Gann’s Square of 9 put to the test
William Gann was a stock and commodities trader who lived around the turn of the century and employed unusual and esoteric methods for forecasting markets which sometimes involved complex mathematics, key ‘anniversary’ dates, the use of angles and Astrology.
Arguably the most important Gann method is a spiral of numbers called the Square of 9.
The Square of 9 starts with a “1” at the center and unfolds with each subsequent number added around in a square as illustrated below.
The first square of numbers around the center completes 9 digits in total thus giving the square its name.
In its simplest form the Square of 9 can be used on its own as a square root calculator for forecasting possible future support and resistance levels, and it is on this aspect that this article will focus.
If a security has made a high at, for example. 368 it may find support at 295 if it falls, because 295 is the next number across on the Square of 9 going towards the center.
The maths behind this are simple: the square root of 368 is 19.183326. From here all you do is subtract 2 and then re-square to get 295.
In order to find the next resistance level higher on the other hand you would simply operate the equation in the same way but instead of subtracting 2 from the square root you would add 2 to the square root. Using the example of 368 you would then re-square to get 449 – which is the next adjacent number on the outside of the square.
It is said that on its own, the square of 9 can be used to successfully forecast future support and resistance levels, even without recourse to complex time charts and Astrology – but how well does it work in practice?
Tested on EUR/USD
In order to assess how well square of 9 levels worked as support and resistance junctures they were tested on Eurodollar over the last 10 years. Initially Monthly data was tested but then weekly and daily data was used as well.
For the monthly experiment the Square of 9 values were calculated from the EUR/USD’s all time low at 0.8227 in 2000. The subsequent levels higher were calculated using the equation above and gave 18 levels up to 1.6054 which was close to the all-time-highs at 1.6039. The levels were as follows:
Random Control Group
In order to test the success of the Gann levels they were compared to a control group of randomly generated levels between the EUR/USD’s all-time low and high. The random levels generated were as follows:
The experiment used monthly highs and lows and cross-referenced these against the Gann levels and the Random levels. Where they fell within a 100pip band of the level they were deemed to have touched it.
Only Monthly highs or lows were used which marked a change of ‘ ‘trend’ even if the change was only for a single month’s duration. Monthly highs or lows were not included if they were part of a consecutive uninterrupted sequence of up – or down months.
The results for the last 10 years showed that from a total of 38 significant trend changes
Gann levels were touched 10 times whilst Random levels were touched 8 times.
Overall the Gann levels performed marginally better as points of support and resistance compared to random levels.
Weekly and Daily Data
Weekly and daily data were also tested. To simplify the methodology all weekly highs and lows for were used and not just those which marked a change of trend as in the monthly data. This was because it was assumed highs and lows would tend to mark support and resistance levels more often than other data points thus the data should still be valid for testing.
A further control group was also introduced which consisted of the Gann levels +100 pips. This was so as to create a control with a similar – but still different – spread to the Gann levels. This was in order to eradicate any bias the random group may have exhibited because it tended to have levels clustered in the 1.20s and 1.50s which might unduly increase the number of touches recorded.
For the weekly data touches were included that fell within a 50 pip band around the levels tested, whilst for daily data the band narrowed to 30pips.
The results from the experiments are shown below:
|Level||Touches:Weekly H/L||Touches: Daily H/L|
|Gann +100 pips||104||355|
The experiments show that there is little evidence to suggest that prices respect Gann levels generated by the Square of 9 more than any other levels. The monthly data showed that price bounced off Gann levels 10 times vs 8 times for random levels – more but nevertheless an insufficient margin of difference to determine a bias.
If Gann levels had strong support and resistance qualities then they would be expected to contribute to making weekly and daily highs and lows given these tend to reflect stronger areas of support and resistance. In tests to verify this, however, the random level actually tended to coincide with price high and lows more often (152 and 412 vs 105 and 338) than the Gann levels – showing that a randomly generated set of levels actually may have predicted the spot of weekly and daily highs and lows better than the Gann levels on their own.
In addition when compared to Gann levels plus 100 pips the data showed that Gann levels were not substantially better at marking highs and lows with only 1 touch more than the Gann +100 level on the weekly and actually less touches (338 vs 355) for the daily data.
Whilst these experiments were by no means definitive they didn’t appear to show that Gann levels on their own work particularly well at marking highs and lows and only worked slightly better at marking major highs and lows in monthly data than random or derivative levels.