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Monday, 4 June 2012

Shoulder-Head-Shoulder and Discrete Mathematics

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There was an interesting argument that this was not a Shoulder-Head-Shoulder (SHS).

The argument went as follows:
"I bet to differ.:) this may not be a head and shoulder pattern because if it is a h&s ,the price projection 16000-8000 = 8000. Then 8000-8000=0. for this head and shoulder pattern will give a target of near to zero. I don't it is possible for a index to go to zero unless all the index component stock goes bankrupt. Just my 2 cents."

For readers' learning purpose, this is my opinion:
"That is why i did not give a projection. It was intended as a chart to show a big distribution over the long term. Technical Analyses are rigid, doesn't necessarily mean everything needs to be rigidly applied. No price projection able to be obtained does not necessarily mean it is not head and shoulders."

It is still a Shoulder Head Shoulder in price structure. What I was particularly interested was the logic given as it reminded me of Discrete Mathematics in Computer Science (yes, the field I was trained in!). This was the logic argued: Head and shoulder implies a price projection to be obtained and no price projection implies not Head and Shoulder. Can such a logic hold? We can apply logic theories in Discrete Mathematics.

In the theory of logic in Discrete Mathematics, "A implies B hence not B implies not A" such an argument is not true. Similarly, "Head and Shoulder implies Price Projection hence No price projection (b/c IBEX=0) implies not Head and Shoulder" such an argument is also not true.

To illustrate a counter-example: German implies speak German (A implies B / SHS implies price projection), going by the logic argued on why it is not SHS, it will conclude that don't speak German implies not German (not B implies not A / "unable to have price projection implies not SHS") and this is not true. Because you can don't speak German but still a German. A German can don't speak German because he is living abroad but that does not make him less German just because he don't speak German. So the logic of not B implies not A following an A implies B cannot hold.

Discrete Mathematics or logic proves that the logic "unable to have price projection of zero implies not Shoulder-Head-Shoulder" cannot stand. Sometimes humans are confused by logic themselves, that is why humans will sometimes accept something illogical. This is the same for financial markets: throw some confusion bombs and the logic of no logic as well as the no logic of logics will be accepted by market participants.

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