Archive for the ‘Dow, Elliott and the TRIADS’ category

Dow @ 20,000

Proportion is mathematical. This is why Elliott beautifully illustrates the proportional structure on markets. In this update we question some Elliott assumptions and highlight some observations on Dow Jones Industrial and the overall market structure.

Fig. 1: This is a classic five wave structure from 1789 to 1990. The 1990 highs seemed like a top, but markets continued to extend more than a decade after the respective high well into 2000.

Fig. 2: Elliott Wave structures give 2000 top a high importance. This importance rests on the super cycle fourth wave low at 1982. If that low is assumed to be in 1975 and not in 1982, the count would change. This would suggest that the all time top is still not in place and markets could extend higher above 2000 all time highs.

Fig. 3: This is the five wave structure from 1932 lows.

Fig. 4: This is the five wave structure from 1975 lows. As one can see the time taken by the second wave is marginally smaller than the time taken by the IV cycle wave (3300 days). The difference appears large on a visual chart with an arithmetic scale, but on a log scale both price and time suggests that the Dec 1974 and Aug 1982 price structure (1 and 2 cycle wave) can be compared with the Jan 2000 and March 2009 structure (III and IV cycle wave).

Fig. 5:  All the above cases suggest that if we extend the channel high of the supercycle count (Fig. 3) the DOW structure can see an extension till 20,000. Terminal waves are very tricky and this is not any terminal wave. This is a terminal wave of all available history of markets. Two decades of error in a history of pattern watching and Elliot counting from Dark Ages in 1330 should be acceptable.

Till 12,000 and 11,000 supports  stand firm on DOW, this preferred stands firm for us.


Mukul Pal, is a Chartered Market Technician, MBA Finance and a member of the reputed Market Technicians Association (MTA). He has more than a decade of Capital Market experience dealing with derivatives and global assets. He has worked for Bombay Stock  Exchange, multinational Banks and brokerage houses in leading research positions before starting on his own in 2005. He is the President of the MTA Central and Eastern European Chapter.

The Intermarket Rieki

Confirmation and non confirmations are at the heart of technical analysis. Whether it’s the Dow Theory speaking about the confirmations between Dow Industrial and Transports as a tenet for a trend continuation or it’s an intermarket ratio line breaking a multiyear trendline, we are always seeking an evidence for continuation or reversal of a trend.

Pattern identification is a high skill and also at the heart of technical analysis, but there are a few published rules regarding the workability and backtested results of non confirmations. Non confirmations are as prone to failure as any other market pattern.  Times have changed. New age technicians should accept that market complexity has increased and the days of Joseph Granville confident fanfare forecasts may take a while to return. Accuracy needs more than visual skill today.

This is the reason …

This article is written for ATMA

Time Triads, Time Fractals, Time Arbitrage, Performance Cycles are terms coined by Orpheus Research. Time Triads is our weekly market letter. The report covers various aspects on TIME patterns, TIME forecast, alternative research, emerging markets, behavioral finance, market fractals, econohistory, econostatistics, time cyclicality, investment psychology, socioeconomics, pop cultural trends, macro economics, interest rates, derivatives, money management, Intermarket trends etc.

Demystifying Elliott Waves

Elliott waves can be recreated using the geometrical Time Triads.

It’s a rare chance that you have not heard about the Elliott Wave Theory. Named after Ralph N Elliott, the theory redefined Charles Dow’s theory of 1880′s where Dow talked about three legged bull market, and compared markets with ripples, waves and tides. Born on 28 July, 1871 Elliott was a genius just like 6 Nov, 1851 born Charles Henry Dow. They both had the ability to identify market patterns and hypothized a theory that stands firm till date. The Elliott forecast of a multi decade bull market made in 1935 at the bottom of the great depression can easily pass as the best financial forecast of all times. The work was generational in nature and was carried ahead by a string of elite practitioners Charles J Collins, A J Frost, Hamilton Bolton, Richard Russell and the famous Robert Prechter whose priceless contribution was instrumental in getting Elliott the much deserved attention.

Figure 1.

Elliott wave hypothized that markets move in a 5-3 structure (Figure 1.), which created trends and counter trends. This structure happened at all time frames from the smallest tick data till century old data structure. Phelps Brown and Sheila V. Hopkins, (Oxford) estimated 1000 years of price history also has 5 wave structure. There are a total of 13 patterns which summarize all the price action and all technical analysis. Elliotticians have occasionally mentioned that technical analysis is a foot note in Elliott. If you read the historical work of Bolton, the accuracy is unprecedented. Prechter has written extensively illustrating how Elliott subsumes all conventional price patterns. Prechter claims it to be a science.

However despite the generational success and body of knowledge, there are heaps of criticisms against Elliott. First: Prove the science and mathematics (David R Aronson). Second: Standalone Elliott is fatal (Constance Brown). Third: Patterns are illusionary. Humans see what they want to see (Hersh Shefrin). Fourth: Markets are patterned but cannot be used to predict (Benoit Mandelbrot). Fifth: Price action is random (Nassim Taleb). Sixth: Markets are efficient (Eugene Fama). Seventh: Human beings like stories (Robert Shiller). There are many other issues concerning the practice of the technique. It’s a visual skill, which needs to be nurtured. There are not always perfect counts. Forecasting Time using Elliott is weak. A student has to go back in price history, which is always not easy, especially owing to the fact that society got used to high tech gadgets, computing power and Elliott wave counting softwares. We got used to fast solutions.

The criticism is not about just Elliott, it’s about everything technical. Head and shoulder pattern has come under much criticism from behaviorologists, statisticians and fundamentalists. Aronson goes ahead and carries a complete case called ‘head and shoulder’, objectification example. He systematically proves it bust. Aronson has been comprehensively harsh with Elliotticians and calls it a power of good story. This is what he says “The story gives Elliott analyst the same freedom and flexibility that allowed pre Copernican astronomers to explain all observed planetary movements even though their underlying theory of an earth centered universe was wrong”. First and foremost, Aronson’s labeling Prechter as a great story teller is highly critical. As Prechter has demonstrated enough accuracy over years and contributed to serious literature on markets and psychology. Second just because Elliotticians could not scientifically prove the mathematics does not make the Elliott wave a grand story, as we will explain ahead.

Figure 2.

Understanding the science in a theory takes time. Elliott did not use Fibonacci mathematics when he first hypothized the theory. At a suggestion he picked up books on Fibonacci and found it very compatible. In figure 2., you can see that Elliott can be counted mathematically in terms of exact numbers. The first subdivision is a cycle, one trend up and one trend down, which corresponds to Fibonacci numbers 1 and 1. The second subdivision when the uptrend divided into five waves and the down trend divides into three waves again correspond to Fibonacci numbers 5 and 3. As we go on subdividing we keep hitting numbers from Fibonacci sequence not only if we consider up trend and down trend separately, but even if we aggregate them.

How did Elliott miss it in 1934? Why is Elliott so countable? Does counting not make it mathematical? And why has nobody ever asked why Fibonacci and Elliott are so linked? What is the connection? Both change in prices, and Fibonacci numbers labeling the wave are exponential functions (Figure 3.). The magic of Elliott and Fibonacci lies in their exponential nature. There is such an extensive overlap of research historically that though Euler’s number ‘e’ (2.71828)) dates back to 1727, we have studied it in different forms, we never attempted to unify the forms. Starting from the marginal utility function, Pareto curve, Poisson distribution, fractals, are all linked with the exponential function just like Elliott.

Figure 3.

Though Prechter mentioned that nothing much has been constructively added to Elliott since its creation, Tony Plummer’s seminal book was the first to demystify Elliott. The book first published in 1989 showcased a stylized pattern of time and suggested that time should nest and be fractalled. Plummer also went ahead and said that Elliott’s five wave structure was not the law of nature but the three wave structure of cycle was the real law of nature. This was a large thought, which we at Orpheus extended ahead into Time Triads, a hierarchy of triangles subdividing and multiplying by 3. Last feature we recreated the omnipresent head and shoulder formation (Plummer’s stylized pattern of time) by using Time Triads. Head and shoulder lost its mysticism as it could be created by a set of Euclidean triangles. The pattern was mathematical and fractalled. We created the pattern by assigning Cartesian coordinates to the units of Time Triads.

This is not the first time triangles have been used to create mathematical structures. Spidron is a field of triangles crumpled and twisted into a wavy crystalline seahorse’s tail. Then there are Koch Snowflakes which are created from inverted triangle or a V shaped structure. We have Pascal triangles. The oldest Pythagorean Theorem came from triangles.

Can time triads create Elliott wave structures and lay all the illusion of market patterns finally to rest and make market fractals a complete and validated science? This has been a quest for us since we coined the term Time Triads, Time Fractals 12 months back. Time Triads grow and decay exponentially with a factor of 3. We took two head and shoulder patterns created using Cartesian coordinates and did the same additive technique. We obtained a nine legged structure (Figure 4.) impulsing up and a nine legged structure moving lower. Elliott defines nine legs as an impulsive structure. Five wave structures are known to subdivide into nine waves.

Figure 4.

Elliott wave talks about a stage in market when a corrective can drop 90%. The illustration (Figure 4.) is a complete cycle of a bull and bear market moving up and coming down in 9 legs. Another classic illustration of an Elliott structure is illustrated in Fig 5. Here we have an impulse followed by a sideways correction. This structure also has 9 legs moving up, and 9 legs moving sideways. There is no magic about 18 legs (9+9). There are 9 triangles making a larger triangle. And 9 triangles have a total of 18 sides. The magic of Elliott disappears. Now one may say what about the 13 patterns? We have assumed an idealized form of Time where larger Time does not influence smaller Time that is no translation. A computerized model where we account for translation can generate all the 13 patterns of Elliott.

Figure 5.

There are no incomplete peaks in nature. What goes up invariably comes down, even if the uptrend is a century long. Growth and decay are parts of nature and markets. The reason Elliotticians could not prove the theory till now was owing to the fact that the big picture of time was missing. Time is bigger than generational knowledge. Time Triads just like Elliott can pinpoint where we are today and where we are headed tomorrow. There is no magic, it’s all geometry.

A Dow Theory


The generational theory can be refined by understanding the significance of TIME

Charles Dow wrote ideas explaining the movement of the Dow Index (DJI). Robert Rhea compiled them and called it ‘The Dow Theory’. A majority of market theories and tools have come after that. The theory still makes the introductory pages of any basic technical analysis book after 125 years. Though we have studied it as a student and quoted it with reverence, we want to challenge it today.

This is not because the theory is any less profound or we have stopped looking up to it, but time refines everything, even historical theories. I don’t know how Charles Dow would have reacted to this article. The humble Wall Street editor who never used to get angry taught us everything we know today. He changed the world.

We are a trend focused society with our economic, fundamental, behavioral, cultural, statistical and scientific trends. The Dow Theory also talked about trends. Trend is what we technicians are taught to identify, to ride and get off before reversal, or to ride it down as a sharp shooter. Trend means bias, uptrend is a positive bias and down trend is a negative bias. Dow’s simple theory gave form to this bias.

He said that markets move in stages, accumulation, speculation and distribution stage. He gave market a three stage form, characterizing three degrees of price trends, a primary, secondary and minor (noise). There are clear tenets he defined in his work. Fig. 1 shows some illustrative examples how Dow’s observation of three stages was a clear observable pattern.

The first tenet of the Dow Theory is that prices discount all information and expectations, to the point that they are predictive of events. If information was supposed to be assumed by price and information has a positive and negative bias, one could assume that the theory studies the bias in price, which forms a three legged structure. Fundamentalists say that information (the cause) affects the price (gives it the bias). Bias measurement is tough, but the theory laid down a solid framework to interpret it. There is a large bias, small bias and smallest or unseen bias. The very fact that prices trend for years, also suggest a polarity in bias. However, the theory despite its simplicity and workability has come under criticism of being late.

The late part is what we would like to address here. Why is the theory late in telling us that the Dow is reversing? Why there was clear tenet in the theory saying that trends exist until definitive signals prove that they have ended? Why did Dow want to give the trend a benefit of doubt during reversals? The reason for such confusion was because unknowingly Charles Dow was studying time. It’s just that he did not realize it. Fig.1 illustrates the same three stages structures, but with unbiased time cycles underneath it. The cycles illustrate time not the bias in price. There are three time cycles defining every three stages in DJI structure. The reason the theory was late or slow was because the price bias was out of sync with time, delayed. In some cases the bias was too large to understand (200-2009) and sometime minimal (1970-1982). Since 1965 there has been average fixed time cyclicality.

Aristotle said the earth was stationary, Newton said it moved, Einstein came and said that the stationary and the moving status depended on the reference frame you looked at it from. Einstein’s relativity theorem explained time. Einstein could do it because he started looking at relative motion. Even Dow did this as he talked about relative movement of one index to another. What he was doing was unknowingly detrending, discounting bias and understanding time. One of the theory’s tenet said that relative movement of the railroad indices against DJI explained the status of the trend on the Index, whether it was ready to reverse or not. Here again, Dow was focused on the trend of two indices and not the time. If both of the indices make higher highs, trend is in place, if not the trend is under question and could reverse.

Can the new railroads, the Dow Jones Transports (DJT) ever secularly outperform Dow Industrials? No. There is no Dow Transports without Dow Industrials. This means that DJT best performance is when it reaches parity with DJI’s average performance. What does it means in terms of trend? Transports have a limit of outperformance against the DJI. When it reaches there, the worst of DJI weakness is over. And the blue chip index should rise not only against DJT but also reverse the ongoing trend.

In Fig.2 we have illustrated the DJI (in price bars) along with the relative cycle line between DJI and DJT. The movement of the underlying cycle suggests that whenever Industrials reached an extreme performance against Transports (point F, G) DJI topped and vice versa. A simple relative cycle, timed the two historical tops of DJI in 2000 and 2008.The current status of the cycle also suggests now that DJT out performance is reaching a historical high against DJI suggesting that 2009 should witness a multi month reversal in DJI.


There are various other tenets of the theory which we can systematically be challenged. They all point to the same thing. One; the theory was generational because it was partially in sync with time. Second; the reason the theory was late was because it focused more on understanding the price bias and not the underlying time. Third; the idea of lower low or higher high in confirmation is a crude tool to understand time. Relative cycles are the real tool, objective and unbiased.

Fundamentalists and Technicians debate a lot about cause and effect. One says it studies the cause, while the other claims to study the final effect, the price. The debate made sense till the time there were many causes affecting the price. The debate ceases to exist when time becomes the only cause. Till we start focusing on time, indicator failure will remain a reality and life will look random. Predictability is about time, accepting or not accepting it is something else.

The Law of Nature

The S-curve, which is mainly used in population studies, is now redefining business strategy and stock market forecasting.

“The history of the world is nothing but the biography of great men,” said Thomas Carlyle, the 19th century historian. It’s strange but the more we try to understand markets, the more it pushes us back to econohistory. In March this year we had written about Thomas Malthus (1766-1834), economic history’s greatest pessimist who talked about hunger and starvation. Though the science of forecasting is still young and underdeveloped, Malthus made an amazing forecast of a crisis by the middle of the 19th century. And his population studies are turning things upside down more than 150 years after his death.

In 1838 after reading Malthus’s essay on the principle of population Pierre F Verhulst, a Belgian mathematician, published the Verhulst equation. However, it was only in the 20th century that Alfred Lotka of Johns Hopkins University and Vito Volterra of University of Rome generalised Verhulst’s growth equation to model competition among different species.

These are the origins of the S-curve. S-curve fitting, a natural and fundamental approach to forecasting, is reliable with high confidence levels. Physicists have shown that everything in nature can be quantified, from matter to light. Spectacular consequences of putting natural law descriptions in a discrete form have been the subject of chaos and fractals. I had a chance to meet Theodore Modis, a physicist from Growth Dynamics Inc, recently in Vienna. Along with Alain Debecker, a mathematician from Lyon University, he wrote about the S-curve and the bridge between continuous and discrete formulations spanning 150 years of developments in mathematics. They also wrote about how it starts with Verhulst and finishes with Mandelbrot, intricately linking order with chaos. The paper also mention how chaos-like states can be expected before and after logistic growth ie historical picture is nothing but an alternation of logistic growth with periods of instability. The chaotic fluctuations belong to the end of a growth phase as much as to the beginning of the next one. A well established S-curve will point to the time when chaotic oscillations should be expected. What’s more interesting about this paper is that it sites the Kondratieff cycle (56 years) as a way to position growth periods.

According to the S-curve, society pushes natural growth factors to an invariant status such as income spent on travelling at 15 per cent, sleep to work ratio of eight hours, mammal heart beats of 1 billion in a life, hospital infections at 14 per cent, average car speed at 30 miles per hour etc. These invariants happen as respective growth curves hit respective ceilings. In competing products, these ceilings and invariant status can also explain substitution. For example, when wood usage hits a ceiling, coal takes over; as coal fails, oil takes over and as oil will exhaust, it will be substituted by natural gas and so on. There are some rules to the S-curve growth. It proceeds in stages and each stage represents the filling of a niche with limited capacity. And just like economic growth, political growth also shows alternation between order and chaos. According to the curve, logistic growth is natural growth in competition.

Modis has extended the S-curve model to stock markets assuming stocks to be species competing for investor resources. He trashes the Gaussian bell curve since there is no natural law behind it and suggests that all marketers using bell shaped curve for strategy are headed for failure. Cyclicality can give strategy answers regarding cannibalisation and future growth. The author also junks the goodness of exponential fits and proves how correlation does not imply good fit. Exponentiality according to him means extrapolation on a log scale, which can’t predict. He also goes ahead and says that a pattern can be used to make forecasts, as long as it represents a natural law that guarantees invariability.

According to Modis, volume and value obey the law of competition directly. He also made some bold prediction on the Dow Jones starting June 2008. He predicts prices not higher than 14000 with lower targets lying at 8000. Other forecasts are about world population, which he claims should have a final ceiling at nine billion people, cumulative oil production in the US should hit a ceiling at 220,000 million barrels by 2030, Microsoft needs to undergo a major change for survival and the next energy growth assets should be natural gas and nuclear power. The substitution aspect of the curve is clearly cyclical and it seems we have no choice but to move to renewable energy source after hydrogen nears a ceiling on the S-curve.

Despite a thorough track record and mathematical grounding, the S-curve suffers from a few kinks. It really does not account for any other fractal apart from the S-curve. It does not take into account Fibonacci numbers or ratios, seems more for investment than trading, has a clear disbelief on price patterns, looks for parameters that intimately relate to competition and fundamental mechanism, saw the post-1999 period as one for stagnation than the one for crash, accepts sunspot cyclicality as a good predictor but not fractals or Elliott Wave, which are cyclical by nature.

Walter E White’s contribution in 1968-70 only reinforces the gaps in the S-curve. White said that Elliott Wave analysis suggests a general relationship between static forms in plants and animal life and dynamic waves of time. The origins of this relationship may be found in fundamental ideas of arithmetic, logic, algebra, geometry and trigonometry dating back to 500 BC. Elliott Wave has a cross-subject application and the idea of shock or chaos is fundamental. White’s contribution quotes Kierkegaard (teacher of Neil Bohr of quantum mechanics fame) saying that “in life only sudden decisions, leaps, or jerks can lead to progress”. All this brings Elliott waves in sync with the chaos and order that mathematicians have been talking about for over 150 years. Above this the relationship between the logarithmic spiral, the Fibonacci series and the golden ratio has been known for about 2,500 years, making Elliott pattern based on a natural law.

What’s strange is that while mathematicians were working on a growth decay natural model, Ralph Elliott was refining Charles Dow’s market fractal theory. The noise against Elliott keeps rising everyday while pure Elliotticians keep defending it. In August 2007, Robert Prechter highlighted the comparisons and improved predictability of the wave principle over Sornette’s log periodic cycles. According to Prechter, Elliott is a science with clear rules though practicing it is a craft.

The S-curve also offers competition to the wave principle. However, with the open gaps and the new school of thought that economics and finance are two different subjects altogether, the challenge is alive. After all, double decimal accuracy forecast delivered by Elliotticians over the last 60 years on all trading time frames and with practitioners like Hamilton Bolton delivering as much as 11 accurate yearly forecasts in 13 years, the S-curve has a tall benchmark to compete. The only research aspect which really suffers with the S-curve gaining ground is the investigative equity research, the last vestige of equity research which still holds some water, while the Fibonacci reality of markets remains a notch ahead of the S-curves.

Market Fractals

Fractal is a form, which appears everywhere in nature both at macroscopic and microscopic levels. Trees, clouds, DNA’s, atomic structures are all fractals. Physics, chemistry, biology, astronomy are full of fractal patterns. Mass psychology is also a fractal. Not very many books and articles are written about this universal truth.

A fractal means a mathematically definable structure which replicates itself across time and size scales. It’s like a building block of creation. A fractal at the heart of every natural creation. Break a Pine tree branch and you see the tree itself. Kenneth G. Libbrecht of Caltech came up with Snowflake physics identifying 35 classification of snowflake fractals. Natural patterns appearing again and again.

The first time a fractal was observed in markets was as early as 1880s, when Charles Dow constructed the DOW 30 and wrote his theory about the first economic fractal. We have to credit the man and his business acumen valued nearly $5 billion today and creating an industry worth trillions of dollars.

He said markets move in a wave like fractal, a tide, a wave and a ripple. There is an accumulation stage, a speculation stage two and greed and public participation finality. After which the form ends and corrects. And then the structure starts again. Dow was the first to see the mass psychology form in financial markets.

DOW 30 survived the centuries but somewhere we lost his fractal. It never got that well deserved attention, unlike modern accountancy, which started somewhere in 1880′s.

Dow identified the fractal and called it an economic theory. Elliott redefined Dow’s work and made an applied forecasting tool called the wave theory. The scale dramatically changed as fractals got seen not only on a multi year business cycle scale, but on every time frame. And on every broad asset and anything traded or non traded statistics with a socio economic aspect and implication. Be it Labor market parameters, macro economic parameters or simply global car sales, just anything.

The reasons which could explain everything about market and economics couldn’t explain why metals, energy, agro commodities, industrial commodities, forex etc. looked alike. And where reasons failed Fractals stood firm, inexplicably.

The wave theory is one tool that works across markets, across subjects on both economic and socioeconomic levels to forecast. This fractal can predict prices of say BRENT CRUDE for a tick, a minute, a day till multi years and decades in future without knowing about the Oil crisis, hurricanes, supply gaps and all that causes that may come in the future. The tool predicts the future without the breaking news, which may come years later.

So why did such a great tool took a back seat and never emerged? 1800′s was too early to understand mass psychology. Stock markets were fancy things. The mass psychology lacked critical mass, the speculator new little about leverage. Leverage reached world scale a century later. And something more was hot, information and its causal implications. There was an information and explanation for what markets were doing. And the great depression was long forgotten as the new generation took over. Econohistory owing to its black aspects was never interesting reading. Who wants to know how many banks failed in an era where a banker is celebrated? 125 years and we are still giving reasons, building businesses and knowledge technology systems unmindfully defining the fractal that defines us. The fractal that is larger than life and continues to move relentlessly with cyclical precision.

We have reached some conclusions, why we forgot the fractal. Human mind is the least understood part of the human body. Recent attempts to map the brains throw interesting light on the subject. Emotion is a key driver for the brain. We are brain dead without emotions. Further work has proved that the lizard brain (Reptilian Complex) rules our impulses, our herding tendencies, how we behave in the society and our stock market games. The lizard also explains why humans remain penny wise and pound foolish. Why we make things complex rather than simplifying them? Why we can’t stop or pause consuming as a society? Why panics happen? Why fear is a bigger motivator than greed? And why complacent society means low volatility? Reptiles also explain why Fractals don’t interest us?

Fractals are not stories we love to hear. The patterns are contrarian by nature looking at exits on greed tops and entry in busts. Fractals by very nature stand alone. They are unconventional. And above this they are a lot visual. People are different and so are their ways to learn.

Drucker classified them as group which learns by reading, or writing. This all leaves us with a small fractal lovers, only a few who can question the status quo standing alone uncomfortably. Fractal needs courage to stand against 200 years of economics and say there is no economics without psychology, and psychology is itself fractaled, patterned.

Everything has its limitations. Even fractals are not fool proof. But they are definitely better than fundamental ratios like Price Earning ratios which fail the back test miserably with no forecasting value whatsoever. Understanding fractals may take a few hours but integrating them in and above economics may take years and then like Eels said, “one day the world will be ready to see and wonder how they didn’t see it”