Understanding W.D. Gann's Price Square
Spiral of Prices Used to Forecast Market Reversals
Mar 22, 2009
The extremely successful market trader, W.D. Gann analyzed financial markets of commodities and stocks in both price and time to formulate his market analysis techniques and forecasting philosophies.
Gann recognized that certain mathematical series and sets of numbers were independently relevant to locating price support and resistance from a historical low or high. The analysis would be enhanced if the price spiral could be superimposed by the cycle of time.
The following description is restricted to the workings of Gann's price square as a tool to identify market reversals. It is therefore a part of Gann's overall analysis methodology.
The Price Spiral
The price spiral appears in Gann’s visual graphs and tables, from which he derived potential price turning points. There were two aspects to these tables:
- The historical low of a stock price, a point of major psychological significance.
- The relationship of subsequent price levels to the historical low. These would be mathematically related.
The Price Square
The lowest historical price would be placed in the middle square of a piece of graph paper. The next price, measured in whole units, would be placed one square to the right, and the next price would be placed one square down. The process would be repeated, circling clockwise, until a full square was complete.
Figure 1 shows such a square (using unity as the lowest price). The next stage of the process was to draw diagonal lines dividing the whole square into quarters and eighths. Gann regarded any prices falling along the dividing lines as potential reversal points.
Problems with the Price Square
Close inspection of the square reveals the presence of Fibonacci numbers on the dividing lines. The first eight numbers in the summation series, shown in brackets, are:
(1), (2), (3), 4, (5), 6, 7, (8), 9, 11, (13), 15, 17, 19, (21), 23, 25, 31, (34)
The next Fibonacci number is 55 and it just misses a line. Hence, while the square would pick up Fibonacci reversals at lower price levels, it would not necessarily pick them up at higher price levels. Moreover, the observer would not easily tell the presence of the Fibonacci sequence.
Natural Number Series
Gann found that price reversals were likely to occur after prices had moved by certain amounts. Often, these levels would be mathematically related to a common number, one that might be the lowest low, and this could be used as the base number in the square.
Explicit numbers were based on “natural” number series, four of which were considered to be important:
- Squaring each numbers from 1 to 12. That is, 4, 9, 16, 25, …, 144
- Doubling sequence: 2, 4, 8, 16, 32, etc.
- Trebling sequence: 1, 3, 9, 27, 81, etc.
- The Fibonacci sequence: 1, 2, 3, 5, 8, 13, 21, etc.
In addition to number series, Gann emphasized four specific families of ratios. These are based on fifths (1/5, 2/5, 3/5, 4/5), sevenths (1/7, 2/7, ...6/7), eighths (1/8, 1/4, 3/8 ...7/8), and twelfths (1/12, 1/6, 1/4, ...3/4).
The Rule of Three for Market Reversals
According to Gann, a price level was more likely to be a turning point if the price was the calculated outcome of at least three complementary measurements. For example, the coincidence of three Fibonacci numbers at the same price level would indicate a more probable potential turning point.
The Gann Square can determine significant support and resistance levels on a chart. Gann's additional approach was to use time constraints over the price square, either relating to the price square or independent of it.
References:
- “Forecasting Financial Markets – Technical Analysis and the Dynamics of Price”, Tony Plummer. John Wiley & Sons. London. 1991
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