Archive for the ‘Time Triads’ category

Market Quotes

If you shut down our power grid, maybe we will put a missile down one of your smokestacks.

A US military official in response to Hacker attacks on Pentagon

Much of our pleasure and pain in life stem from expectations of future and these pleasure and pains have profound implications for behavior.

Stanley Jevons

We feel less concerned about future sensations of joy and sorrow simply because they do lie in the future, and lessening of concern is in proportion to the remoteness of that future.

Bohm Bawerk

In nature there are no rewards or punishments there are only consequences.

The movement of money from one area to another is inherently unsustainable and destined to reverse itself. The money pilling up in the pockets of the citizens of the gaining country will encourage them to go out and buy things, while the loss of purchasing power in the losing country will lead its citizens of the gaining country will encourage them to go out and buy things, while the loss of purchasing power in the losing country will lead its citizens to tighten their belts and buy less; prices will rise in the gaining country and fall in the losing country. This shift in demand will in time reverse the flow of money back to the country that first suffered the outflow. As a result it is impossible to heap up money, more than any other fluid, beyond its proper level.

David Hume, Of the Balance of Trade

Discovery consists of seeing what everybody has seen and thinking what nobody has thought.

Albert Szent-Gyorgi, Nobel Prize Winner, Medicine, 1937

‘I had to do so much with so little, for so long, that I can do anything with nothing.’

Chris Gardner, quotes his mother

Buying at the start of a bubble is “rational”

George Soros talking on Gold

Against a world average of around four hospital beds per 1000 population, India lags behind at just over 0.72.

KPMG Health Care Report

You can’t suddenly make India a China.

Surya Sethi, World Bank Official commenting on India’s Power sector

As a general rule, it is foolish to do just what other people are doing, because there are almost sure to be too many people doing the same thing.

William Stanley Jevons

Formal education will make you a living, self education make a fortune.

Jim Rohn

More money was lost trying to get the last TICK than was made catching the whole move.

Bernard Baruch

Simplicity or singleness of approach is a greatly underestimated factor of market success.

Garfield Drew

The crowd is actually correct most of the time and it is at turning points that they get things wrong.

Humphrey Neill

The element of time can no more be eliminated from successful speculation… than from any other business.

Thomas Gibson, The facts about speculation 1923

Stocks don’t sell for what they are worth but for what people think they are worth.

Garfield Drew

Danger of losing your position in the middle of the trend.

Edward LeFevre’s, Reminiscences of a Stock Operator.

“It looks as if 1000 in the Average could be our next major target.”

Hamilton Bolton,April 1964, Dow Jones Industrial 812, Extracts from Elliott Wave Reviews, The Writings of A. Hamilton Bolton

“The market can stay irrational longer than you can stay solvent.”

John Maynard Keynes

“The Efficient Market Hypothesis can land you in jail”

Dismal science, dismal sentence, Sep 7, 2006 - The Economist Print Edition

In one respect markets are like houses. They take longer to build than they do to tear down. Markets spend most of their time advancing rather than declining. This means that the lead characteristics of momentum indicators are usually more pronounced at market peaks than at troughs.

Martin Pring on Market Momentum

“The laws of nature, and incidentally economics, are ruthless, which is as it should be”

Ralph N Elliott, Biography, R.N.Elliott’s Masterworks

“Logic always applies, if your premises are correct and knowledge sufficient”

Robert Prechter,The Writings of A. Hamilton Bolton

“It is foolish to short emerging markets, they are so euphoric that it is too dangerous”.

Emerging Market Investor, Apr 06

“Phenomena of mass action (are) under impulsions and controls which no science has explored”

Bernard Baruch, Extraordinary Popular Delusions & the Madness of Crowds, 1932

B waves are phonies. They are sucker plays, bull traps, speculator’s paradise, orgies of odd-lotter mentality or expressions of dumb institutional complacency (or both). They often involve a narrow list of stocks, are often “unconfirmed” by other averages, are rarely technically strong and are virtually always doomed to complete the retracement by wave C. If the analyst can easily say to himself, “there is something wrong with this market”, chances are it’s a B wave.

Frost & Prechter

When markets are topping, there is always another top. And when markets bottom there is always another bottom.


There has been no change in demand and supply. How did prices fall from $78 to $58 per barrel?

P Chidambaram, Finance Minister, India
CII (Confedration of Indian Industry) and the World Economic Forum, Nov 27, 2006

The less secure we are economically the more secure we are economically.

Carl J. Schramm. The Entrepreneurial Imperative

Most, probably, of our decisions to do something positive, the full consequences of which will be drawn out over many days to come, can only be taken as the result of animal spirits - a spontaneous urge to action rather than inaction, and not as the outcome of a weighted average of quantitative benefits multiplied by quantitative probabilities.

John Maynard Keynes, The General Theory of Employment Interest and Money, 161-162

Greed arrogance and unscrupulousness are the way of the world

Economist - Teaching of Conrad Black’s Father

Peasant Logic - Scare your opponent enough, and he will give you what you want.

Khruschev’s Cold War

Journalism needs to become a community service rather than a profit centre.

Craig Newmark, of Craigslist

“January 1 will enter history books as a moment of irreversible change toward a more secure and prosperous future,”

President Traian Basescu told Romania’s parliament.

75% of all stocks move up with a bull market, and 90% of all stocks move down with a bear market.


Vivid examples of planning failures and partial reforms—for example, a quarter of all shoes sold in Hungary in 1951 were officially classed as substandard.

Mr Eichengreen

“I got into this market to make $100,000 a year and feed my family and to allow my wife to stay home with the kids. I never in my wildest dreams thought we’d be here at the center of the U.S. equities market.”

Dave Cummings, BATS

“I think what the Fed is trying to tell us is that it is between a rock and a hard place. And when you’re between and a rock and a hard place, you just can’t move,”

Drew Matus, senior economist at Lehman Brothers Holdings

There are only three sports - bullfighting, motor racing, and mountaineering.


The “great redeeming feature of poverty,” George Orwell wrote after his excursions in the social gutters of Paris and London, is “the fact that it annihilates the future”.

Uproar is the music of capitalism

Joseph Schumpeter

Putting a biomass water-heater in the basement tends to be easier than sticking a windmill on the roof.


Ethanol can be produced in backyard plants.


Markets tend to do a better job then the STATE and Economists


“If you’re not at the table, you’re on the menu.”

Saying in Washington

20% of Denmark’s energy come from WINDS


The carbon market is truly innovative. The trade is not actually in carbon, but in not carbon.


The five dirty industries covered by ETS (Emissions Trading Scheme) are ELECTRICITY, OIL, METALS, BUILDING MATERIALS AND PAPER .


“In business, you reward people for taking risks. When it doesn’t work out, you promote them because they were willing to try new things. If people come back and tell me they skied all day and never fell down, I tell them to try a different mountain.”

Bloomberg 0607

“SKY - high copper prices; rock bottom education”

Student Banner in CHILE, 1006

10 million Indonesians live on $1 a day, and 100 million on $2 a day


A new theory is attacked as absurd;then it is admitted to be true, but obvious and insignificant; finally, it is seen to be so important that it’s adversaries claim that they themselves have discovered it.

William James

One day the world will be ready for you and wonder how they didn’t see it


In business, success often depends upon the relative age of your ideas. And today, people of all ages are in trouble because their ideas aren’t just old, they’re obsolete. One example of an old idea is that of the traditional job. Jobs are a centuries-old concept created during the industrial revolution. Despite the reality that we’re now deep in the Information Age, many people are studying for, or working at, or clinging to the Industrial Age idea of a safe, secure job.


One notorious sceptic of the Asian miracle was Paul Krugman, who had argued before the crisis that Asia’s growth was the result of “perspiration rather than inspiration”, based on increasing inputs of capital and labour rather than productivity gains, and would therefore prove unsustainable.

East Asian Economics, 10 year Crisis Anniversary

Once China’s currency the Yuan, is fully convertible, Honk Kong will be just another Chinese port.

Hong Kong Pessimists

Gay households is growing five times faster than the population itself. The last consensus in 200 counted 600000 same sex couples. Most Fortune 500 companies paid offered the same health insurance to employee gay partners as to spouses first time last year.

Gary Gates

If factories go, there will be nothing left


Nation is not at war, the military is at war

US Military commanders

A superpower can lose a war - in Vietnam or Iraq - without ceasing to be a superpower.

Robert Kagan

4.6% of World’s (Defense spending) population in USA with a 27.5% World GDP spends 46% of total World defense budget ($1.2 trillion.)

US Factsheet

The trouble though, is that America’s forces were designed for sprints not marathons


I am proud to be a speculator. I am proud that my humble attempts to predict Tuesday’s prices on Monday are an indispensable component of our society. By buying low and selling high, I create harmony and freedom,

Victor Niederhoffer

There is always an easy solution to every human problem — neat, plausible and wrong.

H. L. Mencken

There are no failures, merely different outcomes.

Penny Thornton

Just when you think you’ve found the key to wall street, they go and change the locks.


What is TIME? (TED Video)

This video was created for the TED 20 May Conference in CLUJ Napoca

TEDx conference in CLUJ

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.

Divergence Cyclicality on SSRN

Time Triads, Time Fractals, Time Arbitrage, Performance Cycles are terms coined by Orpheus Research. Time Triads is our weekly market letter. The report covers Time Cycles on global assets and forecasts. The report uses alternative research techniques to study emerging markets and carries updates on behavioral finance, market fractals, econohistory, econostatistics, investment psychology, socioeconomics, pop cultural trends, macro economics, interest rates, derivatives, money management, Intermarket trends etc.

The Weekend Effect

The name Friday comes from the Old English Frīġedæġ, meaning the “day of Frige”. The same holds for Frīatag in Old High German, Freitag in Modern German and Vrijdag in Dutch.

The idea of patterns and order is used conveniently by behavioural finance to challenge conventional economics. But the question of why that order exists has not been researched.

Last time, we mentioned how behavioural finance used the idea of mean reversion to prove that classical economics idea of order and randomness were inconsistent. The new subject went all the way to prove this inconsistency and illustrate that extreme losers outperformed the extreme winners consistently.

During my lecture on behavioural finance at the Babes Bolyai University in Cluj (named after János Bolyai, the famous Hungarian mathematician who established non-Euclidean geometry in 1860, and Victor Babes, one of the early bacteriologists), I was questioned if patterns worked, then one should focus on finding that pattern.The question was genuine, but behavioural finance does not give an answer to this. On one side, it uses the idea of seasonality to challenge economics, while on the other side, it does not give a pattern solution. The subject somehow avoids the idea of seasonality totally, preferring to concentrate on explaining human follies than on other working patterns in markets. Is this not an inconsistency in behavioral finance?

I was discussing this gap in behavioral finance research with Dr Nistor, with whom I had authored the idea of performance cyclicality and showcased seasonality among BRIC (Brazil, Russia, India and China) countries’ performance in 2007. We were wondering was the idea of seasonality and time tough to deal with? When inter-temporal choices clearly presented itself to behavioural finance experts, why did not they talk about the idea of ‘time’ more? Was it a tougher road to take talking about patterns when the subject had a charted path to illustrate error-prone human decision making? Well, we don’t know why behavioural finance research credits cyclicality as an existing phenomenon but does not go further?

In 1931, M J Fields from Harvard wrote a paper on weekend effect in the journal of business. The paper was investigating the conventional Wall Street wisdom at the time that “the unwillingness of traders to carry their holdings over the uncertainties of a weekend leads to the liquidation of the long accounts and a consequent decline of security prices on Saturday”. He found prices not only rose on Saturdays but also were on average 52 per cent time more than the Friday to Monday average for the 717 weekends he had studied.
Till 1945, Saturday used to be a trading day. Fields’ idea was revisited by Frank Cross in 1973, who found that in S&P500, there were 60 per cent positive Fridays, but only 40 per cent positive Mondays. Cross said, “The probability that such a large difference would occur by chance is less than one in million”. This is known as the weekend effect, which talks about strange order. This order is thoroughly used to challenge randomness in classical economics, but the question why this order in time works is unanswered by behavioural finance.

This article was written for Business Standard

For regular updates on behavioral finance and investing ideas subscribe to Orpheus Research Update.

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.


Time Duration Decay in Emerging Markets Journal

Time Triads, Time Fractals, Time Arbitrage, Performance Cycles are terms coined by Orpheus Research. Time Triads is our weekly market letter. The report covers Time Cycles on global assets and forecasts. The report uses alternative research techniques to study emerging markets and carries updates on behavioral finance, market fractals, econohistory, econostatistics, investment psychology, socioeconomics, pop cultural trends, macro economics, interest rates, derivatives, money management, Intermarket trends etc.

The Toronto Cycles

Abstract: This paper applies performance cycles to the top 100 stocks of Toronto Stock Exchange. The idea of time cyclicality and performance cycles has been explained as a method of market cyclicality in the following academic papers and published literature.

1: The Divergence Cycles0
2: The BRIC Model from a Japanese Perspective - Pre and Post Financial Crisis Review and Forecasts1
3: Time Fractals2
4: Temporal Changes in Shiller’s Exuberance Data3
5: Time Duration Decay in Romanian Capital Markets4
6: MTA Knowledge base – Performance Cycles5
7: Mean Reversion Cycles6

In performance cycles, assets are ranked based on price performance or any other fundamental or statistical parameter.  Performance like everything else is driven by time cyclicality. The asset rankings take the form of an oscillator, which moves from 0.1% to 100% for a group of 1000 assets. The performance cycles can be drawn form any time frame starting 1 min to multi years. In this report performance cycles for stocks on TSE are illustrated for minor, intermediate and primary time frames. Performance cycles nest like a hierarchy of various degrees.

Fig1. Performance is hierarchal

Ranking the assets.


Fig2. Toronto 100 with FXF (Canadian Dollar ETF) ranked based on performance for 3 months

Source: Authors work. Data provided by Thomson Reuters

Ranking the assets - II

The high ranked assets are outperformers over the last 3 months and the low ranked assets are respective underperformers. These rankings move cyclically and create performance cycles for individual assets on different degrees of time. Below we have illustrated the rankings of 3 month and 6 months together. A stock could be the best performer over 3 month but not best over a 6 month period.

Fig3. The ranking in percentile over 3 and 6 months.

Performance Cycles - If we look individually at the stock rankings for 1 month, 3 month and 6 month, the create performance cycles. The left hand side is the percentile. The right hand side is the price. The performance cycles of 1 month (red), 3 months (blue), 6 months (grey dashed). The cases illustrated here take three stocks PWT, UUU and AEM. These are extreme performers and according to performance cycles extreme performers in a group of assets should see a reversal in performance. The top performer should underperform and vice versa. We have marked red arrows when the 1 month (red) cycle pushes below the 3 month (blue) cycle from high rankings and when the large 6 month (grey) cycle is also pointing lower. In case the 1 month red pushes back above 3 month, the trade is closed and reinitiated again if the initial condition persists.




Performance cycles are a method of illustrating asset seasonality on a multiple degrees of time. When as asset reaches an extreme above 90% performance or sub 20% performance, the asset performance reaches an extreme and which makes it prone to reversal in previous trend. The performance cycles can assist in sector selection, stock selection, risk management, model portfolio construction and of course trading. Below we have tabulated the rankings in percentile of 3 month and 6 month for the assets under study.

Bibliography - Index

1: The Divergence Cycles0

2: The BRIC Model from a Japanese Perspective - Pre and Post Financial Crisis Review and Forecasts1

3: Time Fractals2

4: Temporal Changes in Shiller’s Exuberance Data3

5: Time Duration Decay in Romanian Capital Markets4

6: MTA Knowledge base – Performance Cycles5

7: Mean Reversion Cycles6

For regular updates on performance Cycles on Toronto Stock Exchange assets write to us today for a free trial for Orpheus Time Analytics.

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.


The Divergence Cyclicality

Abstract: Divergence is an understudied subject loosely defined as an unpredictable random error. The classification of divergences as small or large is also at the heart of efficient or inefficient market theory debate. This paper explains how divergence is cyclical and can be quantified and used as a predictive model.

Keywords: divergence, cyclicality, relative performance, rate of change, assets, rank, distribution

Smith, Pareto and the divergence debate.

Life is all about making sense of information. This information could be personal, economic, or societal kind. When we comprehend information, we make a decision, which we assume to be correct. So, at a certain level, we try to understand performance and how to perform as individuals in order to make performing choices. Performance assumes a kind of order. We try to create order in decision making from disorder in the external world. This disorder could also be called divergence. Divergence is a phenomenon seen in nature and markets. It is something that needs explaining and can be unexplainable at times. It is linked with change or rate of change1. Divergence is also assumed to be random2. Divergence happens as prices move away from a theoretical value calculated statistically or fundamentally3. Divergence is not considered normal. Divergence is also known as non confirmation in technical analysis4 (the study of market patterns). Divergence also creates news, as something that is not normal is strange and worth talking about. For example when company beat analyst expectations (disappoint) and there are large changes in price action. Divergence can also be seen in information and data also.

Adam smith5 (1723-1790) talked about the invisible hand, what we don’t know something unpredictable, a kind of divergence. Vilfredo Pareto6 (1848-1923) talked about non homogeneous wealth allocation. 80% of the wealth is with 20% of people. This unequal allocation was a divergence. Charles Dow7 (1851-1902) talked about a basic tenet of markets in his now famous Dow Theory. If Dow industrials8 and Dow Transports9 were not moving together, it was a non confirmation10, a case of divergence. Dow Industrials made higher high in January 2000, while Dow transports did not. Divergence case was indicated by Charles Dow as a reason for divergence. Markets changed trend after the respective divergence. Ralph N Elliott11 (1871-1948) talked about truncation12, double extension13, throw over as rare (divergent, non normal) rare formations in classic Elliott wave theory. Edward Norton Lorenz14 (1917 – 2008) talked about Chaos and how small changes in early conditions lead to totally new behavior (unpredictable divergent behavior), leads to the butterfly effect.

We can see cases of divergences in current times. John Murphy15 talked about linkages between markets and assets. Gold and dollar generally move opposite. When Gold strengthens, dollar weakens and vice versa.  There are times when gold and dollar don’t follow this relationship Murphy calls it an Intermarket failure. Sam Stovall16 talked about sector performance divergences. Sector price performances vary as the economic cycle changes. There is a stage in the economic cycle when Utility sectors outperform financials and there is a stage in the economic cycles when utility sectors underperform financial sector. Putting simply sector differ or diverge in performance from each other in different times.

Robert Shiller17 talked about divergence between market data and fundamental value as earnings don’t have a commensurate effect on price performance. Shiller fluctuations are divergence cases. Mandelbrot18 talks about extremities, large divergences which cannot be explained by the normal distribution Gaussian curve. Nassim Taleb19 says black swan is random, rare, unpredictable, an extreme divergence.. Robert Arnott20 talks about how growth diverges from value and creates cyclical opportunities. Robert Prechter21 has done extensive work on social mood divergences; rising hem of skirts, films we watch, sugar we consume, social mood diverges from one extreme to other.

The inefficient22 market school of thought is based on large divergences while the efficient market school of thought is based on small divergences. Coming to look at it the debate between market efficiency and inefficiency, revolved around divergence. If it is small, it is normal distribution, if it’s large, it’s inefficient and exponential distribution.

Large divergence is a reality between high, low, negative correlated assets. For example there was a 60% net change in price performance between gold and palladium from July 2009 till January 2010 and 55% between Brent23 and Exxon24 from July to October 2008.  Even 100% divergences between sector peers are not too rare. They happen regularly.

How can we define large divergence? Is small divergence any less important than the case of large divergence? Sam Stovall sector rotation outperformance and underperformance can be seen as divergence of 12% net change in price performance between Dow Industrials and Dow Financials from October to November 2009. Stovall did not discuss small consistent repeating semiannual divergences of 5% between Dow Industrials and S&P 500. Small divergences are as important as large 100% repeating divergences between two sectors. Behavioral finance25 talks about divergences as anomalies that are tough to capture. Is it because divergences are tough to isolate, measure, explain, quantify?

Robert Shiller explains why markets are inefficient using various time series of present value of dividends and plotting them against stock prices illustrating more than normal fluctuations. His proof that markets are inefficient is based on the fact that large divergences can’t be explained. Divergences are everywhere, in capital markets, economics, sciences and we still consider them somehow non forecastable, extremities, errors, non normal behavior, non ordered, and chaotic.

To understand divergence one can go back in the history of how data interpretation evolved. Mandelbrot said nature was full of extreme divergences and the Gaussian bell curve had more fat tails that it could explain. The divergences from mean were large. Though Mandelbrot was correct as divergences in nature were large and divergences on occasions don’t revert to mean, but the question to be asked is why did Gauss not see the large divergences from mean? There could be many reasons. Could it be because Gauss was handling Astronomical data, which was more ordered than other data found in nature? Or maybe because data interpretation was a nascent science and hence the first obvious visual pattern Gauss could see was the mean line.

As time passed and data interpretation came off age, the size, quality and quantity of data enhanced. There was more data to fit, a lot of it. The attention moved from data to divergence in data. Larger the divergences became visible, fatter the tails26 became. Whatever was Gaussian suddenly started to look exponential.

We, as humans, are somehow not designed to understand extremes, but mean and average. The society understands average salary, average GDP and so on. Average has safety, comfort, which extremes lack. Technical analysts are familiar with moving average but a majority of us can’t visualize the average27, which is always changing, mixing, transforming. A lot of other parameters extend from the idea of mean. What would happen to correlation if the mean was dynamic? Small divergence around the mean was considered efficient and large divergence made everything inefficient.

The first question one may ask about historical and contemporary divergence cases is if these divergences are cyclical. John Murphy states that Intermarket linkages are cyclical, as money moves from soft to hard assets and from commodities to bonds. Sam Stovall’s economic sectors cyclically move in and out of performance. There is repetitiveness in sector rotation, cyclicality in divergence. Robert Shiller’s case of bubble formations is cyclical. Mandelbrot’s repeating extremities and Nassim Taleb’s recurring random events are periodic. Repeating extremities are the reason fractal geometry and butterfly effect exists.

Taleb’s Black swan is a subject of study because there is not only one black swan. The black swans come again and again, periodically. Robert Arnott’s investing out of growth into value and vice versa is cyclical. Robert Prechter’s social mood diverges cyclically positive mood to negative mood and back. Behavioral Finance talks about investor’s errors and repeating Long reversals. The subject of behavioral finance would not be valuable if long reversals didn’t repeat.

Top performers underperform and top underperformers also perform. Dow Industrials underperforms S&P 500 and vice versa. Similar cyclicality can be seen between gold and copper. Gold underperforms and outperforms copper cyclically, the pairs diverging 8% to 10% cyclically in a quarter28. Small and large divergences are cyclical. Divergence cyclicality introduces an order in divergence. Because the focus was around mean, everything around mean was considered noisy and extreme. The idea of divergence cyclicality is a study of extremities, the study of cyclicality of error, it also proves that mean could be more dynamic than believed.

Clifford Pickover29 in his book “The math book” tells us that “Simple computer programs, which attempt to find regularity in sequences, may not “See” the regularity in Champernowne’s number30. This deficit reinforces the notion that statisticians must be very cautious when declaring a sequence to be random or patternless.

On one side Mandelbrot’s idea of extremity robs us of the beauty of the bell shaped curve, and on the other side it’s the same bell curve, which is used to disprove patterns in nature.”  The paradox is really very sad. We are busy debating about randomness and order never even once thinking of the error that creates it all. Divergence cyclicality can reconcile the efficient and inefficient school of thought. It can explain that both Gauss and Mandelbrot are talking about the same mean. But it’s Mandelbrot who takes the argument to the next level by assuming larger divergence around mean as more important than the smaller divergence around the mean. Both of them speak about mean reversion31, one saying it works, while the other refutes it.

Divergence cyclicality on the other hand is more focused on defining a pair, a group, than defining an average. Divergence cyclicality can be the new predictive model that takes data interpretation to the next level, by introducing time cyclicality into data and suggesting that the basic pattern of order (small divergence) or randomness (large divergence) is cyclical.

Quantifying Divergence.

Human beings are always ranking choices. Though this intuition seems like a system, rankings between a group of people can show a lot of variability as the process of ranking is individual, non standardized and emotional. Humans also try to understand by grouping assets or parameters together. They try to look for similar features, characteristics and this is why economies, regions, political affiliations are grouped. BRICS, MAVINS32 and PIGS is an example of grouping associated with similar ranking economies. The global competitiveness report is a ranking process on global economies on a host of parameters (World Economic Forum, “The Global Competitiveness Report 2009-2010”).

Though this intuitive ranking reflects in the investment process, majority prefers absolute over relative performance. There is less news on relative performance but more on absolute performance. “Gold made a new high today” can be an investment news but “gold outperformed silver by 10% in the last quarter” is rarely published. Investment portfolios rarely get benchmarked to other assets like dollar or gold to understand year to date relative performance against key global benchmarks.

Investors use a similar ranking and grouping process to diversify, but maybe because the comfort and confidence is low regarding this ranking and grouping system that the majority investors diversify less. Behavioral finance clearly highlights that investors diversify less (Modern Portfolio Theory and Investment Analysis by E. Elton, M. Gruber and others”). Diversification is also suggested as an action point to reduce risk but owing to limited diversification and inability to benchmark portfolio performance investors are unable to comprehend a macro portfolio of global assets on a relative basis are more prone to geographical biases.

The majority of investors fail to understand that the assets traded today are also paired against a currency. Dow Industrials (.DJI) is paired against dollar and Sensex is paired against Indian Rupee, Nikkei is paired against Yen.  Even EURUSD is a pair made from two currencies. Yield curves are studied to understand interest rate trend. A yield curve is a spread between long term and short term interest rates.

Pair ideas are everywhere whether we speak about Risk vs. Return, Demand for cash vs. Demand for assets, Risk aversion vs. loss aversion, Pessimism vs. Optimism,  Perceived risk vs. actual risk, Relative vs. Market Value, PE (Price Earning Multiple) vs. Market Value, Liquidity vs. Solvency ratios, Supply vs. Demand.

Pair trading is an active strategy globally because it offers an opportunity to capture divergence. We studied divergence in various pairs and one could see increasing and decreasing divergence patterns. We made a case of Boeing and Oil (Brent) and exhibited a case of divergence cyclicality. Visually one could identify lows and highs in divergence and the no divergence stage.


Figure 1: Boeing and Oil (Brent) divergence cyclicality
Source: Authors work. Data provided by Thomson Reuters

Divergence analysis, a study of cyclicality as relative performance or spread analysis has no units, it is a statistical ratio. Divergence analysis connects ranking, pairs and relative performance. Relative performance is the price performance of one asset netted against performance of another asset. The two compared assets can be a stock against its Index, a sector index against another sector Index, a portfolio against the composite index etc. Relative performance can also be understood as alpha. A negative relative performance is underperformance while a positive relative performance is outperformance. It can be constructed with the following steps.

The data for an Index and its constituents are collected in the following format. The asset and its benchmark are compiled together. In this case the closing price data of Dow Jones Industrial Average (DJIA) is plotted along with the closing price of its components like Alcoa. This is illustrated in table 1.

Table 1. Closing prices for Dow, Alcoa, Disney, Dow, Walmart

Table2. Ratio between the price and the benchmark

Source: Authors work. Data provided by Thomson Reuters
In table 3, a 60 period averaging is done to look at quarterly tendency in daily change in relative performance values.  Alcoa table 3 value for 4 Apr 08 = Alcoa (9Jan table2 value+10 Jan table2 value+ …+3Apr table 2 Value)/60

Table 3.  60 days period moving average on data

Source: Authors work. Data provided by Thomson Reuters

We plotted a rate of change (ROC) on this relative performance. ROC is an indicator that shows the difference between today’s closing price and the close price N days ago. It is also referred to as momentum and can be understood as the absolute difference: Rate of change can also be represented as a fraction. ROC plotted on relative performance was an improvement on illustrating divergence cyclicality. We employed this process in our paper. This was an attempt to quantify divergence. To qualify one signal from the other we had to find a way to focus on extreme divergences. The larger the divergence we could isolate, the better we could quantify it. This was when we decided to look at divergence in a group of assets because a group divergence is higher than a pair divergence. The group focus helped us intensify extremes. To create groups we used relative performance and we ranked them.

Ranking the assets.

We integrated a global portfolio with the following 54 assets. Forex (EUR USD, AUD USD, GBP USD, CAD USD, JPY USD, CHF USD, Yuan Rnmbi, Indian rupee, NZD USD), Energy (Crude, Natural Gas, Gasoline, Heating Oil, Petroleum, Carbon Emissions, Brent, WTM, Energy Index), Metals (Precious Metals, Tin, Zinc, Nickel, Copper, Platinum, Silver, Industrial Metals Index, Gold), Agro (Coffee, Corn, Grains, Livestock, Sugar, Wheat, Soybeans, Cotton), Thematic and Global Equity (Coal Mining Fund, Shipping Fund, Dow Industrials, Sense, Agricultural Equity, Water, Nuclear, Russell 2000, Russell 1000 USD), Bonds (US 30, US 5Y,  US 10Y, US 2Y, INR Bond Index, China Bond Index, Australian Bond Fund, Global Bond Index, Sweden Bond Index) and benchmarked the portfolio to dollar.

Figure 2. Global portfolio of 54 assets

Source: Authors work. Data provided by Thomson Reuters

We numerically ranked33 the portfolio according to assets, sectors and on aggregate bases. Now we could not only see the top performers and worst performers but also how rankings were dynamic. The worst was becoming the best and vice versa. We could now qualify one divergence low from the other. The best ranked asset paired up with the worst was a divergence extreme that could indicate performance cyclicality. And since divergence did not differentiate between assets, we could even talk about performance cyclicality between zinc and coffee, suggesting that zinc should outperform coffee as coffee was the top ranked and Zinc the worst and divergence (performance was cyclical). This dynamic performance when plotted as a time series took the form of an oscillator. The dollar oscillator illustrated below suggested dollar outperformance against various forex pairs and vice versa as it moved from one extreme to another.

Figure 3. Dynamic performance (as oscillator for dollar)

Source: Authors work. Data provided by Thomson Reuters

Instead of histograms for one date we plotted the historical data for just one asset, Bank of America.  A smoothing using two moving averages of 20 and 30 days elucidates the cyclical nature. The oscillator shows how the stock moves up in performance against DJIA and rest of the 29 components (the benchmark) and vice versa.  When the oscillator hits the bottom the stock has hit underperformance low against DJIA and hence should reverse and start outperforming. On the other hand if the oscillator touches a high or tops, the stock has reached the top of its outperformance against DJIA. The stock should now reverse its performance and start underperforming DJIA. The image below suggests a start of outperformance for Bank of America against DJIA.

Figure 4. Bank of America asset’s relative performance oscillator

Source: Authors work. Data provided by Thomson Reuters

The numeric ranking and relative performance cyclicality opened up many other advantages. We looked at Hedge Efficiency when we paired the index against it future (Derivative). Using the ranking and performance cyclicality approach we could identify that the real time to hedge was when futures were underperforming the spot prices or in other words the divergence reached an extreme between the two assets. We tested the Nifty (Indian Index) against its Future and isolated more than a risk free return consistently.

Fig.5.  Hedge efficiency

Source: Authors work. Data provided by Thomson Reuters

Cases.  Fig. 6a. 6b. 6c. 6d- Asset Energy – Exxon (benchmarked with Brent)

Fig. 6e. The Relative performance oscillator for Exxon

The Relative performance oscillator (Fig 6e.) for Exxon indicates outperformance against Brent if the oscillator turns up and vice versa. We have tabulated four turn points. From 03 July 08 to 17 (arrow 1 to 2) Sep 2008 Exxon bet outperformed Brent by 52%. In this period Brent fell 63% while Exxon dropped just 11%. Similarly when the oscillator turned down Exxon underperformed Brent by 24%. The two cases are illustrated above in Fig.6a, Fig.6b, Fig.6c and Fig.6d. The table below carries individual performance and net performance between the two assets.

Source: Authors work. Data provided by Thomson Reuters


The reason for the divergence debate is because divergence is ubiquitous. It is how nature and markets function. Divergence cyclicality drives this growth and decay process. Divergence cyclicality is also the reason markets keep moving from efficiency to inefficiency. History of research did not make an effort to understand divergence as it was thought to be noise, error which cannot be used as a predictive model. This paper proved that divergence can be understood by grouping assets and ranking them. This way extreme and large divergences not only become more comprehendible but also quantifiable. This quantification can be used to pin point performers and underperformers around the world whether it’s a social trend, economic regional cycle or traded assets. Divergence cyclicality is a predictive model that can change how we understand nature and markets.

Download the paper from SSRN.


Mean Reversion Cycles

The Journal of Finance. Werner F. M. De Bondt, Richard Thaler.

Average of 16 Three - Year Periods Between January 1933 and December 1980. Length of Formation period: Three Years. Cumulative Average Residuals for Winner and Loser Portfolio of 35 stocks (1-36 months) into test period.

We read about the McGregor’s X and Y theory. X theory suggesting that people need to be blamed and Y is about self motivated people. How could you rebuke people and get results out? The psychologist Daniel Kahneman, winner of the 2002 Nobel Prize in economics, pointed out that regression to the mean might explain why rebukes can seem to improve performance, while praise seems to backfire. This explained why the X theory leaders delivered.

Behavioral finance (B) case where losers outperformed compared to winners over longer period of times is just another extension of the mean reversion theory. If it was not for mean reversion B may never have become main stream. It was mean reversion which actually allowed the subject to crack open the 250 year old classical economics armor. How?

Historically, economists and statisticians have seen randomness and patterns together. Very few attempted to explain this phenomenon. Jacob Bernoulli’s (1654-1705) work on the Law of large numbers talked about probabilistic fate (order) in random events. Abraham de Moivre (1667-1754) probability became ‘The doctrine of chances’. Pierre-Simon Laplace (1749-1827) who created the method of least squares gave a pattern to a set of probabilistic observations. Francis Galton (1822-1911), built on the idea and wrote about mean reversion.

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This article is written for Business Standard

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.

Mukul @ TEDx

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The 3D Time


If 3D Time and 3D Space were interchangeable, we have a unified theory of science which is easier to comprehend than the complex string theory. The recent work on possibility of multiverse rather than universe bring us closer to understanding the cosmos and the closer we get to understanding cosmos, the closer we get to understanding Time. The Big Bang mystery of expansion and contraction has been challenged by a new theory which uses dark matter to explain why the big bang may not contract but expand forever.

On one side this confirms the second law of thermodynamics (increasing entropy) but on the other side it opens up another debate regarding the symmetry of time. Physical processes at the microscopic level are believed to be time symmetric as laws of physics remain true even if the direction of time is reversed. However at a macroscopic level there is an arrow (direction) of time that exhibits such time-asymmetry. Time takes the direction of entropy, moving in the direction from low entropy to high entropy. Increasing entropy is the reason why we can’t convert a broken egg back into an egg or why we can’t stop aging or decaying. Arrow of time is the reason future and past is distinguishable.

On one side the arrow of time explains the life that we live in this universe and on the other side if the second law of thermodynamics was a rule, life as we know it won’t be possible. This contradiction works against a unified theory of science as it fails to explain why low entropy can co-exist in a high entropy environment like the expanding universe. In other words how can order exist in world that is meant to be disordered?

Boltzmann brain was hypothesized as a self-aware entity which arises due to random fluctuations out of a state of chaos. The idea is named for the physicist Ludwig Boltzmann (1844–1906), who advanced an idea that the known universe (order) arose as a random fluctuation. Boltzmann proposed that even in a near-equilibrium state, there will be stochastic fluctuations in the level of entropy resulting in only small amounts of organization. The data disproved this as the level of order was much higher than being due to a random fluctuation. Above this the fact that we are close to finding more habitable planets like earth challenges that life is indeed a rare fluctuation.

Sean Carroll retweaked Boltzmann working and explains that though fluctuations in a high entropy state could explain the reason for life, living in a fluctuation (an extreme rare event) is not enough to explain the visible order. There was a large proof of habitable life in thermal equilibrium (which is not conducive to live).

Cosmos clustered and formed galaxies and states of low entropies more frequently than expected. There were more than a few fluctuations in nature. There were more than a few low entropy states in a large entropy environment. Sean suggests that the answer might lie in events before the big bang. Assuming there was nothing before the big bang was not convincing enough. There was a need for a better theory than general relativity. Sean explains how high entropy systems continually create low entropy big bangs. This was the reason we were a part of a multi verse and not a universe. These conditions create lack of thermal equilibrium and the reason for life. Multiverse also explain why time is symmetric even if live through one arrow of time.

Though Sean is unsure regarding his multiverse, time fractals suggests a symmetric time and confirm Sean’s view. Symmetry of time means there is a moment when time symmetry starts and time when the symmetry completes before starting again. A low entropy moment is when a time cycle starts and highest entropy is when a cycle peaks. The two aspects of time, the repetitive and change time also explains why though time is ordered it also brings relentless change. Putting simply time is the reason why we live in a measurable and ordered world with an unpredictable future. The reason history does not repeat but rhymes is because evolution goes on with changing time. Repetitive time is the reason the entropy starts again and why despite high entropy in one universe we have another low entropy beginning of a new universe in a similar time.

Low to high entropy can also be seen as efficiency to inefficiency. More entropy is the reason for more inefficiency than efficiency in nature. We can also describe entropy process as a shift from homogenous to heterogeneous, normal curve to fat tails, mean reversion to divergence. High entropy seems to be a natural feature of everything around us. Entropy is the reason life is full of extremes, inefficient extremes. Because time is symmetrical in all directions and is fractalled we can experience coexistence of high and low entropy in similar time.

Universe is one arrow system. But since time is symmetrical and 3D in nature time can have various arrows of time in all directions. This is the reason why multiverse is a reality. Our paper on Temporal Changes suggested changes in time duration being the reason for inefficiency in markets (more than a few fluctuations). Using cosmic Time to illustrate a similar inefficiency would prove that 3D space is an extension of 3D Time. And life is not a rare fluctuation it is an order caused by the vibrating string called Time.

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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.