February 2001

"We know that the moon's effect on our planet is great--it is vitally connected with the movement of all fluids.  The moon is also believed to effect human behavior in strange ways, especially during a new or full moon.

"In an experiment conducted on an arbitrary set of commodities for the year 1972 (Todd Lofton, July 1974, writes about his observations) it was shown that short-term movements of prices react with some uniformity with respect to the phases of the moon.  In fact, the commodities chosen for observation--silver, wheat, cattle, cocoa, and sugar--showed an uncanny ability to form a rising market following a full moon and a falling market after a new moon."  -Commodity Trading Systems and Methods, P.J. Kaufman, p. 205.

That last statement, "a rising market following a full moon and a falling market after a new moon", intrigues me.  I wondered whether it is true or false, of value or worthless nonsense.  Fourteen years ago as I would travel back and forth between Boise, Idaho, and Salt Lake City, Utah, one of my customers lived near the highway at the half way point of the trip.  Several times I stopped in and visited with him.   He owned several large farms in southern Idaho and traded sizeable positions in live cattle futures.  His office had large custom made chart tables where his secretary would manually update daily bar charts on three feet by four feet graph paper.  The reason I mention this customer is because his charts were marked with symbols for the moon phases.  I have great respect for this trader because he has been trading for a long time, trades big positions, and takes trading seriously.  I wish now I had paid more attention to how he used the moon phases that he marked on his charts.

Anyway, I can't do research unless I have tools to work with.  So, moon phases were added to the Cycles tool in Ensign Windows.  The moon phase parameter is simply a check box to indicate the moon symbols are to be shown on the chart.

The first two Show options are used to display cycle arcs on the chart.  For this research, I am only interested in having Moon Phases shown on the chart.  I selected a dark gray color for the new moon image.  Full moons will always be shown in white.  I did not go hunt down the perfect example.  I am simply using a current daily Feb Live Cattle chart as my example since cattle was mentioned in the Kaufman book, and my customer puts moon phases on his manually drawn cattle charts.  Here is the LC1G cattle chart showing moon phase symbols.  (Some moon phases occur on weekends and holidays.  In that case, the moon symbol is shown on the nearest trading date.)

Cattle have been in a strong up trend since their $70.050 low on September 13th, 2000, which happens to be a Full Moon date!  This low turning point is not shown in the example.

Let's rate the correlation in the chart for the week following the new moons and the full moons.  I will include the net change of the moon day as the first of 6 trading days.   The theory is "a rising market following a full moon and a falling market after a new moon".  So, how well does this cattle chart correlate with the theory?

Full Moons (expect rising market)

• Nov 10th, 2000.  Excellent  - This day was a low turning point followed by a $1.325 gain.

• Dec 11th, 2000.  Excellent - This day was followed by a $1.15 gain in 6 days.

• Jan 9th, 2001.  Superior - This day was a low turning point.  The huge 6-day gain is $4.025.

New Moons (expect falling market)

• Oct 27th, 2000.  Poor - Not too bad until the strong up day on Nov 3rd for an up move of $0.825.

• Nov 24th, 2000. Excellent - Rare correction in this strong up trend.  Down move was $1.225.

• Dec 26th, 2000.  Good - Down move in 6 days is $0.425.  However, better down move followed.

• Jan 23rd, 2001.  Excellent - 6 day down move is $2.45.  The Jan 30th close, not shown, was $77.625.

I would give the theory pretty high marks for correlation on the current LC1G chart.  The low turning points on the full moon dates of Nov 10th and Jan 9th jump out.  The high turning point on the new moon date of Nov 24th jumps out.  The correlation of the other new and full moons is pretty good as well.  And to top it off, the annual low occurred on a full moon on September 13th, 2000!  My personal conclusion is that there is value in the theory that the moon influences human behavior.

Tip:   Pay attention to the phase of the moon.

As a result of this research, my brother has added the moon phase as another input to his personal cattle market neural net forecasts.  You are encouraged to do you own research and arrive at your own conclusions.  The material presented here has been limited to the examination of one cattle chart for seven recent moon phase dates.  Thorough research should involve evaluating lots of charts and lots of moon dates.

William Dunnigan did extensive research in the early 1950's and published in 1954 and 1955.  He used the square root theory as part of his calculation of a profit objective.  He considered this method a 'golden' key and received recognition for his work in various journals.  The square root theory is that prices move in units of the square root, meaning prices at $64 (8 squared) would move to $49 (7 squared) or to $81 (9 squared).   The forecast price is one point up or down, based on the square root.  The theory says a price may move to a level that is a multiple of the square root.

Since LC1G was used as an illustration in the first article, I thought you might be interested to see the square root theory applied to the cattle chart.   Nothing is a better teacher of a principle than an example.

Let's forecast a price based on the Sept 13th low of $70.050.  The first step is to normalize the price to the range of 100 to 1000 by adjusting the decimal point.  Find the square root of the normalized value, add 1 point or a multiple number of points, and square this value to obtain the forecast price.

1)  Normalize 70050 to be 700.50
2)  Square root of 700.50 is 26.467
2)  Adding 1 gives a value of 27.467
3)  27.467 squared is 754.43, which is the midpoint of the up move in the middle of November.
4)  Adding 2 gives a value of 28.467
5)  28.467 squared is 810.37.   So 81037 is a forecast price.   The Jan 16th high was 81075!!!!

Now, is it just a coincidence that a major high is within 4 cents of a price calculated from a major low price?   Or, does that make you want to look for this principle in other charts?

Tip:  A price may move to a level that is a multiple of the square root.

As I studied the LC1G daily chart some more, I see that there is a significant high of $75.500 on Jan 7th, 2000 (not shown in the chart above.  However, Jan 7th is shown in the next chart).  It can be used to forecast the Sept 13th low as follows.

1)  Normalize 75500 to be 755.00
2)  Square root of 700.50 is 27.477
2)  Subtract 1 gives a value of 26.477
3)  26.477 squared is 70105.   So 70105 is a forecast price.   The Sept 13th low was 70050, or just a 5 cent difference!

I did not start out writing this issue with the intent of focusing so much on the cattle chart.  But I just have to show you the results of the next thing I looked at.  Since the square root theory was uncanny in forecasting both the annual low and the annual high of the LC1G contract, I decided to place a Gann Square on the chart with the vertical midpoint on the Jan 7th, 2000, high.   The square was placed with the left edge on Jan 7th, and stretched so the horizontal midpoint aligned with the Sept 13th low.   The bottom of the square was placed on the Sept 13th low.  Those were my decisions for placement of the square.   This is the image I obtained.  I'm sorry the image has to be so small to fit in the newsletter.

Measure Time

I placed the left edge on Jan 7th, 2000, and stretched the square so the horizontal midpoint would align with the Sept 13th, 2000, low.   What I find interesting is that the Jan 16th, 2001, high is aligned with the 3/4 point of the square!  This time is marked by the red arrow above the square pointing to the highest high on the chart.

I also noticed  that Jan 6th, 2000, was a New Moon!  And, my first article pointed out that Sept 13th was a Full Moon.

Price Support and Resistance

I marked the chart with arrows where I want you to observe the support or resistance provided by the fan lines that extend from the 4 corners of the square.  Uncanny!  It leads one to conclude that there is a mathematical basis for price movement.  Price movement is not purely random.

Reverse Engineering

The application of the Gann square looks great in hindsight.  But I want to be empowered with principles that would have enabled me to apply the square back in Feb 2000 as insightfully as can now be done.  The Jan 7th, 2000, high of $75.500 is known.  One point up and one point down price forecasts can be made as illustrated in the previous article to use as left side top and bottom corner points aligned with Jan 7th.   A one point up forecast price from $75.50 is $81.10.   A one point down forecast price from $75.50 is $70.10.  All of that can be done in Feb 2000.

The final piece of information needed is a way to calculate in advance the width of the square.  Let's go fishing for clues by reverse engineering the present Gann square application.  There are 250 calendar days between Jan 7th and Sept 13th which can be computed using this ESPL script:

begin
  writeln(encodedate(2000,09,13)-encodedate(2000,01,07));
end;