10. THE R.W. BABSON METHOD OF TRADING BY MEDIANS AND 1/3 OF THE PRICE MOVES. The power law of volumes and the law of financial action ( the Newtons laws of action) .

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.The statistical quantities from the front-office in trading need to me measured are the price position in the channel around the average, the velocity (1st derivative) and the acceleration-deceleration (2nd derivative), which is done as statistical quantities by a hypothesis test or confidence interval. The support-resistance levels can be measured also by action-volume histograms.  The measurements are done with convenient indicators, and can also define in a statistically valid way, not only , the channels , the trend, reversal, and Eliot-waves but also the spikes. In addition for the back-office of trading we need to measure the probability of success of trade based on the past history of trades, to apply the Kelly criterion, and also the average rate of increase of the trading funds and its variance again from the past history of trading.   (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. Linear time series models or derived like ARMA, ARIMA, SARIMA etc are destined to fail for particular patterns like those described in the post 32, because the true equations are non-linear and in addition with random, time varying coefficients that derive the random emergence of the 4 basic observable patterns (see post 32 ). In addition the standard application of the time series by the researchers,  focuses  on stationary time series after they extract  a stable exponential trend, while in the reality the main concern should be the random path of the average value of the prices that shapes the patterns and is neither constant exponential trend neither zero ! The "statistical momentum conservation" might then be nothing else than an hypothesis that the random and time varying 1st order in time steps , partial correlation of the prices , is always positive. This can be easily tested statistically. E.g. in the cross exchange rate EURUSD but also in the indexes, the partial correlation of the current to the previous time step bar is measured indeed positive, in almost all time frames, except at the daily time frame, where the cyclic behavior prevails. In the daily time frame the partial correlation is negative , which means if one day is up the next day it is more probable that it is down. In addition, the cyclic behavior is even stronger in pairs of two days with negative partial correlation (two days up two days down etc). In searching for random cycles or periodicity, of say a single index or even instrument , the valid statistical practice requires the creation of a sample of paths over a time interval of  a whole period, by collecting  the pieces of the path at different periods as the market move as far as the searched periodicity is concerned may be considered as moving independently at independent periods. 

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 , conjoint analysis, correspondence analysis, multidimensional scaling etc , goal programming etc are possible to utilize for a more detailed theory of 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 less hypothesis we use in applying statistical hypotheses, the better. That is why non-parametric statistics is better. An exception is our knowledge of the application of the Pareto distribution in various aspects of the market which we is parametric. 

That is why we avoid applying very complicated with many hypotheses and time consuming to estimate models to forecast the markets, but we prefer to respond to the market, by measuring only in a valid statistical way, the average position of the price, and the channel around it, the velocity (trend, 1st derivative) and acceleration-deceleration (2nd derivative)  of the prices. 

The statistical quantities from the front-office in trading need to me measured are 
1) the price position in the channel around the average, 2) the velocity (1st derivative) and 
3) the acceleration-deceleration (2nd derivative), which is done as statistical quantities by a hypothesis test or confidence interval. 
4) The support-resistance levels can be measured also by action-volume histograms.  The measurements are done with convenient indicators, and can also define in a statistically valid way, not only , the channels , the trend, reversal, and
5)  (Eliot) waves but also 
6) the spikes. 
7) It is required also an in advance in the past measurement and discovery of the basic stable cycles in the markets (see post 5)
8) An in advanced in the past measurement and discovery that trends duration and length, and volumes follow the Pareto distribution (see post 11,25 etc). 
In addition for the back-office of trading we need to measure the 
9) probability of success of trade based on the past history of trades, to apply the Kelly criterion, and also 
10) the average rate of increase of the trading funds and
11)  its variance again from the past history of trading.

The back-office statistical quantities in 9), 10), 11) are related , by simulation as e.g. in the simulator in post 43.

I have also created a simulator to experiment with different rules of withdrawals. 


There are many who complain that the indicators have lag, and prefer not to use indicators at all, but only the prices. This is rather stupid! The indicators when are measuring a statistical quantity  MUST have lag, because we are not interested for the price at the now only, but in a short-term past horizon too, which defines the statistical momentum which is statically conserved. It is not a race of speed, it is  a challenge of successful perception. The science of statistics is the best for the moment one can have , from the collective scientific thinking, and collective consensus, and we must  be honest and humble to admit is restricted abilities, but also trust , respect it and be confident for the success   when applying it. When we are applying the statistical mode of thinking for the markets, we never run serious dangers of being "burned"and "busted" in our deductions, as statistics claims everything only up to some probability, or probability inequality and intervals.  

There are some also that claim to have "intuitive guessing" about how the markets will move beyond the observable state of the markets. This of course cannot be included easily in  the standard statistical inference. But it seems to me that sometimes, this is in certain human and social environmental conditions is too much to ask from yourself, and it may fire-back to systematic opposite to the actual markets moves guessing! I believe that fortunately pure statistical inference from the observable states of the market only,  may be adequate for very profitable trading.   

Next we state intuitively the Laws of action of Newton for the markets, or the law of statistical momentum conservation as result of demand-supply polarity (see also post 22 ) and the Pareto law which is derived from the inequalities in the markets. 




0) The Power law of Volumes.

The distribution of the volumes, in a given granulation of time, follows a power or Pareto distribution. If take the logarithm of the sizes then the distribution becomes a straight line. This low follows and is an inherited property in the volumes of transactions, from the  well known and proved law of power or Pareto distribution of the sizes of (financial or nations) organizations. As a consequence more than 80% of the volume transactions are made from less than 20% of the organizations. 

1) The law of momentum conservation.

This law is somehow called in trading, "the law of trend following". On this conservation of the trend is based the success oof the trend following, as when a trend is detected, and we open positions we can have profit, only if the trend continuous for some time, which the trend conservation. Here the rule of volume enters too. The volume corresponds to the inertia mass (which is variable therefore), and as the momentum is measured as the product of speed and inetria, so the "momentum" of an instrument is estimated as the product of the price change during a bar (Close-Open),with the volume of transactions during the bar.  The reason that such a low exists in the financial  markets is closely related to the previous 0th power law of the volumes or  law of power or Pareto , which follows from the well known and proved low of power or Pareto distribution of the sizes of (financial or nations) organizations. If take the logarithm of the sizes then the distribution becomes a straight line. As a consequence more than 80% of the volume transactions are made from less than 20% of the organizations. At each time moment only organization is the winner (this holds even if two such maximal size organizations, are coupled in a domination mode interaction under some Voltera equations, see below)).  Thus when a very large winner organization decides according to their intentions to make a "transaction" , it will be so large, that it has to be executed in to a sequence of smaller packets, in a time interval, that will create a temporarily sustained conserved momentum or trend. 

The volumes measurement do provide better forecasting. The true rules of volumes are
1. A momentum acceleration is a true acceleration, if the volumes are increasing too.
2. A momentum deceleration is a true deceleration, if the volumes are decreasing too. 
Ofcourse the converse does not hold: An acceleration can be true, even if the volumes are not increasing. But if they are increasing we are sure it is true acceleration. The same with the deceleration.

2) The law of force and acceleration
While the law of the conservation of the momentum of financial activities is essential to have the ability of profit, in practice it is not the trend that has to be detected, as most people think but rather  the acceleration-deceleration of it.

In the financial markets, the "force" is through imbalance of  demand-supply and volume of orders and transactions.

To give a kinaesthetic key metaphor: Imagine your friend is driving the car with you inside, and you want a signal that he is going to turn 360 degrees backwards. If you wait to measure by the momentum of the car, it will always be after he has turned back and after some meters for the car to build opposite momentum. So it will be always late. While if you go by the acceleration as signal, you will feel the deceleration of the brakes quite before he turns the steering wheel. This simple realisation when converted to indicators is the basis for good anticipation (prediction, forecasting). It is like reading tomorrows newspaper.According to R.W. Babson it was what made him multi-millionaire. Present time traders use to term it as divergence in appropriate indicators.
Also according to the interpretation of volume as "inertia", the "force" of the coupling of the (non-Marhalian) demand-supply of populations, is best measured by the derivative (change) of the "momentum" (which involves also the volume) , and not only of the price.
Thus low volume times will have low inertia, thus big changes in the prices (high volaitlity) with small demand-supply forces.

3) The law of action-reaction

This law works through the law of polarity (see post 9) of demand supply, In other words that whenever there is a force of demand also a force of supply (and vice versa) is active in the markets. Also known in the slang of trading as Bulls-Bears. It was the favorite law for trading of Roger Ward Babson who was claiming that it was what made him multi-millionaire.

The action-reaction of Demand-Supply is in detailed described by the 3 modes of the coupling equations of Demand-Supply (see post 22 and 32).

For similar metaphor of laws from physics to social action, see also the interesting talk of the Google marketing manager on Physics and marketing at TED.com


http://www.ted.com/talks/dan_cobley_what_physics_taught_me_about_marketing.html


 In short the basic 3 modes of non-linear  interaction of populations or volumes  orders are


a) Win-Lose (Domination or pray-predator)


b) Lose-lose (Competition)


c) Win-Win (Cooperation)






You can even conveive 3 phases of the evolution of capitalism according to what


prevails statistically the a) Domination (Win-Lose) or Tyranny b) The


Competition (lose-lose) or the present state of capitalism c) The Cooperation


(Win-Win) or Meta-capitalism.






These 3 modes give rise to 4 patterns of price action (singularities)


a) Lighnings (or spikes)


b) Winds (or Trends in the  market)


c) Cyclons (or wavelets or technical analysis' triagles and rombs)


d) Calmness (flat noise or ranging market)



THE R.W. BABSON METHOD OF TRADING BY MEDIANS AND 1/3 OF THE PRICE MOVES. 

Here is the link where you can read the Dr Alan H. Andrew method and Roger Ward Babson method to implement the present law of Newtonian  momentum conservation and action-reaction through equality of  2 last successive waves (median lines method or pitchfork) . This method predict the next wave (from the previous) as well as the next reaction (or retrace). It is also one more application of the principle that the prediction based on the smallest discrete step memory (here one last full period wave) has also the least prediction error (exactly as in ARMA(1,1) time series as in the philosophy of Box-Jenkins). In the absence of a longer time frame trend, the  action and reaction are equal.  It also is used to place both the take profit and stop loss which are both  tight and trailing with SL<=TP. In particular this method shows that "random" deviations of the exact rule, are propagated in the next prediction creating therefore the way that markets move in  "seemingly" random ways. This method has much similarity with the forecasting method of ARMA(1,1) time series except here it is not numeric or algebraic  but rather pictorial  geometric or vector space analytic. In this method the part ofthe price motion that is predicted is rather small , but probably quite certain and occuring very often! 

Roger Ward Babson (https://en.wikipedia.org/wiki/Roger_Babson) had correctly predicted the great depression crisis of 1929 with his method above. He was friend with I. Fisher, and both became ill with tuberculosis, a deadly disease at their time (like cancer nowadays). But both with their confidence and keen self-discipline through working in the open fresh air and healthy life, managed to cure themselves. R.W. Babson became multi-Millionaire and thought so much as his lucky concept the action-reaction Newtonian law, to predict the seemingly random fluctuations of the markets, that he bought the house of Sir I. Newton.

http://www.trading-naked.com/alan_andrews_course_1.htm


also


http://amgallo.com/trading/bisects.htm


and
http://www.medianline.com/


A book:
http://www.amazon.com/Best-Trendline-Methods-Andrews-Techniques/dp/0965051838/ref=pd_bbs_1/002-2167389-1442403?ie=UTF8&s=books&qid=1194482162&sr=1-1


and another book


http://www.median-line-study.com/median-line-books.html#finding


and still another book
http://www.amazon.com/Trading-Median-Lines-Mapping-Markets/dp/0972982906/ref=sr_1_3?ie=UTF8&s=books&qid=1309594739&sr=1-3