26. The 5 stages of a trader

It is helpful in general to be able to assess yourself within the long Journay of a trader.

The 5 stages of a trader that are:

1) The Novice. In this stage you try to lose as little money and time as possible till you learn what are the laws of the markets, and how a trading system should be.

2) The Advanced Beginner. At this stage you have designed, discovered or just learnt from other people, a winning system that you practice and make some money.

3) The Competent. At this stage not only you already possess a gaining trading system, but you gradually improve it so as to increase the return on investment and reduce the variance of the profits or improve other characteristic parameters that describe the system performance.

4). The Proficient. From this stage a big change occurs to you as a trader. You no longer try to improve the trading system. What you do is that you work, and play more with your subconscious attitudes, beliefs and emotions, relevant to  the states of the market and the ability to practice the system as the anticipation and forecasting the markets.You trade for the joy and satisfaction of feeling in contact with the substratum psychology of social economic behaviour of the societies as it is proved by being able to anticipate it. You trade rather for the    "return on energy" as Brian Tracy has put it, than for the "return on money". Or you explore how, the rather rare ability, to create safety and wealth from the conduction of your system, influences your subconscious and your psychological impact on other people (even if , and better so, you mention nothing of your successful trading). You also begin to plan and organize what to do with the surplus wealth that is created.  And plan to fund some activities of interest to society and other people.

5) The Expert. This is a stage where one of your main concerns is your state of mind, and scientific or cognitive principles.E.g. teach others, or publish relevant scientific papers or books contributing to the science of economincs and the knowledge in general.At this stage also you may occupy yourself seriously in directing how the surplus wealth is re-distributed in scociety in the best way. E.g. through grants, scholarships, institutions, investments etc. As Aristotle was puting it , it is in the reach of every man to spend money and to the reach of many men to receive money; but few only have the virtues so as to qualify to decide to whom, why, when how much and in what way the money are given, so as to serve in the best way,  the best purposes in society.

THE TOP 6 FACTORS OF ATTENTION IN MANUAL TRADING

1) NEVER USE ALL YOUR FUNDS FOR TRADING.  DIVIDE THEM TO TRADING AND NON-TRADING FUNDS BY THE RATIO f=R/a^2 RULE (see below for this ratio or in posts 3,13,33). THE DIVISION OF FUNDS AT EACH PERIOD IS ADJUSTED TO CONFORM WITH  THIS PERCENTAGE RATIO. NEVER WITHDRAW PER PERIOD FROM THE NON-TRADING FUNDS MORE THAN HALF OF THE AVERAGE PROFITS OF THE TRADING FUNDS PER PERIOD. This division and adjustment of the funds has been applied for many years in buy and hold investments by  professor Michael LeBoeuf. 

2)  THE ONLY CERTAINTY, WHILE TRADING IS ALSO OUR  FIRST PRIORITY: WE MAY DETERMINE THAT OUR LOSSES AT EACH POSITION WILL NOT BE LARGER THAN A SPECIFIED PERCENTAGE DEFINED BY THE KELLY CRITERION (see below or posts 3, 13, 33)

3) FOCUS ON MACROSCOPIC INSTRUMENTS LIKE  STOCK INDEXES WITH PERMANENT STRONG LONG TERM TREND, even if you want to trade at short time scales. (e.g. of the American Economy which is young and strong and indexes like Dow Jones, SnP500, Nasdaq etc)

4) FOR VERY LOW RISK AT OPENING POSITIONS ON THE PREVIOUS INDEXES WITH PERMANENT STRONG TREND, OPEN AT TERMINAL SPIKES AGAINST THE TREND. This is the Bill Williams technique. 

5) THE ASSESSMENT OF THE PATTERNS OF THE MARKET REQUIRES THAT IT IS DONE IN MANY SUCCESSIVE TIME FRAMES CHARTS. This is a basic recommendation by Alexander Elder, which, by now, it is a common knowledge to traders


6) BE FLEXIBLE IN FORECASTING THE MARKET AND DO NOT HESITATE TO FOLLOW PROMPTLY ANY UNEXPECTED CHANGES OF THE TREND OF THE MARKET. 

25. The Pareto (or power) distribution of the size of financial organizations and escalation (pyramiding) as precocious tactic.

Preliminary Remark about Pareto and Log-normal distributions.
It is custom in the economist to model the financial inequalities with the Pareto distribution (see e.g. https://en.wikipedia.org/wiki/Pareto_distribution  ) which is essentially a polynomial function. The exact model of the inequalities is even worse and is closer to the log-normal distribution (see e.g. https://en.wikipedia.org/wiki/Log-normal_distribution ) where the severity of the inequalities is modeled with exponential functions.But here in this book we may keep talking about the Pareto distribution which is celebrated term among the economists

It is well know to economist that the probability distribution of the (capitalization) size of  business organizations and domestic economies is the Pareto (or a Power) distribution.(Law 7 of compensation or deeper causalities in the 12 laws of post 9) (see also http://en.wikipedia.org/wiki/Pareto_distribution).

As the organizations inherit their relative size to the relative size of volumes of their packets of transactions , and a continuing trend depends mainly on the population size of orders of the organizations , we deduce that the length and duration of spikes and trends follows also a Pareto (or Power) distribution.The same distribution holds for the volume sizes.

Knowing that, it is not difficult to prove that the optimal trading of Pareto-duration distributed trends is one of pyramiding. Therefore even without the position size variations due to random fluctuation adjustments of the minor component of trading, the optimal major component of trading is not that of a buy-and-hold but requires pyramiding or escalation after the Kelly criterion that defines the position size with the conditional probability of  success of the trade . And while for the identification of the trend , the largest time frames give the best trends, for pyramiding the highest resolution time frames give the best choice.
We must not conceive the pyramiding as a greedy tactic, but rather a precocious tactic. Because till the end of pyramiding we never exceed the maximum allowed percentage of exposure of the funds , at the worse case scenario of losing. Instead the pyramiding is a gradual build of the position, where we approach the a maximum allowed percentage of loss of funds in the worse case scenario, gradually as we become more confident that the trend goes on, and while at the same time with a trailing  it will close if the trends stops. 

A better word for pyramiding is escalation. We described above that the escalation (pyramiding) due to the on going continuation of the (constant) trend is the optimal solution. But there is also escalation for different reasons than trend continuation. If for example we are uncertain about a trend, and we utilize say 4 indicators to detect it, and the more of them confirm the trend, then the higher is the reliability of the trend. Depending on the degree of reliability of the trend we might want to escalate (pyramid) the position. We call it trend-reliability escalation or pyramiding. We contrast this to the trend-continuation escalation (pyramiding) that we discussed initially. Furthermore, we may want to classify the trend according it is intensity as Low, Medium, and High. If we escalate the position according to if the trend is Low (smaller position size), Medium (higher position size) and High (highest position size), the we call it trend-intensity escalation (pyramiding). As alternative to the trend-intensity we may utilize acceleration-intensity, therefore making the last the of pyramiding, the acceleration-intensity escalation of the positions size and leverage/exposure. All these three types of pyramiding are different, have different rules and different importance and effect.
The trend-intensity escalation or pyramiding is relevant to the percentage allocation of a portfolio of trading of the 4 patterns as in the post 32. But we want to focus here mainly to the trend-continuation pyramiding.
In the trading practice of Bill Williams as it is described in his books, ("Trading chaos" and "New trading dimensions") he is applying a pyramiding from 1 unit to 5 units as trend-reliability escalation , and when the trend is clear and reliable he goes on pyramiding from 5 units, by increasing by 4 units, then 3 units, then 2 units, as trend-continuation escalation.

Here is an argument on which a proof can be based for the optimality of the escalation or pyramiding, when the trend duration follow a probability density distribution with a tail like the Pareto distribution.

Let us assume that the trend lengths follow a Pareto probability density distribution.

 

We focus on the conditional probability pc that if the trend has already length at least  L0 it will continue to length at least L0+dL . Such a conditional probability is a quotient of the probability density that the trend has length already at least L0  and also has length at least L0+dL, thus  p(L=L0+dL) and divided by the probability density of the trend having length at least L0; thus pc=p(L=L0+dL)/p(L=L0)=[from the formula of Pareto density]= ((a*(L0+dL)^a)*a*(L0)^(a+1))/ ((a*(L0)^a)*a*(L0+dL)^(a+1))=[we cancel the a's]=

 (((L0+dL)^a)(L0)^(a+1))/ (((L0)^a)(L0+dL)^(a+1))=[we cancel exponents]=L0/(L0+dL) .

Now  we can see from the last formula that when the L0 in creases the conditional probability of the trend continuing still further a bit more when it already has length L0, also increases! Notice it is not the absolute probability that increases, as the longer trends have smaller probability, but the conditional probability.
Intuitively this might be so because as the finite duration trend get longer and longer, the conditional probability that it will last one more time step get higher, at least due to the relative size of the next step and the duration of the trend so far. 

This means that if at each time step we have to re-decide our trading, the longer the trend hitherto the more probable it will go on, so therefore the larger the lot size we should choose (as the Lot size depends on the conditional probability of the trend continuing. 
This is also one of the proofs based on the Pareto distribution, of the law of statistical momentum conservation of the moves in the markets.  This is direct consequence of the stable Pareto distributed, inequality of the size of the business  organizations, which  is inherited on the volumes of transactions and size of the packets of orders of buying or selling, that are realized in repetitive way in the markets. 

And after the Kelly criterion (see  post 55 and also https://en.wikipedia.org/wiki/Kelly_criterion ) the position size or exposure depends on the conditional transition probability of success of the trade.  But this is exactly the pyramiding or escalation practice. OED.
In particular the above arguments suggests a linear increase of the escalation position size over the trend so far, in other words a quadratic increase of the overall position over the trend length so far.

Another way  to make the same conclusion (of the optimality of pyramiding)  is through the Kelly formula of the optimal account percentage to risk in a stop-loss and thus lot size as described in the posts 3, and 32.

From the post 32, we see that the optimal leverage of the trade and thus its  lot size too, is given by the formula

OptimalLeverage=(((((TP/SL)*p-(1-p))/(TP/SL))*Equity)/SL*10)*100

which is derived from the Kelly formula

f=(bp-(1-p))/b  (see  http://en.wikipedia.org/wiki/Kelly_criterion)

Now if from this formula we start the trade with Lot size  L and we expect a StopLoss=SL and a TakeProfit=TP1, and when the market reaches at this price level we realize that now the new anticipated TakeProfit=TP2>TP1, then from this formula is easily deducible that, all other being constant, the leverage of the trade also is to increase; in other words the lot size of the trade. Thus pyramiding or escalation.

A simple way to verify the Pareto or Power distribution is to make the histogram of the
High-Low of bars, e.g. daily bars and/or weekly bars and/or monthly bars etc, or the daily volume size.  

For a recent presentation on the role of power distributions in forecasting 
see the video
http://www.ted.com/talks/didier_sornette_how_we_can_predict_the_next_financial_crisis.html

We conclude that must not conceive the pyramiding as a greedy tactic, but rather a precocious tactic. Because till the end of pyramiding we never exceed the maximum allowed percentage of exposure of the funds , at the worse case scenario of losing. Instead the pyramiding is a gradual build of the position, where we approach the a maximum allowed percentage of loss of funds in the worse case scenario, gradually as we become more confident that the trend goes on, and while at the same time with a trailing  it will close if the trends stops. 

24. The 4 basic principles in trading

There are 3 contexts of laws required in trading . The appropriate LAWS OF THINKING for trading, the appropriate LAWS OF FEELINGS for trading , and the appropriate LAWS OF ACTIONS for trading. 

The Successful trading is based according to these three laws on
1) POWER OF COLLECTIVE  SCIENTIFIC THINKING: A GREAT AND SIMPLE SCIENTIFIC PERCEPTION OF THE FUNCTION OF THE ECONOMY THROUGH SOME GLOBAL STATISTICAL LAW. E.g. The law of Universal attraction in economy: that big money attracts more big money in the capital markets, and this by the balance of demand and supply makes securities indexes of the companies , that are indeed the big money, to have mainly stable ascending trend, whenever one can observe such one. Valid statistical deductions can be obtained with simple statistical hypotheses tests about the existence or not of a trend, with sample size half the period of a dominating cycle). (STABLE GREAT SCIENTIFIC THOUGHT-FORM  OR BELIEF FACTOR IN TRADING. )

2) POWER OF COLLECTIVE PSYCHOLOGY: A LINK WITH THE POSITIVE COLLECTIVE PSYCHOLOGY.(E.g. that the growth of security indexes also represent the optimism of the growth and success of real business of the involved companies. And we bet or trade only on the ascension of the index, whenever  an ascending trend is observable). (STABLE GREAT POSITIVE COLLECTIVE   EMOTIONAL OR PSYCHOLOGICAL FACTOR IN TRADING. )


3) POWER OF INDIVIDUALS SIMPLE , CONSISTENT AND EASY TO CONDUCT PRACTICE. (e.g. a trading system with about 80% success  rate that utilizes essentially only one indicator in 3 time frames, simple risk management rules of stop loss, take profit, trailing and escalation, and time spent not more than 20 minutes per day. In this way there are not many opportunities of human errors in the conduction of the trading practice. Failed trades are attributed to the randomness and are not to blame the trader). (STABLE SIMPLE AND EASY PRACTICAL  FACTOR IN TRADING)

We may make the metaphor that successful trading is the ability to have successful resonance with the  activities of top minority of those who determine the markets.

In trading there are 3 components in the feelings that must be dealt with. 1) The feeling of MONEY itself, 2) The feeling of the UTILITY of the money 3) The feeling of the RISK of the money each time. What is called usually money management in trading is essentially RISK MANAGEMENT. 



VALID STATISTICS AND PREDICTABILITY
We must make here some remarks about the robust application of statistical predictions in the capital markets.

1) The theory that the efficient markets and in particular that they follow a pure random walk is easy to refute with better statistical experiments and hypotheses tests. The random walk would fit to a market where the sizes of the economic organizations are uniformly random. But the reality is that they follow a Pareto or power distribution, therefore this is inherited in the distribution of the volumes of transactions and also in the emerging trends or drifts. 

2) The statistical models of time series  are more robust , when they apply to the entity MARKET as a whole and are better as  non-parametric , and not when they apply to single stocks and are linear or parametric. The reasons is that  a time series as a stochastic process , requires data of a sample of paths, and for a single stock is available only a single path. While for all the market the path of each stock or security is considered one path from the sample of all paths of all the stocks. 

3) The less ambitious the statistical application the more valid the result. E.g. applying a statistical hypothesis test, or analysis of variance   to test if there is an up or a down trend (drift) or none, is a more valid statistical deduction , than applying a linear model of a time series and requiring prediction of the next step price. 

4) Multivariate statistics, like factor analysis, discriminant analysis , logistic regression,  cluster analysis , goal programming e.t.c.,  are possible to utilize for a more detailed theory of predictability and of portfolio analysis, and sector analysis of the market and not only H. Markowitz theory. 

5) In applying of the above applications of statistics, the researcher must have at first a very good "feeling" of the data, and should verify rather with statistics the result rather than discover it. 

6) The "Pareto rule of complexity-results" also holds here. In other words with less than 20% of the complexity of the calculations is derived more than 80% of the deduction. The rest of the 20% requires more than 80% more complexity in the calculations.

To make a shortcut to the 12 laws of trading we may state in concise way the 4 groups of principles in trading.

1) The principle of characteristic (exhogenous and endhogenous Rainbow) frequencies that are absolute and eternal. Or the law of rhythms.  In other words all financial (and not only) activities are tuned or modulated by them E.g. 11.1 years solar activities cycle of the global climate, annual cycle, quarter cycle of publication of financial statements of organizations, daily cycle of sessions etc. In the same principle is also the property of the fundamental asymmetry of larger time scales to smaller time scales.
2) The principle of maximum likelihood (or volumes of transactions following, similar and of equal importance to trend following). Dr Alan H. Andrews (Andrew's pitchfork, median line) was a good practitioner of  part of this principle. Also Bernard Barouk rule "Trade the middle 1/3 only; rarely it is possible to open and close at the exact extremes" is also relevant. According to this law it is preferred to open and close a trade at levels where the probability density of the price re-occurring there is maximum. The main reason is the greater number of trades per time unit that can be opened and closed and better forecasting of the trade. The main application of this principle is in the bulk component of trading, called here adjustment and pyramiding. This principle is a consequence of the law polarity that not only derives the 4 basic price patterns, but also the existence of poles or support-resistance levels. And also of the law of causality and randomness.(see also post 32, and how the flat-waves and stationarities are traded)

3) The principle of momentum conservation and acceleration.(in the financial activities of demand and supply) or trend following. It is a consequence of the law of action. The most useful part of this principle is that part about  acceleration and the consequential divergence of appropriate indicators.  The largest time frames give the best trends. 

4) The principle of optimal adjustments and pyramiding. The best application is the back-office application on the tradable funds compared to the non-tradable cash, during a relatively constant trend of the equity line. Together with adjustment goes also the continuation escalation or (Pareto) pyramiding. The continuation pyramiding or escalation is a consequence of  the Pareto or Power law of the duration of the trends which is a consequence of the law of attraction. Both adjustment and pyramiding, can apply to the front office, in the form of a grid trading based on the constant percentage of funds risked.  (It relevant to moyenne or martingale-like and anti-martingale-like  position size adjustments, but it is different). The highest resolution time frames give the best practice for the adjustments.

We notice the common fallacy here that succesful trading can be based only on the principle 3) that of "trend following". Most of the traders just apply the trend following and ignore the other 3 principles.

From the 12 laws of the financial markets, probably the 5 most important to derive the  above 4  principles are the law of rhythms  (mainly daily and sessional)  , the law of action,(mainly the part about acceleration) the law of polarity (leading to the 4 price patterns)  the law of attraction. (as leading to Pareto distribution and size escalation) and the law of causality and randomness (leading to the optimal adjustment). 

The principles 1) and 3)  are rather in the realm of front office, while the 2),4) rather in the realm of middle and back office. Also the 2), 4)  are more significant for automated trading rather than manual trading.

The principle 3) defines the major component of trading (based on the trend) while the principle 4) defines the minor component of trading (based on the neutral random fluctuations ). The major component of the trading is usually conducted manually and it has a characteristic optimal focus frequency (usually of one session or one day). And this manual conduction cannot be substituted  by automated trading by a robot. The minor component of trading is usually conducted by a robot , it has a characteristic frequency which is the highest possible that the spreads allow, and is so fast and exact that cannot be substituted by manual trading. The overall is the concept of "manual driving of robot" a concept discussed in post 6.


The optimal adjustment principle accounts for the perpetual micro-retracements of the prices that is a basic source of perpetual profit. While the maximum likelihood principle focus on detecting the lines of maximum density of the price action (including the support-resistance lines but also non-horizontal least squares lines or Dr A. H. Andrew's median lines), that garantee  repeated opening and fast closing of the trades (maximum likelihood of closing the trade). These two principles have priority in detection  compared to  the principle of trend following, and are the holy-grail key to escape from the phsychology of dualism of up or down. So the 1st thing to detect is not if the trend is up or down (dualism) as the markets by default for  more than 60% of the time, are ranging and are almost neutral, but the 1st think to detect is the maximum density lines.

The above 4-principles of trading follow from the basic assumption of the components of  the dynamics of prices and volumes in the markets. A classical assumption is that the prices P(t) at each time are the superposition of at least 3 components P(t)=T(t)+S(t)+F(t) , where the T(t) is a non-periodic almost constant long-term trend (especially applicable more for  stocks , securities), a seasonal  term S(t) with properties of periodicity (in this blog we also assume that S(t)=S1(t)+S2(t)+...Sn(t) the seasonal terms is again the superposition of many other  terms at characteristic rainbow frequencies , all of them with properties of periodicities) , and F(t) is the term of stationary neutral random fluctuations (ranging market).

Referring to the 4 basic patterns spikes, trends, waves, and stationarities, obviously spikes and trends belong to the Term T(t), waves to the term S(t) and stationarities to the term F(t). And obviously the major component of the trading refers to the terms T(t) and S(t), while the minor component of the trading to the term F(t).
There is a correlation of spikes and trends.Longer and more stable trends start with spikes.

THE TOP 6 FACTORS OF ATTENTION IN MANUAL TRADING

1) NEVER USE ALL YOUR FUNDS FOR TRADING.  DIVIDE THEM TO TRADING AND NON-TRADING FUNDS BY THE RATIO f=R/a^2 RULE (see below for this ratio or in posts 3,13,33). THE DIVISION OF FUNDS AT EACH PERIOD IS ADJUSTED TO CONFORM WITH  THIS PERCENTAGE RATIO. NEVER WITHDRAW PER PERIOD FROM THE NON-TRADING FUNDS MORE THAN HALF OF THE AVERAGE PROFITS OF THE TRADING FUNDS PER PERIOD. This division and adjustment of the funds has been applied for many years in buy and hold investments by  professor Michael LeBoeuf. 

2)  THE ONLY CERTAINTY, WHILE TRADING IS ALSO OUR  FIRST PRIORITY: WE MAY DETERMINE THAT OUR LOSSES AT EACH POSITION WILL NOT BE LARGER THAN A SPECIFIED PERCENTAGE DEFINED BY THE KELLY CRITERION (see below or posts 3, 13, 33)

3) FOCUS ON MACROSCOPIC INSTRUMENTS LIKE  STOCK INDEXES WITH PERMANENT STRONG LONG TERM TREND, even if you want to trade at short time scales. (e.g. of the American Economy which is young and strong and indexes like Dow Jones, SnP500, Nasdaq etc)

4) FOR VERY LOW RISK AT OPENING POSITIONS ON THE PREVIOUS INDEXES WITH PERMANENT STRONG TREND, OPEN AT TERMINAL SPIKES AGAINST THE TREND. This is the Bill Williams technique. 

5) THE ASSESSMENT OF THE PATTERNS OF THE MARKET REQUIRES THAT IT IS DONE IN MANY SUCCESSIVE TIME FRAMES CHARTS. This is a basic recommendation by Alexander Elder, which, by now, it is a common knowledge to traders


6) BE FLEXIBLE IN FORECASTING THE MARKET AND DO NOT HESITATE TO FOLLOW PROMPTLY ANY UNEXPECTED CHANGES OF THE TREND OF THE MARKET. 

23. The 3 Levels of decisions in trading

Comparing trading with a financial organization we may classify the decisions in 3 layers or levels or tiers:
a) Front Office (direct interaction with the market and its changes and in trading mainly the entry decision based on indicators etc))
b) Middle Office (operational risk management decisions, and in trading decisions relative to the growth dynamics of a composite position , like pyramiding, martingale-like adjustments, reinvestment etc)
c) Back Office (clearance and accounting, and in trading mainly the exit decision , like take profit, global take profit , trail out, stop loss etc).


It may sound strange but maybe 80% of the ability to have a smooth equity line (with small DrawDawns) is based mainly on the middle and back office decisions rather than front office decisions.


In Back Office decisions the next parameters must be controlled by the trading system
1) The % risked per trade (in the worse scenario of the trade losing)
2) The % risked on all open positions or Floating Draw-Down.
3) The starting Draw-Down
4) The maximum Draw-Down
5) The maximum percentage of the margins of all open positions over the balance minus the % risked on all open positions (The active free margin from the point of view of the trader).
6) The profits reinvestment rule.
7) The percentage of the pool  funds of the account that do not participate in trading, and are used to withdraw for consumption, and optimal adjustments of the ups and downs of the funds that are used for trading.

22. The law of polarity: The 3 types of interplay of the demand supply (Domination, Competition, Cooperation) and the 4 basic price patterns

Before reading this post the reader is advised to read the post 9, of all laws of the financial markets, and the post 10, of the lower law of volumes (law of attraction) and the law of action (Newtons laws) 

There are 3 contexts of laws required in trading . The appropriate LAWS OF THINKING for trading, the appropriate LAWS OF FEELINGS for trading , and the appropriate LAWS OF ACTIONS for trading. 
The Successful trading is based according to these three laws on
1) POWER OF COLLECTIVE  SCIENTIFIC THINKING: A GREAT AND SIMPLE SCIENTIFIC PERCEPTION OF THE FUNCTION OF THE ECONOMY THROUGH SOME GLOBAL STATISTICAL LAW. E.g. The law of Universal attraction in economy: that big money attracts more big money in the capital markets, and this by the balance of demand and supply makes securities indexes of the companies , that are indeed the big money, to have mainly stable ascending trend, whenever one can observe such one. Valid statistical deductions can be obtained with simple statistical hypotheses tests about the existence or not of a trend, with sample size half the period of a dominating cycle). (STABLE GREAT SCIENTIFIC THOUGHT-FORM  OR BELIEF FACTOR IN TRADING. )

2) POWER OF COLLECTIVE PSYCHOLOGY: A LINK WITH THE POSITIVE COLLECTIVE PSYCHOLOGY.(E.g. that the growth of security indexes also represent the optimism of the growth and success of real business of the involved companies. And we bet or trade only on the ascension of the index, whenever  an ascending trend is observable). (STABLE GREAT POSITIVE COLLECTIVE   EMOTIONAL OR PSYCHOLOGICAL FACTOR IN TRADING. )


3) POWER OF INDIVIDUALS SIMPLE , CONSISTENT AND EASY TO CONDUCT PRACTICE. (e.g. a trading system with about 80% success  rate that utilizes essentially only one indicator in 3 time frames, simple risk management rules of stop loss, take profit, trailing and escalation, and time spent not more than 20 minutes per day. In this way there are not many opportunities of human errors in the conduction of the trading practice. Failed trades are attributed to the randomness and are not to blame the trader). (STABLE SIMPLE AND EASY PRACTICAL  FACTOR IN TRADING)

We may make the metaphor that successful trading is the ability to have successful resonance with the  activities of top minority of those who determine the markets.

In trading there are 3 components in the feelings that must be dealt with. 1) The feeling of MONEY itself, 2) The feeling of the UTILITY of the money 3) The feeling of the RISK of the money each time. What is called usually money management in trading is essentially RISK MANAGEMENT. 



VALID STATISTICS AND PREDICTABILITY
We must make here some remarks about the robust application of statistical predictions in the capital markets.

1) The theory that the efficient markets and in particular that they follow a pure random walk is easy to refute with better statistical experiments and hypotheses tests. The random walk would fit to a market where the sizes of the economic organizations are uniformly random. But the reality is that they follow a Pareto or power distribution, therefore this is inherited in the distribution of the volumes of transactions and also in the emerging trends or drifts. 

2) The statistical models of time series  are more robust , when they apply to the entity MARKET as a whole and are better as  non-parametric , and not when they apply to single stocks and are linear or parametric. The reasons is that  a time series as a stochastic process , requires data of a sample of paths, and for a single stock is available only a single path. While for all the market the path of each stock or security is considered one path from the sample of all paths of all the stocks. 

3) The less ambitious the statistical application the more valid the result. E.g. applying a statistical hypothesis test, or analysis of variance   to test if there is an up or a down trend (drift) or none, is a more valid statistical deduction , than applying a linear model of a time series and requiring prediction of the next step price. 

4) Multivariate statistics, like factor analysis, discriminant analysis , logistic regression,  cluster analysis , goal programming e.t.c.,  are possible to utilize for a more detailed theory of predictability and of portfolio analysis, and sector analysis of the market and not only H. Markowitz theory. 

5) In applying of the above applications of statistics, the researcher must have at first a very good "feeling" of the data, and should verify rather with statistics the result rather than discover it. 

6) The "Pareto rule of complexity-results" also holds here. In other words with less than 20% of the complexity of the calculations is derived more than 80% of the deduction. The rest of the 20% requires more than 80% more complexity in the calculations.

The science of ecology has applied with success, since the time of Volterra, the non-linear coupling equations of a) Domination b) Competition c) Cooperation , for living populations.
But during the last part of the 20th century the science of psychology ( Dr Gottman) has also applied with success (in helping couples to avoid divorce and resolve issues) the same equations as interplay in the couple of the underlying true emotions (as accumulated positiveness or negativity) during conversations.
And ,I , (as far as I know), apply for the first time the same equations to model the qualitative dynamics of Demand and Supply in the financial (and capital) markets. (a non-Marshalian approach to the demand supply, where the demand and supply are not considered independent).

We may classify 1) demand, or buyers as three types 1.1) Those that buy when the market prices increase following compelling behavior and mimicking other buyers. We call the buyer-bulls. Then 1.2) those buyers, that buy when the market prices fall, we call them buyer-bears, 1.3) Those that simply want to buy whatever the prices are doing. We call them buyer-horses

2) Supply or Sellers are also of three types 2.1) Those that sell when the market prices fall, following compelling behavior and mimicking other sellers. We call them seller-bull. Then 2.2) those sellers that sell when the prices rise. We call them seller-bears. 2.3) Those that simply want to sell whatever the prices are doing. We call them seller-horses

The combination of those 3 cases in any situation in the markets, as populations of demand and supply create 3*3=9 cases , that lead to 3  types of coupling Domination (buyer-horses/seller-horses or buyer-horses/seller-bears or seller-horses/buyer-bears ) Competition (buyer-bulls/seller-bulls or buyer-bears/seller-bears) , and Cooperation (buyer-bulls/seller-bears, or seller-bulls/buyer-bears),  as below. 

The qualitative analysis of their dynamics (as non-linear coupling systems of equations) give that

1) The Domination interplay creates waves , of stable, or diminishing or expanding amplitude, or flat stationary (ranging) fluctuations. More often produced by small populations of demand-supply and in smaller time scales.

2) The Competition interplay creates mainly Spikes and rarely constant trend. More often produced by medium size populations of demand-supply, and in mid-term time scales.

3) The Cooperation interplay creates constant trend.More often produced by large populations of demand-supply and in larger time scales.

As a result we have the 4 basic patterns of the price activity
a) Stationarity (ranging fluctuations), (in the average about 40% of the time)
b) Waves (e.g. special elliot waves usually called triagles in technical analysis),(in the average about 30% of the time)
c) Constant Trend (drift or momentum),(in the average about 20% of the time)
d) Spikes (extreme slope trend for a short time),(in the average about 10% of the time).

For example a currency pair (e.g. EURUSD)  is already a coupling of two economies (US and EU) , and this coupling is mainly or is rotating among the above three modes: Domination, Competition, Cooperation. Different economies are inclined to dwell more on one mode than another, depending on the global fundamentals of the economies, their trade, and interaction.

And the  most predictable effect modulated by  cycles (see post 5) is the reaction to an super-exponential moves (a blow-up at the end of trend in the form of super-exponential move or terminal spike).  (See e.g. https://www.ted.com/talks/didier_sornette_how_we_can_predict_the_next_financial_crisis    and http://www.er.ethz.ch/ Such super-exponential terminal patterns of trend may occur usually as result of overgrowth  of the one of the two populations in a demand-supply coupling rather that of domination and not so much of competition or cooperation. See also post 32. The frequency of emergence and the size of such  super-exponential blow-ups follows the law of inequalities in other words the Pareto or Log-normal distribution and is thus by fat more often than pure randomness would predict!).

THUS THE ORDER OF BETTER PREDICTABILITY IS 
1) LONG TERM PERMANENT TREND

2) A CYCLE IN THE ORDER OF PREDICTABILITY DESCRIBED ABOVE AND REALIZED AS REACTION TO SUPER-EXPONENTIAL TERMINAL MOVE (OR SPIKE).

Here in the chart below which is with the prices after taking the logarithm, we may watch deviations from the linear moves (super-exponential moves) and their highly predictable reaction lasting in the average 3.75 years. during 30 years!

The most usual pattern coming out from Domination is the waves. The most usual pattern coming out from competitions is spikes, and the most usual pattern coming out from cooperation is   a trend. The full qualitative mathematical definitions of domination, competition, and cooperation as well as the proofs that only the above 4 price patterns are the possible solutions is outside the scope of  a rather practical Blog like this.

The price waves created by the demand-supply follow of course the laws of periodicity and universal attraction or economic inequality as far as period and amplitude is concerned. 

If we plot histograms of the High-Low of bars at various time-frames it becomes apparent through their multiple histogram peaks, how, trends, and spikes are distinguished (Fan principle).

In the next part of the post we display the equations and diagram of the 3 interplays of Demand Supply.

1) The equations of domination  in non-linear demand-supply coupling (non-Marshalian demand-supply) are as the equations of pray-predator in ecology (Voltera's equations)

2)  The equations of competition  in non-linear demand-supply coupling (non-Marshalian demand-supply) are as the equations of competition in ecology.

3) The equations of cooperation  in non-linear demand-supply coupling (non-Marshalian demand-supply) are as the equations of cooperationin ecology and social behaviour.

All the above 3-types of dynamic coupling have been applied also in the psychology of social behaviour, and even in the psychology of behaviour of couples in the marriage 
(see "The mathematics of marriage" by Gottman, Murray, Swanson, Tyson, and Swanson, MIT press 2002. See also for the Voltera's equations "Models in Ecology" by J. Maynard Smith, Cambridge University press )
All of the above 3 types of non-linear coupling have been solved and their solutions have been classified. 
From their solutions come the 4 patterns described at the beginning of the post and elsewhere in this Blog.
The support-resistance levels of the prices represent the poles of the dynamic system, that correspond to the carrying capacity of the subpopulations of demand-supply.
For a non-coupled single population the equation is the equation of logistic growth of a population, and the asymptotic upper bound is the resistance level

http://mathworld.wolfram.com/PopulationGrowth.html

http://mathworld.wolfram.com/LogisticEquation.html