The All Ords as an Indexed Function of Pi
Table 1. Major Highs of The All Ordinaries Index 1937 to 1987 as an indexed function of Pi 10/6/27 = 1
If you consider that all market movements are part of a longer term cycle of activity it only makes sense that the constant Pi 3.14159 would be some how involved, it is the basis of all cyclic behaviour and therefore should show up strongly in the data.
If you take the first high of the Australian market after the great depression of 74.5 and multiply it by Pi you get the number 234.04, you can see in the chart below there was a high in the market at 239 if you repeat this the next number in the series is 735.28.
This is surprisingly close to the high of the Fraser resources boom at 746 in Jan 1981.
The next number in the series is 2309.96, the exact high of the 1987 market was 2312 on the cash and 2343 on the SPI. So after decades of market action the same constant keeps reappearing, the final number in the series is 7256 which is considerably higher than the final high of the 2007 market @6873.
This however does not disprove the underlying function but is does suggest that the function is elliptical. No matter how you care to look at it markets are a wave function, or to put is simply it is a cycle.
It is no great surprise that Pi would turn up somewhere as a constant, after all it is the most basic function of money and markets to circulate hence they are circular.
74.5 9 * Pi = 234.04 The high of the early 1960’s
239.1 * Pi = 735.28 The Fraser Resources boom
735.2 * Pi = 2309.96 The high of the crash of 1987 Exact @2312.5
In short all we are looking at is a set of concentric circles where the diameter each new wave front is the circumference of the previous wave front or boom time high.
This has significant implications for calibrating and modelling this data and becomes particularly interesting when considered in terms of Euler’s Proof when market trend and direction is measured in terms of growth and decay of an exponential system as measured as an exponential step function .
Greater resolution can be obtained by using the roots of pi as C = Pi^-(2^n) which you can see in the table and charts below.
Table 2: The All Ords 1937 high to 1987 high scaled to the square root of Pi.
- 74.5 * Pi^1/2 = 132 .04
- 132 * Pi^1/2 = 234.04
- 234 * Pi^1/2 = 414.84
- 414 * Pi^1/2 = 735.28
- 735 * Pi^1/2 = 1303.25
- 1303 * Pi^1/2 = 2309.96
Although this in itself does not provide a predictive method as such it does however suggest that there may be a far more accurate ways to price markets when the broader calculus implications are taken into account.
In particular when all of this is translated onto the complex plane and integrated as a track record of a notional trading algorithm on an example market such as the SP500 for the last twenty years where the track record in the indicator panel is point per contract.
Long and short of it is that this is self evidently not an entirely random system and is driven by a wave function which should really come as no surprise.