (there are interchanges of titles) and with renewed energy the tenants resist a new rise, but in a rise type (8) there is only reticence to sell at this price, but there is not effective interchange of titles.
In other words, a steady rise by entrance of money is not the same, as a virtual rise caused by withdrawal of titles. This is known by all the stock exchange players, even though in the short run the effect on the quotation of equity is the same.

Paradoxically, the strongest rise, which corresponds to premise (2) was not considered by Hamilton healthy but rather speculative, because under it demand increases but supply decreases and therefore in the short run it will be very profitable but short lived.

In the falls he reasoned the other way around , that is , a decrease if produced under premise (3) is not the same as other fall produced under premise (9), or another intervening the strongest premise (4).

In repetitions he found the first geniality applicable in his original mode of reasoning, as he found out that premise (6) never happens in markets.
This is logically so because what is natural is when supply detects that demand increases it ceases to be available until prices go up, and when demand notices that supply increases it ceases to go up awaiting the fall of prices. This is so because supply wants prices to go up and demand wishes prices to go down.

However, premise (7) which also implies repetitions, happens in markets, where sometimes the withdrawal of supply and demand is so strong that a limit case when nobody wants to buy or sell may occur.

The TECHNIQUE employed by Hamilton to show all the considerations explained before and many others on the same basis which could be drawn, consisted in the use of vectors, one to express the "force of demand" and another vector to express the "force of supply", in such a way that when the two vectors are pointing up, it is the sign of "free rise" in stock exchange parlance, and when both vectors are pointing down it is known as "free fall".

Figure 4 Figure 5

The explanation is evident as in the first case, when the first vector – on the left hand side –, points up it means that the force of demand is maximum, and if at the same time the second vector – on the right hand side –, points up too, it means that the force of supply is minimum and this is also a rising factor.
Thus, when both vectors are rising, both will point upwards, indicating in this way that at this moment in the life of the graph EVERYBODY IS WISHING TO BUY AND NOBODY WANTS TO SELL, producing a vertical rise of the graph characteristic of a free rise.

In the second case, we have the reverse. The first vector, pointing down indicates that the force of demand is minimum and this is naturally a pulling down factor. But the second vector which is also pointing down indicates that the force of supply is maximum and this is a pulling down factor too. This means that in the life of the graph NOBODY WANTS TO BUY AND EVERYBODY WANT TO SELL, which will translate in a vertical descent of quotation which typifies the "free fall".

1.1.3.1.- SYSTEMATIZATION OF THE FORCES OF GRAPHS. DIAGRAM OF HAMILTON.

To SYSTEMTIZE and unfold all possible vectorial turns, including the two extreme cases explained before, Hamilton drew the following diagram:

Figure 6

The fact that free rise, – both vectors pointing up –, is located in the upper left hand corner of the diagram, has no importance. It is there because it was the decision of Hamilton, and after he did so the logical consequence was to situate the free fall in the most distant point: the lower right hand corner.

Once the two previous positions were set, the other logical consequences were, the left hand side of the diagram should belong to the rising tendencies as the free rise, end point of the rising tendencies. is located there. The right hand side of the Diagram must belong to the falling tendencies because at this side is located the free fall or end point of the falling tendencies.

To develop the schema of the turning vector of the left side of the Diagram, which we have explained that should correspond to behaviours of demand and supply which generate rising tendencies, Hamilton wondered:

What characterises a rising tendency and what characterises a falling tendency ?

The response to the first question was, as it can not be otherwise, "what characterises a rising tendency is that supply is small compared with demand", which translated into vector parlance means that the demand vector may turn, but the supply vector remains pointing upwards along all the rising stretch.

The response to the second question was, and again it can not be otherwise, "what characterises a falling tendency is that the demand is small compared with supply", which translated again into Hamilton’s jargon means that demand vector will remain pointing down along all the falling stretch, while the supply vector turns.

The shape of what is said above in the diagram is:

Figure 7

From this disposition of the demand-supply vectors, the closing of the Diagram is immediate, because if in the lower left corner, the demand vector (the first one) points down, and in the other end (lower right corner) points down too, it means that it does not turn in all the stretch. But the supply vector (the second), which in the same left corner points up, in the other end (the right corner) points down, therefore this vector turns along all the lower stretch.

Figure 8

As far as the closing of Diagram in its upper part is concerned, it can be observed that in its right corner, the demand vector (the first) points down , but in its other end (the upper left corner) the same vector points up, therefore the demand vector turns all along the upper stretch, while supply keeps pointing up along the upper stretch of the Diagram

Figure 9

To end we have to characterise all the intersections with the turns of the demand-supply vectors, the central point of the Diagram. Hamilton represented it with two non oriented vectors, and named them chaos, as for him they represented the maximum non definition, that is, "from chaos or the central point when we move to the periphery of the Diagram order is born". Therefore, when we advance towards the centre of Diagram from any point of the periphery, non definition, that is, difficulty of prediction increases.