W.D. Gann, a successful stock and commodity trader, developed multiple technical analysis tools based on geometric angles. These were used to draw lines on charts to help identify important support and resistance areas where each angle was a division of time and price. These angles, when drawn in groups, are what make up the Gann fan, which is a useful indicator for all technical traders. Based on Gann’s geometric angles, it can be used to identify important support and resistance levels as well as measure relative performance.
Gann fan application is rooted in basic trendline analysis, which is instructive in understanding how and why the Gann fan is used. A quick review — focusing on the elements that apply to Gann’s approach to trading — will lay the foundation for a discussion about Gann fans.
Trendlines are one of the most accessible and most widely used tools in technical analysis. They typically are drawn during directional market price movement. An uptrend is drawn up and to the right as the trend continues to make higher-highs and higher-lows over time, while the downtrend is drawn down and to the right as the trend continues to make lower-highs and lower-lows over time.
The most basic definition of a trend is a typical uptrend (downtrend) will need two highs (lows) to provide evidence of a trend and three highs (lows) to confirm that the trend is valid. Another important point about trends is that the longer a trend has been intact, and the greater the number of times it has been tested (the number of times that the support or resistance levels have held after being reached), the greater the significance of the trend and the less likely that the trendline will be broken.
The average trendline will have a 45-degree slope as viewed on a typical price chart, but that slope can be steeper or flatter than 45 degrees. Because 45 degrees is the average slope of a trendline, one with a 75-degree slope, for example, will tend to revert back to the 45-degree slope over time. A slope that is greater than 45 degrees typically will not be sustainable for any significant amount of time. Conversely, a slope that is less than the average typically will accelerate (steepen) until it moves back in line with the equilibrium level of the slope.
The 45-degree angle was the most important to Gann and it is represented with a one-to-one movement of time relative to price. Whenever the price of an asset trades in an uptrend (downtrend) and it reaches a prominent top (bottom), the price typically will decline (rally) off of this high (low). W.D. Gann divided this price action into eighths, as well as thirds, and market action would be watched near these levels because of their historical significance.
According to Gann, the most important retracement levels are 50%, 37.5% and 62.5%, ranked in descending order of importance, with the rest of the levels believed to have diminishing importance the further they are from the 50% retracement (see “Retracement table,” right). Some of these retracement levels should be familiar because they are similar to those used in other schools of technical thought, such as Elliott Wave Theory. The 50% retracement is simply one of the most common retracement levels watched by chartists, and the 33% and 67% retracement levels are both used in Dow theory.
With respect to trend angle and the one-to-one relationship between time and price, it is important to think in terms of units of time, and units of price, to understand why the degree of the angle is important. Because the 45-degree angle is represented by a one-to-one relationship between price and time (that is, when time moves forward by one unit, price moves forward by one unit as well), a one-by-two relationship will be equal to 63.75 degrees and, inversely, a two-by-one relationship will be equal to 26.25 degrees, where each inverse relationship is equal to 90 degrees. The one-by-two angle means that as time moves forward by one unit, price moves forward by two units. The two-by-one angle has an inverse relationship (time moves forward by two units as price moves forward by one unit).
Thought of as a right triangle, the calculation of these triangles is easy and can be done using the two known sides (the two-by-one or the one-by-two multiplied by the price relationship) and a known angle within the right triangle (the 90-degree angle that every right triangle has).
“Gann angles” (below) shows triangles manually drawn on price charts. The first chart is a one-by-one angle so both side B (time) and side C (price) equal one unit, with angle X being equal to 45 degrees. The second chart demonstrates the same concept, and uses the same equation, except that it has a two-by-one angle and side B (time) is equal to two, side C (price) is equal to one and angle Y is equal to 26.25 degrees. The third chart has an inverse relationship — it is a one-by-two angle instead of a two-by-one angle — so side C (price) is equal to one, side B (time) is equal to two and angle Z is equal to 63.75 degrees.
In “Multi-view” (below), the triangles from each figure are combined and, to clean things up a bit, everything is removed but the trendlines. This figure is the Gann fan in its most basic form. The second chart in this graphic shows the Gann fan as drawn by technical analysis software, in this case Track ‘n Trade.
Working the angles
In the chart used for the figures, price traded below the 45-degree trendline, indicating that the current rate of change likely will increase in the future, assuming the current trend persists, so that it moves back toward the historical average rate of change.
In addition to measuring the rate of change, the Gann fan trendlines also act as support and resistance levels, and, according to W.D. Gann, when one of these trendlines is broken, the price typically will move to the next trendline. For example, looking at our Gann fan chart in “Multi-view,” if price breaks the two-by-one trendline, it likely will move down and touch the three-by-one trendline, which will become the new support trendline while the previous two-by-one support will become resistance. If the opposite occurs and the one-by-one trendline is broken, the mirror image of this condition will play out, with one-by-two becoming the new resistance level and one-by-one becoming the new support level.
The Gann fan also can be used as an indicator of relative performance (compared to the market as a whole), depending on which angle the current price is above or below. According to W.D. Gann, the 45-degree angle is the average rate of change, so variation from this historical average can be viewed as relative over-performance or under-performance. That is, if the stock price is above the one-by-one angle, then it has been outperforming the market on a relative basis; if it has been trading below the one-by-one angle, then it has been underperforming the market on a relative basis.
According to Gann, the Gann fan should be drawn from important tops and bottoms, moving from the left of the chart to the right. Also, this should be done on a one-to-one basis (that is, the area that the Gann fan covers should be square), so that the Gann fan is proportional and accurate.
Alone, the Gann fan provides reliable information, but combining it with other technical analysis tools, such as percentage retracements, also can be beneficial because the tools can be used to help confirm a signal. For example, if percentage retracements are used with the Gann fan, then horizontal lines will be drawn on the chart as well. The horizontal lines (typically the 37.5%, 50% and 62.5% retracement lines), combined with the three most common Gann fan lines (the 26.25-degree, 45-degree, and 63.75-degree), identify the center of gravity of the chart, according to Gann. If there was a 50% retracement to the 45-degree trendline, the combination of the two indicators would increase the overall significance of the support level.
Kent Kofoed is a research analyst with Gecko Software.