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Chart Symmetry

Randgold; Durban Deep; Dow Jones in Terms of Gold

February 22, 1999

Chart Symmetry is designed around the observation that prices tend to change direction along certain preferred gradients. Different preferred gradients are linked though the Fibonacci ratio. When a preferred gradient has been identified and confirmed, it and its derived gradients can be used to search for patterns that help to describe the shape of the chart and which then enable the analyst to anticipate certain developments.

The values shown for the lines are the values of the lines at the next time interval after the chart close. It is not a prediction that the price will suddenly move to reach that line overnight, but provides the reader a measure of the move that could take place if the price pattern does develop in the direction of that trend line. The steeper the line, the greater will be the change in the line value over time.

Inverse symmetry on Randgold
One feature of price behaviour that is of assistance during the search for patterns is the fact that preferred gradients are not sign-sensitive, i.e. by changing the sign of a preferred gradient the inverse trend that results is usually also a preferred gradient. This works either as the direct inverse or as a shallower or steeper derivative.

This weekly chart of the dollar price of Randgold is generated by dividing the rand or JSE closing price of Randgold by the investment rand rate and then multiplying by 3 to get the ADR price in US cents/share. This could differ slightly from the New York close, which reflects price changes after the market in Johannesburg has closed.

In this analysis, the master gradient, M, is the resistance line of the steep bull market Randgold enjoyed from 1994 to 1996. On two earlier occasions this line had acted as support, which makes it a watershed line – support and resistance – a very important gradient. Lines D to A are the direct inverse of M. They were generated from selected points on the chart using the same gradient as M, but with sign reversed. Line F6, the current support line, is the sixth derivative of M.

The regular increase in the spacing between the four lines is a frequent alternative to the more common occurrence where channel lines are spaced an equal distance apart. (See chart of Durban-Deep for example.) Good obedience to the preferred gradient defined by line M is illustrated by the behaviour of the price along lines D and C, which implies that lines B and A should also play a prominent role in the development of the chart.

On Friday, 19 February, Randgold at a calculated $1,93 closed just a fraction below key resistance at line B after practically touching the line on the 19th. The question is whether a break will happen or whether resistance will remain intact. Line B has a value of 209 US cents on Friday, 26 February. Two scenarios can be developed:

Scenario 1: Resistance holds and forces the dollar price lower to remain below line B – either because of a fall in the rand price or because the rand has firmed against the dollar, or both. This happened last week.

Because of the steep gradient of the line, which takes it lower to a value of about 144 US cents by the end of March, it seems unlikely that the break would not have happened by then. Even if the break upwards through resistance at line B is delayed by some weeks, the result should be much the same as described in Scenario 2.

Unless, of course, the gold price declines to the extent that Randgold's price remains below line B, in which case the price would have to fall to below $1,50 five weeks from now. Then line B would continue to act as key resistance in a bear market for Randgold, probably until support at F6 can be tested..

Scenario 2: The break upwards through line B takes place this week or next and the dollar price extends the recent quite steep rise until it meets the next strong resistance level at line A. Line A currently has a value of $9.67 cents. Because of the down sloping gradient its value declines to about $9.02 by end March. This means that if a new bull market takes off soon and it then requires about 5 weeks for the price to reach as far as line A, resistance would come into effect at about $9,00. If the price reacts either faster or slower, the resistance level at line A would be correspondingly higher or lower by the time it is reached.

Line A is the line of inverse symmetry – it extends from the peak of the previous bull market, with the same gradient as the bull market resistance line, M, with sign reversed. When reached it should be substantial resistance. While line A holds, the long term bear market in Randgold that started with the peak at the cross-over of M and A, is still intact. Therefore, any rise in the price only as far as line A should be seen as merely a major correction in the bear market. A clear break above line A is needed to confirm the start of a completely new bull trend.

For this reason line A is seen as important for the future development of the chart – a move up to A is needed to complete the current pattern. When the new bull market takes off, the price sooner or later will find resistance at line A, depending on how fast the price increases. What happens then will be decisive for the longer term fortunes of Randgold.

Durban Deep

The daily chart of Durban Roodepoort Deep in US cents/share has a large megaphone, M-F2 as its main feature. F2 is the second shallower derivative of M. The evenly spaced shallow bull channel A-D has a gradient equal to the fourth derivative of M.

Natural megaphones – broadening formations with boundaries that can be derived from each other – are very strong formations and are not easily broken. No wonder the price here has recently turned downwards as it approached line F2 for the fifth time.

Scenario 1: The price , calculated at $2.25 for Friday, has just about reached support at line D at $2.22. A break lower through line D would be very bearish indeed and would mean either a complete collapse in the value of the rand or a steep fall in POG. Or both.

Scenario 2: The price reverses its bearish trend at support at line D – this week or next – to break higher at F2 ($2.44 at the moment). The break through the megaphone is likely to be explosive, with line C, currently at a value of at $4.59, as target. Resistance at line C, when reached, should hold for some time at least.

Dow Jones in oz of gold
Chart Symmetry offers the advantage that it can be used to determine whether there is a common link between two financial price variables. If the chart that results when two variables are appropriately combined – either by being multiplied, or by dividing one by the other – shows evidence of symmetry, then it can be argued that there is some link between the two variables. The link could be quite obvious, as in the case of Randgold where it is not surprising that the dollar price of Randgold – traded in the US through ADR's – shows strong evidence of symmetry. The gold price in yen also has symmetry, probably through the dollar-yen rate, but perhaps also because the Japanese follow and react to the yen price of gold. (This chart has broken steeply higher into a bull market!)

I think that at first glance not many people would expect a connection between the gold price and the Dow Jones Industrial Index.. It requires quite a close link between two variables to sustain the presence of preferred gradients and their fixed interrelationship over a long period of time and do so with a high degree of accuracy. Surely, one would think, US equities and gold do not have enough in common to achieve symmetry?

This chart was generated by dividing the daily closing values of the Dow Jones by the PM fix of the gold price. The master line, M, is the rising support line of the bull trend of the past 30 months during which the Dow outstripped the gold price, gaining a relative 118% on gold over the extent of the chart. Lines F1 and F2 are the first and second shallower derivatives of M and were generated from a single point on the chart, using calculated gradients.

Lines A-D are the second steeper derivatives of M. They form a similar channel to the one on the chart of Randgold, where the spacing of the lines also increased constantly. On that chart the rate of increase is a constant 40%; here the separation between the trend lines increases almost exactly according to the Fibonacci ratio, or 62%. The good fit of the chart overall and the 'ideal' spacing of lines A-D offer good proof that Chart Symmetry – a phenomenon that arises out of complex self-adjusting systems (or chaos theory) – applies to the combination of the Dow Jones and the gold price. There is a link between the two prices.

The main feature of the chart is the large rising wedge, F2-F1. Leg 3 of this wedge has just been completed (missing line F2 by only a small margin) and the Dow/gold is now on leg 4 of the wedge, which should in principle take it all the way down to line F1. This support level currently has a value of 27.7. A move to F1 can take place either because the Dow falls or because the price of gold rises, or as a combination of the two.

At a constant gold price, this move down to line F1 would require the Dow Jones to decline to below about 8000 points. On the other hand, if the Dow maintains a level of 9000 points, the gold price has to increase to $327 for F1 to be reached.

Neither development on its own would be very surprising, given today's market conditions. However, the actual changes in the Dow and in the gold price to result in a decline down to a ratio of about 27 is more likely to be a combination of a smaller fall on Wall Street and a smaller rise in the gold price. Since both developments are quite feasible, a decline to a Dow/gold value near 27 over the next few weeks appears quite likely. In fact it would be more of a surprise if a fall on Wall Street to below 9000 points and a jump in the gold price to above $300 do not set in motion sustained trends in both variables that would result in the Dow/gold ratio reaching support at line F1 to complete leg 4 of wedge F1-F2.

In about 25% of cases a wedge breaks prematurely, before leg 5 is completed. Such a premature break – which generally happens in the course of leg 4 – can take place in the direction of leg 3 or in the direction of leg 4. Here a break upwards through F2 would be very bullish for the Dow and bearish for gold. Later, after reaching support at F1, a premature break lower through F1 would be very bear for the Dow and bull for gold.

In terms of probabilities, a move lower to line F1 is the expected development. However, when such a move is complete, and if the Dow keeps on falling, with POG rising, we may well see a break below wedge F1-F2. Readers can calculate the ratio every day to follow its moves between resistance at a ratio of resistance at about 34 and support at about 28 by dividing the Dow closing value by PM gold fix out of London.

In the Aztec language the name for gold is teocuitlatl which means "excrement of the gods."
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