Gann Retracements, Angles, and Fan Lines

By Dr. Winton Felt

In general, the more important up-trendlines advance on an upward slope of about 45 degrees.  The 45-degree line was extremely important in the analysis of W.D. Gann.  He considered it to reflect a situation where prices advance or decline at such a rate that time and price are in perfect balance.  If a trendline gets much steeper than this, prices are probably advancing at an unsustainable rate.  Time and price are not in balance.  If price advances too slowly, the trend is considered untrustworthy.  Again, it may not be sustained.  There is a good deal of latitude on either side of the 45 degree line but when the angle of ascent or decline is extreme either way (greater that 60% or less than 30%) be especially careful.  At one extreme, the stock will not be of interest to the trader.  At the other extreme, risk is high.  W.D. Gann developed some well-defined concepts regarding trends and retracements.. 

Gann looked at stock retracement action in terms of eighths (1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8, and 8/8).  He also looked at price movement in thirds (1/3 and 2/3).  If we convert these fractions to percentages and then place them in a sequence from the smallest to the greatest percentage, we have 12.5%, 25%, 33%, 37.5%, 50%, 62.5%, 67%, 75%, 87.5%, and 100%.  The most important of these are in the middle range from 33% to 67% with 50% being the most important to Gann.  These middle percentages also match well with Fibonacci retracement levels. 

To do justice to Gann's thinking about trendlines, the chart on which the lines are plotted should have an arithmetic price scale, and the size of the price increments should match the size of the time increments (the x- and y-axes must have equally spaced intervals).  Gann identified nine significant trendline angles.   For Gann, the ideal balance between time and price exists when the price increments of a stock match the time increments.  That is, when the price of a security rises or falls at a 45 degree angle (for each time unit, the price rises one price unit). 

Gann angles are set at 82.5, 75, 71.25, 63.75, 45, 26.25, 18.75, 15, and 7.5 degrees.  Lines are drawn at these angles from important tops or bottoms.  Traders at stockdisciplines.com have used Gann lines to look for potential support or resistance.  That is, when a line is penetrated, the assumption is that there will be resistance at the next line (when the stock is rising).  Once it penetrates a line, that line is expected to provide support on any decline.  In other words, the price action of a security is expected to reverse direction at a Gann angle.  The Gann fan lines alternate in their function between acting as support and resistance as the price of the stock transits the line.  Therefore, in an uptrend, when a stock is above the 45-degree line, that line offers support.  If the stock falls below that line, a reversal is signaled and the stock is expected to fall to the next line of support.  Channel lines can be constructed from major highs or lows parallel to the basic 45-degree line.  If the stock declines through the basic 45-degree line, the next line of support would be constructed at a 26.25-degree angle.  The breaking of a supporting line during an uptrend suggests that the price will continue to decline to the next lower line.  The penetration of a resistance line during a downtrend suggests that the price will continue to rise to the next higher line of resistance.