The Arc Principle is a discovery that reveals that all freely traded markets are governed by a hidden order based on the geometry of the circle or “arc”, which expands and contracts based on the Fibonacci ratio. The discovery allows us to use these Arcs in a manner that goes far beyond what has been heretofore reported by others.
In this article, we’ll introduce the discovery of the Arc Principle, where we will begin with the known and move toward the unknown. Gann Angles and the Elliott Wave Principle, taught by W.D. Gann and R.N. Elliott, respectively, are well known to many traders. These trading approaches will be used to demonstrate how the Arc Principle can enhance one’s ability to analyze and trade the markets.
For many traders and investors, the discoveries of Gann and Elliott are beyond reproach. And yet, the Arc Principle shows that Gann did not know everything there was to know about Gann Angles, and Elliott did not know everything there was to know about Elliott Waves. Behind every Gann Angle is an Arc pinpointing the turning point. Behind every completed Elliott Wave is an Arc confirming the wave count.
While the essence of the Arc Principle is simple, the underlying geometry sometimes is not. The patterns are layered and complex. A wealth of new trading techniques flow from this basic discovery. The Arc Principle can be used as a stand-alone forecasting method or used in conjunction with other forms of analysis (see “A picture is worth…”).
There are a number of things to observe on the chart of Halliburton (HAL).
- First, note the blue-shaded turning points. They have been marked with a 1-5 wave count to exemplify how an Elliott Wave analyst might label the impulse wave. Whether this is a correct count or not is not material at this juncture. Just observe that the move ended at the point labeled “Wave 5.” It is a basic tenet of Elliott Wave Theory to look for a significant retracement to commence at the end of Wave 5.
- Next, observe the gold-colored angle lines. They represent a Gann Fan made up of Gann Angles. The lowest angle line intersects the 2008 low, setting off a massive bullish move.
- The primary circle is centered at the 2001 low, with its radius extending to the 2008 high. The radii of the two interior circles are based on the Fibonacci ratio, at 38.2% and 61.8% of the radius of the large circle.
- If you follow the circumference of the smallest circle back in time as far as it goes, it marks the time of the turquoise-shaded 1997 high, shown by a dotted red vertical line.
- Finally, if you follow the circumference of the middle circle forward in time as far as it goes, it marks the time of the gold-shaded 2008 low, shown by a dotted red vertical line. This is the same 2008 low that is intersected by the Gann Angle.
What you have just observed is the “Circle-Back” rule, which aims to determine if a swing is complete and primed for a reversal, and the “Circle-Forward” rule, which aims to identify the next major turning point. You have also observed a Gann Angle turning point that has been confirmed by an Arc centered at the apex of that Gann Angle. The radius of that Arc is the length of the swing from the apex at the end of 2001 to the high in 2008. Note that we are presenting broad principles here. More detail needs to be explained before they can be consistently relied upon in actual trading conditions.
The missing link
The Arc Principle brings the Fibonacci ratio to the methods of Gann and the squaring of price and time to Elliott’s Wave Principle. Neither Gann nor Elliott was aware that Fibonacci Arcs lay at the heart of the markets. In this sense, Arcs are a missing link between the discoveries of Gann and Elliott. A new, more complete picture of each man’s discoveries depends on understanding this link. In fact, both Gann and Elliott might have glimpsed this secret had they incorporated the work of the other.
Elliott deserves credit for recognizing the existence of Fibonacci relationships between waves in the market. But he did not go further. As long as he ignored the insight of Gann — that price must be “squared” with time on a properly scaled chart — it would not be possible for him to discover the circular mapping of market swings. The possibility of discovering this was even further removed when dealing with long-term charts, for then Elliott applied a logarithmic scale, and the circular geometry disappears under such conditions.
Some researchers have sought a link between Gann and Elliott by arguing that Gann’s division of his squares by eighths is very close to the Fibonacci ratio, since 5/8 is nearly equivalent to 0.618. This seems like a rationalization. The fact is that Gann failed to incorporate the Fibonacci ratio into his own work. Tony Plummer, in “The Law of Vibration: the Revelation of William D. Gann,” makes the case that Gann was aware of the significance of the Fibonacci ratio. While this is a viable theory, there is no definitive proof of this.
In order to discover the Arc Principle, it would not have been enough for Gann to start experimenting with the Fibonacci ratio, nor for Elliott to start squaring price and time. They both would have had to further envision the swings in the markets as radii of a circle.
It is safe to say that neither man did so. If Gann worked with Fibonacci Arcs at all, there would have been some hint of this in the voluminous notes and charts he left to posterity. The same holds true for Elliott. If Elliott experimented with Arcs, this too would likely have come to light.
The unseen architecture of markets
Fibonacci Arcs govern virtually every swing in the market. Not a move takes place without them, from the smallest scale to the largest. These Arcs underlie the methods of both Gann and Elliott in specific ways. Most, if not all true Gann squarings of price and time have a geometrically meaningful Arc centered at the starting point, such as the apex of a Gann angle. Similarly, a completed wave in an Elliott Wave sequence will be anchored by an Arc that circles back from the start of that wave to a prior significant turning point. It is the confluence of this unseen architecture with known Gann or Elliott principles that validates the old masters’ theories. Here, “validate” means that the Arc Principle proves that their theories were true; that the inherent order claimed to exist by Gann and Elliott was real, not imagined. For if it was not real, Arcs would not consistently confirm the methods of Gann and Elliott, in precise, repeatable ways.
“Squaring of price and time” shows the Dow Jones Industrial Average during the first half of the 20th century, overlaid with a Gann Angle in gold and a Fibonacci Arc. The radius of the largest blue circle, or “Arc,” is derived by taking the smallest Arc as 100% of the radius, multiplied by the Fibonacci ratio three times (100% x 1.618 x 1.618 x 1.618 = 423.5%).
If you follow the circumference of the largest blue circle forward in time as far as it goes, it intersects the dotted red line at the time of the final 1929 high. If you follow the circumference to its highest point, it matches the price of the market at the 1929 high. There is also the 1 x 1 Gann Angle extending from the high in 1906 through the 1929 top.
The large blue arc and the Gann Angle are actually different ways to express the same squaring of price and time, which is at the core of Gann’s discoveries. However, the radius of that blue Arc was derived from the market swing extending from the 1903 low to the 1906 high. This swing served as the radius of the smallest circle, which in turn determined the radius of the largest by multiplying the smallest radius by the Fibonacci ratio. The confluence of Arc and Gann Angle at the 1929 peak are two parts of one complex geometric whole. This relationship between Arc and Angle is the norm whenever a Gann Angle precisely identifies a major turning point. (The lowest Gann Angle also hits the 1937 high and is matched by a different Arc based on advanced Arc principles.)
“The Arc Principle and Elliott,” shows the same chart of the Dow, only this time the Arc is centered on the 1921 low with radius extending to the 1929 high. We do not draw a specific Wave count, so you will have to imagine how an Elliott Wave analyst would have counted the highs and lows from 1921 to 1929. But there can be no doubt that the move from 1921 to 1929 would be considered an “impulse wave” under Wave Theory, and that counting the subwaves leading up to the high would have as its aim to predict when the trend would complete itself.
Focusing on the Arc, if you follow the circumference of the 23.6% and 61.8% circles (the 1st and 3rd circles in terms of size) of the swing from 1921 to 1929 back in time as far as they go, they mark both the 1914 low and the 1903 low. This is not an isolated occurrence. Virtually every completed Elliott wave on any chart circles back to at least one prominent prior turning point.
But that is not all. If you follow the circumference of the second smallest Arc (38.2%) forward in time as far as it will go, it corresponds exactly to the time the crash ended in 1932. All of the most important turning points in the first third of the 20th Century are encompassed in this one Arc structure. This may be the most prominent example of perfect order in markets, which has gone unnoticed for more than a century.
The Arc Principle is just as relevant in today’s markets as it was 100 years ago. In the second of this series of articles, we will further our introduction to the Arc Principle and present what Elliott did not know about Elliott Wave Theory.
Solving the problems of Gann Analysis
W.D. Gann discovered a new way of forecasting the markets. This month, we focus more on their practical use and discuss how he used them to construct annual forecasts, among other applications.
One of the challenges with early Gann is that he was never forthcoming about his strategies. Indeed, in 1909, Gann clearly stated that he would not disclose his actual forecasting method. However, that doesn’t mean he wasn’t helpful to those who wanted to learn. The evidence overwhelmingly suggests that Gann also had a strong desire to help others in their trading activities.
Gann’s early attempts to reconcile these two conflicting goals included the publication of a daily letter that advised on when to buy and sell stocks, cotton, and wheat (advertised in The New York Herald between April and November 1909). In 1910, he published a booklet titled “Speculation a Profitable Profession: A Course of Instruction on Stocks,” and in 1911, Gann sold a mechanical method, based on fixed rules, for trading in stocks and commodities (see The [New York] Sun, Tuesday, Dec. 19, 1911, page 10).
In 1918, Gann published his first annual forecast, which was his latest means of helping his clients in their trading activities, but without disclosing his actual forecasting method. Gann published this forecast for the stock market for 1919 on Dec. 16, 1918. It included a short textual commentary.
However, Gann’s annual stock market forecast for 1922 included, for the first time, a chart that forecasted the trend of industrial stocks and a separate chart that forecasted the trend of railroad stocks. Also for 1922, Gann produced (apparently for the first time) an annual forecast for cotton and for grains, both of which included commentary and a chart. Gann stated that his grain forecast was “Made up principally for wheat, although corn should follow it very closely (see “Forecasting grains”).
Gann subsequently added additional commodities to his service, and he continued producing annual forecasts for the rest of his life. Then in 1923, he wrote the first of seven books, titled “Truth of the Stock Tape,” and he continued producing courses on trading the stock and commodity markets. Overall, the evidence suggests that from 1909 until his death in 1955, Gann pursued in his professional activities two conflicting goals: Helping others become better traders and keeping his actual forecasting method secret—a model often duplicated.
Annual forecasting challenges
Gann’s method of forecasting the financial markets was based on correctly identifying the underlying cycles that are driving a particular stock or commodity and then analyzing the resultant rate of vibration— as measured by the slope of the trendline —to precisely forecast prices at a future point in time.
Gann’s practical application of his forecasting method shortly after he completed its discovery in 1908 was examined last month in the context of his forecast of the Chicago September 1909 wheat contract. Gann’s forecasting and trading in stocks in 1908 and 1909 followed a similar structure as noted by Richard Wyckoff.
Thus, Gann’s initial application of his forecasting method was to forecast when and at what price an existing and established trend in a particular stock or commodity would end. However, the key problem that Gann encountered some 10 years later, when he started producing annual forecasts, is that they are significantly more complex than his initial application.
With an annual forecast, the prognosticator is not only required to forecast when—and at what price—the current trend will end, but when and at what price all subsequent trends over the next calendar year will end. Thus, the construction of an annual forecast requires a series of forecasts for a particular period, and each of these periods must have an accurate identification of the cycles that will drive a particular stock or commodity, as well as the resultant rate of vibration.
Forecasting cycles of time
Gann started producing annual forecasts 10 years after he discovered his forecasting method. Therefore, he was well aware of the problems of forecasting time cycles. However, in constructing his annual forecasts, Gann devised a number of solutions to the problem of accurately forecasting time cycles.
One technique is that he would simply delay the publication of the annual forecast. For example, although the chart in “Forecasting grains” begins on Dec. 27, 1921, it was published on Jan. 31, 1922. It appears that Gann delayed publication because he was unsure whether, in January 1922, strongly positive cycles would start a strong uptrend or whether strongly negative cycles would start a strong downtrend. Therefore, Gann delayed publication until he observed that wheat had made a significant low on Jan. 16 and then established a stable uptrend. Similarly, it may be noted that Gann delayed the publication of his annual forecast for cotton until April 25, 1922, which was thereby reduced to an eight-month time frame.
Another technique that Gann employed was to make a contingent forecast. In his commentary included in his 1922 annual grain forecast, Gann stated, “If May wheat sells at 1.08 after Jan. 25, it will indicate much lower prices and probably a decline to around 95¢ to 92¢ per bushel.” In this statement, Gann was warning that if the price of the May 1922 Chicago wheat futures contract fell back to its January 1922 low ($1.08 per bushel), strongly negative cycles would be in force, and consequently, the strong downtrend would continue.
Another technique that Gann employed was to forecast a change in trend over several days. From “Forecasting grains,” it can be seen that Gann typically forecasted that a change in trend would occur over several days. For example, Gann forecasted that on May 7-10, 1922, wheat would make its high price for the year and then start a downtrend. This technique reflects the multiple nature of the underlying cycles. More specifically, in this instance, Gann was forecasting that on May 7, negative cycles would start to influence, but they may be insufficiently strong to overpower the previous positive cycles until May 10, 1922, by which date at the latest the downtrend would begin.
Another technique that Gann employed (which was perhaps his most important) was to publish regular updates to the annual forecast. At the end of his annual forecast for grain for 1922, Gann stated that a supplement would be mailed to subscribers each month, “giving any changes that are indicated, if the market is not following closely the trend as outlined.” Gann published regular updates to all of his annual forecasts. Although he marketed, produced, and sold annual forecasts (which are inherently complex), by producing regular updates, Gann was in fact converting his annual forecasts into the more simple, accurate, and reliable type of forecasts that he had previously produced between 1908 and 1918. These focused on when and at what price an existing and established trend in a particular stock or commodity would end.
Forecasting the rate of vibration
In addition to a series of smaller forecasts and accurate cycle identification, an annual forecast also requires a prediction of the resultant rate of vibration, or the slope of the trendline.
To assist in forecasting the rate of vibration, Gann produced a template or chart overlay (see “Degrees of vibration”). It is likely that this was originally drawn up on tracing paper and later on transparent plastic.
First and most important, when constructing an annual forecast, Gann identified the cycles (positive or negative) that would drive the stock or commodity for a particular period in the next calendar year. Moreover, it is also necessary to forecast the likely strength of those cycles.
For that section of his annual forecast, Gann then drew a trendline that best represented the underlying cycles driving the particular stock or commodity. If Gann forecasted that positive cycles would be in force during that period, then the trendline would slope upward. The greater the strength of the underlying cycles, the steeper the slope of the resultant trendline. The slope of this initial trendline is the initial rate of vibration that Gann forecasted for that particular period.
Gann then used the template depicted in “Degrees of vibration” to forecast changes in the initial rate of vibration. Gann placed the origin of the template over the start of the initial trendline and rotated it until the 1 x 1 line was over this initial trendline. From the 2 x 1 line on the template, Gann could then see when the rate of vibration of the initial trendline had halved (or from the 1 x 2 line when the rate of vibration had doubled).
Gann had discovered that when the rate of vibration halves, it constitutes significant price support and, conversely, when the rate of vibration doubles, it constitutes significant price resistance. Thus, by means of his template, in the construction of an annual forecast, Gann was able to integrate his forecast of the underlying cycles with his forecast of the rate of vibration as well as changes in that rate of vibration.
“Forecast breakdown” illustrates this process. This is Gann’s annual forecast for 1922 for grains, but with the addition of the trendlines that Gann would have drawn in its construction with the aid of his template. For example, Gann forecasted strongly positive underlying cycles and therefore a strong upward trend between Jan. 16 and Feb. 20.
However, Gann then forecasted negative cycles between Feb. 20 and Feb. 22-25, the effect of which would be to precisely halve the previous rate of vibration. Gann forecasted that this halving in the rate of vibration would provide strong support, and prices would then rally until March 10-12. At this point in time, negative cycles would once more come into force, which Gann forecasted would cause prices to fall until April 3-6, at which time positive cycles would once more come into play.
Thus, from “Forecast breakdown,” left, we can see that in constructing his annual grains forecast for 1922, Gann in fact made a series of forecasts. More specifically, he forecasted positive cycles producing an uptrend from Jan. 16, negative cycles producing a downtrend from Feb. 20, positive cycles from April 3-6, negative cycles from May 7-10, positive cycles from Aug. 15-17, and finally, negative cycles from Oct. 16-19 to Dec. 31, 1922.
This annual forecast includes three periods of positive cycles, or uptrends, and three periods of negative cycles, or downtrends. Clearly, this is significantly more complex and prone to error than Gann’s initial application of his forecasting method.
The next 100 years
Now that Gann’s forecasting method has been rediscovered, the next goal is its effective and efficient application to the financial markets of the 21st century. Indeed, future research will examine how to best apply Gann’s forecasting method to all the major financial markets.
With regard to its effectiveness, in 1923, Gann suggested that his forecasting method had performed well during the 15 years since its discovery: “The fact that my method of forecasting has stood the test of time is sufficient proof that I have solved the problem.”
An assessment in modern times suggests that Gann’s forecasting method performs well when applied to a number of current markets, especially if they are active.
The prima facie evidence suggests that Gann’s forecasting method is effective. It is no surprise that his techniques remain of considerable interest to investors, particularly those looking for a scientifically based forecasting system applicable to the most active markets and financial instruments.
