What Gann's Square-of-9 means for the Nasdaq 100

August 16, 2013 01:35 PM
Does this portend a change of direction for the Nasdaq?

The complementary relationship between Ralph Nelson Elliott’s Wave Principle and the Gann Square-of-9 proposes an imminent trend reversal of the Nasdaq 100 Index. Though two different predictive tools, natural laws link them to the spiral of the Milky Way. 

What Elliott wave shows

Elliott’s Wave Principle comprises of a repetitive eight-wave pattern that dominates the phases of bull and bear markets. It focuses on the mass psychology of participants as they swing from pessimism to optimism and back. Five waves of advance dominate the market’s buoyancy stages, whereas the shorter despondency phase is governed by the three remaining swings (Figure 1, below). This ever changing investor psychology is reflected in the financial markets’ daily records in the form of price movements, volumes of trades and investor sentiment indices. Upon establishing the location of a stock, or Index, within the Elliott cycle, the pattern tracks its transition from evolution to progression to decay. “Man is subject to the laws of physics and chemistry that govern biological processes on earth, and that these laws are determined by the orbits of the planets. Our physical brain follows the laws of science in determining human actions and not some agency that exists outside those laws” write Stephen Hawking and Leonard Mlodinov in The Grand Design  published in 2010.

As the cycle begins to unfold, Waves I, III and V of the bull phase form long impulses corrected by the short retracements of waves II and IV. As a rule, corrective wave II does not fall below Wave’s I trough, and Wave IV does not fall below Wave’s I peak. Likewise, no corrective bull or bear market wave exceeds the span of its adjacent impulse swing. Impulse Waves I, III, V. A  and C have longer durations than their corrective counterparts (see Figure 2 “Unlocking the secrets of Gann: Will the market crash in August?futuresmag.com)

As the market changes direction, the pattern reverses. Downward trending waves A and C turn long, while upward Wave B ─ the only upswing of the bear market, turns short.

When corrective Wave II unfolds in a complex sideway pattern, of three lesser degree swings, corrective Wave IV manifests a sharp steep decline which typically brings down Waves’ I and III advance of by 50%. Elliott refers to the relation of corrective Wave II style to Wave IV style as “alternation of form” given often Wave II manifests a sharp decline and Wave IV zigzags sideways. Above all, the pattern demonstrates that the up and down swings of the cycle adhere to the boundaries of a spiral. As the market moves up and down, its peaks and troughs correspond to the Golden Mean 0.618 and 0.382% proportions (also known as Fibonacci), and their derivatives 14.6 ─ 23.6 ─ 50 ─ 76.4 and 85.4% (Figures 1 & 2).

Metaphorically, the ‘Wave Principle’ is a road map for the analyst to negotiate the market’s alleys, streets and freeways. Once the market’s position within the pattern is clear, then the way ahead shows the direction of the next swing. The Nasdaq 100 Index at present is at the cusp of bear market Wave ‘B’.


Figure 1 – Elliott’s cyclic model of five-wave advance and an A-B-C decline which subdivides into lesser degree  cycles, the smaller of which these constitutes 144 swings.


Figure 2 - Elliott’s cyclical expansion and contraction model adheres to a logarithmic spiral. 

Ancient use of Gann's Square -of-9 play out?

Next to the zodiac, the Square-of-9 was the world’s first measuring instrument. In ancient times, it tracked and forecasted the spans of seasonal inundations. For over 3,000 years, two adjacent time intervals, aligned on a Square, projected the behaviour of Babylon’s and Egypt’s rivers. A series of longer than usual flood-spans signalled a catastrophic swell, whereas abnormally short intervals spelled drought. The great 40 days and 40 nights flood related in the Genesis legend of Noah is almost certainly an allusion to the Square, given that Noah embarked upon building the Ark well ahead of the flood. 

The scientific transition from the 19th century to the 20th century was, by and large, dominated by Einstein, who sought to reconcile theory and experiment by unifying natural processes under one universal law. His Special Relativity Theory was a hot topic of discussion at the very time that Gann was on his quest to unravel the Holy Grail of markets. Gann was counting, measuring, and practising with hexagons and Squares of 6, 9 and 12 to identify the optimal geometrical swing/time relation at the instance equity changes its course. Yet, none of his records show any reference to Einstein and Elliott, the first famous the Relativity Theory, and the latter for his study of growth and decay cycles of the American stock market. Elliott’s book Nature's Law - The Secret of the Universe appeared in 1937.

Ellioticians and Gann analysts, who traditionally rely on equity values to project markets’ trends, need to be aware that this article focuses on interval duration rather than price ranges. This is because coordinate X of time progresses steadily forward and is void of coordinate’s Y volatility. Price (Y) is an integral function of time (X), as is time of price. Likewise, the terms ‘short’ and ‘long’ in this article refer to spans rather than to ‘buy long’ and ‘sell short’ orders.

Given that the Elliott pattern unfolds over various phases of the economy, each phase is dominated by different economic fundamentals. Each therefore becomes subject to its own, and often complex, rules. Wave I forms the cycle’s visionary phase as it emerges from the doldrums of a preceding bear market. The breadth of Wave III demonstrates a lengthy expansion and growth, whereas decadence and decay accompanied by skyrocketing stock values distinguish the final stages of Wave V. The bear market’s ‘A-B-C’ correction is the cycle’s vacuum cleaner. As it drags equity values back to realistic levels, it roots out corruption and restores transparency and trust. The final stages of bear market’s Wave C pave the way for visionary Wave I of a new cycle to emerge.    

The Nasdaq’s advance from its 1985 low to the 2000 dotcom peak corresponds with Elliott’s definition of bull market Wave V. After 15 years of uninterrupted growth, heavily overpriced dotcom stocks plummeted almost to the levels from which they took off. 

The 2000 – 2003 Wave A’s decline was the first leg of an ‘A-B-C’ bear market, still underway. Wave B, now in its topping stages, has dominated the advance of 2003 -2013. Bear market Wave C is due next (Figure 3). 

Bull market Wave V, which measured 5442 calendar days (cd), and the corrective 902cd Wave A that followed, culminated approximately at the 6.18% Golden Mean ratio (5442 /902cd =6.03 ~ 6.18). Likewise, the 5442cd span of Wave V, and the combined Waves ‘A - B’ 2623cd duration (902 + 1721) ─ in itself, bordering on the Golden Mean value of 2618 (1.6182) ─ formed a 50% advance/decline ratio (5442 / 2623 = 2.07).


Figure 3 – The Golden Mean 38.2, 50, and 61.8% support/resistance levels of the Nasdaq 100 Index

 The Nasdaq’s Wave B can be identified by the three lesser-degree wavelets, ’a-b-c’, which in contrast to the 1985 – 2000 sharp upward impulse, and the 2000-2003 steep decline, formed a scrambled zigzag pattern from beginning to end (Figure 3, above).

What stands out most is that on Aug. 10, 2013 wavelet c was equal to a’s span, each 1721cd long (Figure 4, below). The number 1721 approximates the numeral 1723 on the Square’s south-western diagonal (Figures 4 & 5).Since wavelet ‘a’ fell 2cd short of 1723, ‘c’ could run for a few more days without upsetting the balance. It may well terminate around August 16, 2013, in line with the S&P500 Index.

Pricewise, wavelet ‘a’ gained 1,111 points, whereas ‘c’, based on the highest closing price of 3,141.00, has, thus far, added 2,115. In the unlikely event of ‘c’ gaining 107 more points, by reaching the 3248.00 level, their price ratio will be 1:2 (1111/2222).


Figure 4

The top right corner of Figure 4 shows the formula n(n+1)+1 for determining the numerals of the Square’s south-western diagonal [where ‘n’ is a whole number integer representing the square root of the span (√3774=61.4; 61 x 62 +1=3782)].Note that the square root 61.4 approximates 61.8. At 3774cd, the numeral is too large to fit A4 page.

As stated in “Unlocking the secrets of Gann: Will the market crash in August?” mature intervals bounce off and culminate on the same Square axis upon completing a 3600 rotation from and back to the same point where the preceding interval ended. In cases when a swing terminates upon the Square’s opposite axis, at 1800 angle, it remains incomplete until a 3600 rotation brings it to the axis it bounced off. Having said all that, none of this applies to the Nasdaq100 Index. It behaves differently.

Save for the first swing (Oct. 9, 1985 –Sep. 2, 2000), which terminated upon the northern cardinal, on day 5442 of the run, the other components have thus far adhered to the Square’s south-eastern and south-western diagonals, all terminating at a 900 angle (Figures 5, 6 & 7, below).


Figure 5

 The axis of the 1985 – 2000 swing, which measured 5441cd (also too large to display) can be derived from the formula n(n+1)+n/2+1, where ‘n’ is the square root of the span: √5442 = 73.77   (73 x 74 + 37 +1= 5440.).


  • Sep. 01, 2000 – Apr. 11, 2003 = 901cd = SE Diagonal (Fig.7)
  • Apr. 11, 2003 – Dec. 26, 2007 = 1721cd = 1723 SW Diagonal (Fig. 6)
  • Dec. 26, 2007 – Nov. 20, 2008 = 330cd = 325 SE Diagonal (Fig.7)
  • Nov. 20, 2008 – Aug. 10, 2013 = 1721cd =  SW Diagonal (Fig. 6)



Figure 6 – South-western Diagonal


Figure 7 South-eastern Diagonal

Yet, despite of the Nasdaqs ‘misbehaviour’, a 3600 alignment between lesser degree wavelet ‘c’ and the entire 3774cd ‘a-’b-c’ span (1721 + 330 + 1721) will take place on Aug. 10, 2013, upon the Square’s south-western diagonal signalling the termination of Wave B and the beginning of Wave C’s final decline (Figures 5 & 6).

While the 2000–2003 Wave A and 2002─2013 Wave B will form a 900 angle on August 10 on the south-eastern and south-western diagonals, the upcoming Wave C must terminate upon the Square’s northern cardinal, at a 3600 angle with bull market’s Wave V (Figures 5). 

Gann often reiterated the importance of correct starting points. On pages 77-78 of The Tunnel Thru the Air he wrote: “It is just as easy to figure 100 or 1000 years in the future as one or two years ahead, if you have the correct starting point and know the cycle which is going to be repeated…In order to forecast future cycles, the most important thing is to begin right, for if we have the right beginning, we will get the right ending.”    

Correctly detected peaks and troughs map onto the Gann Square like the pieces of a puzzle. It takes little effort to identify the NASDAQ’s Oct.09, 1985 trough, which, as Figure 5 shows, coincided with the lowest price the Index had reached. However, the respective Sept. 1, 2000 peak and April 11, 2003 trough are less visible on charts. Neither one coincided with the extremities of price (Figure 8).


Figure 8 –The NASDAQ’s 2000 peak and 2003 trough (weekly chart)

Absolute peaks and troughs are determined by lesser-degree wavelets that form the final stages of impulse swings. Even though pricewise the Nasdaq peaked on March 27, 2000, timewise, it was a false top given the 57cd decline and 71cd advance that followed. The longer swing, irrespective of price, determines the trend (Figure 9).


Figure 9

Similarly, between Oct. 10, 2002 and April 11, 2003, the Index’s decline was longer in comparison to the upswing. Though, pricewise, the April 2003 low was considerably higher than the October 2002 bottom, the 53cd up and 161cd down intervals dictated that Sept. 1, 2000 was the true peak (Figure 10).



Figure 10

 Stephen Hawking and Leonard Mlodinov’s forecasting model “is good if it is elegant, contains few arbitrary or adjustable elements, agrees with or explains existing observations and makes detailed predictions about the future which can disprove or falsify it if they are not borne out.".

If there is one weakness to the Gann Square, it is the unknown number of 3600 rotations a market undergoes over the life of an eight-wave cycle. The S&P500 Index, for example, completed nine 3600 rotations over 1621cd (March 09, 2009 ─ Aug. 16, 2013) from the time Wave A ended on day 496cd of the run (Figure 11). How can we know that this 9th rotation was its last?


Figure 11- S&P 500’s 9 3600 rotations upon the eastern cardinal

  The Nasdaq 100 Index, on the other hand, completed only 5.75 rotations from the day Wave A’s 902cd run culminated on April, 11, 2003 (Figures 6 & 7). The bell, indeed, rings when the Square isolates an individual span and maps it onto its geometrical divisions, yet remains silent when a five-wave pattern terminates.


About the Author

Pauline Novak-Reich is the former manager research-foreign exchange at the ANZ’s (Australian & New Zealand Banking Corp.) dealing room from 1980 -1993.