57. Economic inequalities and forex or stock exchanges trading.

ANYONE WHO WILL TRY TO MAKE MONEY SOLELY BY TRADING AND SUCH SYSTEMS OF TRANSACTIONS SHOULD BE AWARE THAT THERE IS A VERY POWERFUL AND ALMOST UNBEATABLE COLLECTIVE WILL SO AS NOT TO SUCCEED!  NO-ONE WANTS  PEOPLE TO QUITE THEIR JOBS AND MAKE MONEY THIS WAY AS IT IS SOMEHOW PARASITIC. IT IS IN SOME SENSE  UNETHICAL AS A PRACTICE ENFORCEABLE  TO  THE MAJORITY. AND OF COURSE NEITHER THOSE WHO HAVE LARGE CAPITAL  WANT THAT A MAJORITY WILL MAKE MONEY THIS WAY, AS THEY WOULD PREFER THAT THEY WORK IN THEIR COMPANIES FOR THEM. ONLY IN SPECIAL CONTINGENCIES AND SITUATIONS SOMETHING LIKE THIS WOULD BE ETHICAL. AND IN PARTICULAR A HIGHER MORALITY THAT WOULD SUPPORT SUCH A PRACTICE, WOULD BE PROVABLE WITH COLLECTIVELY BENEVOLENT DEEDS FROM A POSSIBLE SURPLUS OF SUCH MONEY!

It is mentioned in some places in this blog , and also in its subtitle, that trading may contribute in reducing economic inequalities. How is t so?

Let us concentrate at first on stock exchanges trading (securities, commodities derivatives etc).

 It is known that the economic system operates withing economic inequalities, and the statistical distribution shape of these inequalities is the a power or Pareto statistical distribution. (See e.g. http://en.wikipedia.org/wiki/Pareto_distribution ).

From this it is derived also the Pareto rule: "More than 80% of the wealth of the society is concentrated in less than 20% of the population".

In domestic economies the economic inequalities of annual income are also measured with the Lorenz curve, and the Gini index . (see e.g. http://en.wikipedia.org/wiki/Lorenz_curve  and http://en.wikipedia.org/wiki/Gini_coefficient ).

Let us assume that the traders of stock exchanges have a Pareto distribution of  foresting abilities, so that a tiny minority, has very good forecasting abilities and is winning while  the  majority has inadequate forecasting abilities and is losing. Let us furthermore assume that locally stock exchange trading is a zero-sum game. E.g.  by making the accounting of profit and loss daily (mark-to-market accounting) even on still open positions. This is not literally so in general. Investing in the stock exchanges is not a zero-sum game, as e.g. if all are buy-and-hold investors then all  may win simultaneously or all may lose simultaneously when all securities go up or all go down. 

Now if we may assume that forecasting abilities are not correlated with volume of trading , among the winners will still hold a Pareto distribution of the volume of trading, and among the losers the same. Now a trader who is winning, as we assume a zero-sum  game, will take his profits, from losers that follow a  Pareto distribution of losses. Therefore most of his profits will be from a minority of large players and less of its profits from a majority of small traders. Now if the trader himself is a small trader, this means that his gains are mainly from more rich traders, therefore inequalities are reducing. But if the trader is e.g. the largest trader, then his profits will be from smaller traders, (still most of the profits from comparatively large traders) so inequalities are increasing. As a total of trading in the Stock Exchanges , because the volumes of trading are mainly from large traders, the inequalities are increasing (which is the same with the profits of real business too, outside the stock exchanges). But the isolated effect of winning small traders is decreasing the inequalities , while the isolated effect of losing small traders, is increasing the inequalities!
There is a critical size of the assets of the trader, that decides of his trading increase (regressive trading) or decrease inequalities (progressive trading) . Funds with larger size , and winning trading increase the inequalities, while winning trading with funds of smaller size decrease the inequalities. This critical size is the median of the Pareto distribution. Now this median defines a quite large size of funds , more than one could expect.  

Let us now concentrated on forex trading. The same hold as above, with the exception, that in forex we have a class of largest traders, the major 10  banks, who are systematic forex winners, because they have inside information what will happen with the currencies as their customers exchange currencies through these banks, therefore by knowing the transactions of tomorrow of their customers they know which currency will go up or down, and thus they can win rather safely in forex trading. Of course the forex trading of these major bank-players is increasing the economic inequalities. 

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

56. Another example of automated trading. Stable neutral-trend grid trading.

ANYONE WHO WILL TRY TO MAKE MONEY SOLELY BY TRADING AND SUCH SYSTEMS OF TRANSACTIONS SHOULD BE AWARE THAT THERE IS A VERY POWERFUL AND ALMOST UNBEATABLE COLLECTIVE WILL SO AS NOT TO SUCCEED!  NO-ONE WANTS  PEOPLE TO QUITE THEIR JOBS AND MAKE MONEY THIS WAY AS IT IS SOMEHOW PARASITIC. IT IS IN SOME SENSE  UNETHICAL AS A PRACTICE ENFORCEABLE  TO  THE MAJORITY. AND OF COURSE NEITHER THOSE WHO HAVE LARGE CAPITAL  WANT THAT A MAJORITY WILL MAKE MONEY THIS WAY, AS THEY WOULD PREFER THAT THEY WORK IN THEIR COMPANIES FOR THEM. ONLY IN SPECIAL CONTINGENCIES AND SITUATIONS SOMETHING LIKE THIS WOULD BE ETHICAL. AND IN PARTICULAR A HIGHER MORALITY THAT WOULD SUPPORT SUCH A PRACTICE, WOULD BE PROVABLE WITH COLLECTIVELY BENEVOLENT DEEDS FROM A POSSIBLE SURPLUS OF SUCH MONEY!

In this post we present the finding of another example of a good automated trading. The method is that of grid trading, on a grid of levels 50 pips apart. There is no trend detection. Only trend-neutral grid trading. Grid trading is essentially the trading the the market makers and liquidity providers utilize in fast frequency, and small grid-levels around the bid and ask. 
The market behavior behind such a trading system is double
a) The histogram of draw-down and draw-ups in a chart of prices is a Pareto or Power distribution and not a normal distribution 
( It is a quite well known property and has been proved by many researchers. For example see this one here (from Scotland )

http://www.ted.com/talks/didier_sornette_how_we_can_predict_the_next_financial_crisis

and also this scientist here who is proving this distribution for all the companies, and.......cities. See also post 25.

http://www.ted.com/talks/geoffrey_west_the_surprising_math_of_cities_and_corporations

b)  The smaller the time scale in the markets the longer the time intervals that the market is stationary with trend-less neutral volatility (see also post 12 the inter-scale law of the markets)

This grid trading algorithm is not based on any type of pattern like continuations or reversal, or channels, or on any pattern recognition method or system of indicators, or candle stick patterns etc. That is why it is simple in its programming logic, and the simpler the algorithm the more robust and stable its performance. It is based on the simple statistical assumption that there are horizontal equilibrium levels of the prices (both support and resistances) , around which the markets fluctuate with a constant (random variable) distribution.  

The particular grid trader we present here , applies group-take profit on trades (not individual trades take profit). It applies pyramiding and escalations at 50-pips levels of a grid , which are the optimal trading for trends or micro-trends that have a histogram which follows the Pareto distribution (post 25). It has  a timer of acting every of 15 minutes,

The grid-trader is of less profitability compared to the other examples of automated trading. E.g. here it is about 18% annual at 23% 5-year maximum draw-down. In other words for a 30% 5-year maximum (floating) draw-down the average monthly rate of return is about 2%-2.5%. This is as far as I know the score of the most successful grid-traders in the web too. This performance of 2.5% monthly , or 25% annual , at at a 5-year max Draw-down of 30% is low compared to other automated non-grid trading systems (e.g. those n posts 50, 51, 51 etc) that may go to 10%, 15% even 20% monthly. The difference here is that most of the automated systems have a forward life-cycle (that is , forward duration that are profitable) for 1 at most 2 years. And at the end of their lives they may lose you considerable part (some times all) of the hither too profits.  BUT the grid traders have a much longer life-span that may go far beyond 5 years. In addition the have a uniform flow of profits so that every month is profitable. This compensates for their lower profitability performance. In particular it is seen from the detailed statements below, that EVERY month is profitable, in this grid-trader!

But the advantage is the statistical stability of it which is based on definitely verifiable statistical properties of the markets as above a) and b).

 5-years back-test 2009-2014

Detailed report of the 5-years back-test 2009-2014  is here

https://dl.dropboxusercontent.com/u/107295772/Old_hedge_weaver_likerealestate_grid500_FBack_spraed12_alparioptimal_m15open_2009_2014.htm

And an analysis by the MT4i or Fx-blue site here

http://www.fxblue.com/users/neutral_grid_trader/stats

55. The CORRECTIVE ESCALATED IMPROVISATIONAL INTERPOLATION (GRID TRADING) method in trading after the KELLY CRITERION measurable from the trading history .

ANYONE WHO WILL TRY TO MAKE MONEY SOLELY BY TRADING AND SUCH SYSTEMS OF TRANSACTIONS SHOULD BE AWARE THAT THERE IS A VERY POWERFUL AND ALMOST UNBEATABLE COLLECTIVE WILL SO AS NOT TO SUCCEED!  NO-ONE WANTS  PEOPLE TO QUITE THEIR JOBS AND MAKE MONEY THIS WAY AS IT IS SOMEHOW PARASITIC. IT IS IN SOME SENSE  UNETHICAL AS A PRACTICE ENFORCEABLE  TO  THE MAJORITY. AND OF COURSE NEITHER THOSE WHO HAVE LARGE CAPITAL  WANT THAT A MAJORITY WILL MAKE MONEY THIS WAY, AS THEY WOULD PREFER THAT THEY WORK IN THEIR COMPANIES FOR THEM. ONLY IN SPECIAL CONTINGENCIES AND SITUATIONS SOMETHING LIKE THIS WOULD BE ETHICAL. AND IN PARTICULAR A HIGHER MORALITY THAT WOULD SUPPORT SUCH A PRACTICE, WOULD BE PROVABLE WITH COLLECTIVELY BENEVOLENT DEEDS FROM A POSSIBLE SURPLUS OF SUCH MONEY!

The CORRECTIVE ESCALATED IMPROVISATIONAL INTERPOLATION   from a support-resistance level, trading method. This method is designed essentially for the difficulty of the very short time frame (e.g. even minutes bars, if there is free time during the day) of stationary markets rather than daily or annual trending markets (which are very easier to trade) although it very well apply to trending markets too. 

In the discussion below we must not conceive the pyramiding and escalation 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 or escalation 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. 

The general psychological feeling of the corrective escalated improvisational interpolation, is that it is the simplicity with which we may deal with the chaos of the randomness of the stationary  markets. We may very often start against the market, but what ever the market does we respond continuously and in a rather improvisational  way, till we close following the market. And although   we  are never very exact at forecasting the market,  we are almost always gaining! 


THE TOP 6 FACTORS OF ATTENTION IN MANUAL TRADING ARE

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 WITH MARGIN ,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 OR AT LEAST STRONG AND CLEAR SEASONAL 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). The statistical quantities 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 , and Eliot-waves but also the spikes. 

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

5) READ THE NEWS AND FINANCIAL STATEMENTS BUT 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 RESPONDING TO THE MARKET AND DO NOT HESITATE TO FOLLOW PROMPTLY ANY UNEXPECTED CHANGES OF THE TREND OF THE MARKET, ALWAYS WITH GRADUAL BUILD OF THE POSITION. (This is called by Bill Williams his psychological Holy Grail in trading)

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. 

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)

THE OVER ALL STATISTICAL BEHAVIOR OF PRICE PATTERNS

We notice that although the price patterns are essentially  4 categories in details there are 6 distinct statistical patterns of the random or statistical position, velocity and acceleration of the prices (see post 32).

A class of stochastic processes can be defined as the behavior of the markets based on these   6 basic patterns P1, P2, P3, P4, P5, P5, P7. The Pi i=1,2,3,4,5,6,7 are essentially random  statistical patterns with random and variable parameters of size duration, and relative analogies that define them. E.g. we may have a Pareto distribution of the duration and price height of the patterns because of the inequalities in the markets. The 7th pattern P7 of stationary behavior  we may call intermittency pattern.  We may then assume a class of Markov processes  with random and variable transition probabilities, where each random type of pattern occurs and then a next one occurs. Bu the transition probabilities are not arbitrary! E.g. spikes occur usually at the begging (initial spikes)  and the end (terminal spikes) of trends, up and down trends with stationary channels in between them, shape cycles, that in the average of stable period, and some times of fixed beginning and end. 

The probability that a type of pattern occurs changes also according to the time scale. In 2, 5 or more years annual bars time frames, the non-waving trend pattern is dominating, while say in 5-minutes bars time-frame flat patterns are dominating. 
We notice that, by utilizing only pattern P3, of non-waving trend, and intermittency P7 we may derive all, other patterns with appropriate patterns of transition probabilities of the P3! I have coded a simulator of such a class of stochastic processes, superimposed on many time frames called Multi-time scales Rainbow Walks stochastic processes. 

This is the overall behavior of patterns of the markets, and there are some invariant properties  like 

1) Cyclic behavior as alternation with up and down trend patterns with flat channels at the bottoms and tops  

2) Statistical momentum conservation (see post 10) where the 1st time-step partial correlation of a price is almost always positive, 

3) A Pareto distribution of the duration and height of the patterns, due to the inequalities of the enterprises in the economic system (see post 10, 25, 57,63 )

REDUCING ECONOMIC INEQUALITIES
Since more than 80% of the volume of translations in e.g. FOREX  is from less than 20% of the Banks, it is obvious that a profitable trading method, draws profits mainly from the ultra large capital of the banks. If the traders are households, this means reduction of economic inequalities. That is why I prefer making money with methods that reduce economic inequalities like trading, rather, than selling tools, seminars and indicators, to households that try to make successful trading as that would subtract money from the little players and households.

In the discussion below we must not conceive the pyramiding and escalation 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 or escalation 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. 

The corrective escalation method, is essentially the method behind the grid-trading and grid robot traders. Except in grid trading it is 100% not based in technical analysis of price patterns, while the corrective escalation, requires say 20% of technical analysis and pattern recognition in many time frames.
This method is designed essentially for stationary markets rather than trending markets although it very well apply to trending markets. 
Grid trading robots are best for high frequency trading, and are based entirely on the property of the markets that all draw downs and draw ups of the price charts, follow a Pareto or power distribution. See also post 25 . The next video describes a scientific tested method of predicting in some cases (not all cases) the markets, based on the above property of the markets (that that the draw downs and draw ups of the price charts, follow a Pareto or power distribution) by the Institute of Didier Sornette
http://www.ted.com/talks/didier_sornette_how_we_can_predict_the_next_financial_crisis

The trading method may apply very well to binary options.

According to this method it is not so important the pattern recognition method and the pattern recognition in other time frames, or the focus on the 3rd wave in the current time frame, as it is the interactive-corrective continuous adjustment and escalation of the position. This method is designed essentially for short term , stationary markets with opposite changing micro-trends , rather than long-term trending markets although it very well apply to long term trending markets.  News may be involved in the decision to trade the particular time or may not be involved.  Less than 20% of the success is  in the initial high probability forecasting based on charts, technical analysis, indicators, and pattern recognition, and more than 80% of the success is on the corrective escalation technique after the Kelly criterion of (variable) probability of success. We may start at a support-resistance level, (which may be the boundary of the channel of a continuation pattern, or its final mid level line) and we open position at the most probably direction of little size only.  In predicting we assess the dynamics of the pattern in the focus time frame, but we also speculate and test the opposite prediction, and we assess which is more probable, and in accordance with the most clear pattern dynamics, of the consecutive 3-4 neighbor time frames. If the assessed probabilities are say 55%, 45%, we might not choose to trade, but we might wait to find assessed 80%, 20% probabilities. We always prefer of course the waving patterns after the domination coupling of buyers-sellers, and even better the 1st, 2nd or 3rd vector-wave of channeled trend, at the faster two time frames (spikes included here as 1st and/or 2nd vector-wave).  If we do not predict well and the prices go to the opposite direction we increase and open in the opposite direction , and we repeat it so as to have always a net position size towards where the prices are going. We do not use stop-loss as the role of the stop loss is the level where we open the opposite position. When the market breaks out finally to a direction we escalate (pyramid) and increase further the position. Typical sequences of position sizes are (1,-2,3, 5,4,3,2) or (-1,2,-3,5,4,3,2 ) where mins sign means betting downwards.  We close by trailing or to the next support resistance level. Or we close at the predicted (by Babson median) end of a wave-vector between the 1st and 3rd (in Elliot counting).The starting leverage is usually 1 and increases to 2,3, etc. While the percentages f of risked funds, start with 1% and in the average it is safe if it is at the 5%-6%. In general if p1 is the probability to win a trade, and p2 the probability to lose it (p1+p2=1), and the reward-to-risk ratio is equal to b, then the percentage f of funds risked in the trade should be about f=(b*p1-p2)/b. This is the Kelly theorem (see  http://en.wikipedia.org/wiki/Kelly_criterion ). Nevertheless we prefer to risk initially in the average only 5%-10%, of what the Kelly formula suggests, that is about 2%, and the reason is that after simulations (see post 43), the paths with 2% exposure, are much more smooth and psychologically bearable in their volatility and draw-downs, compared to the exposure suggested by the Kelly formula! The probability of success or forecast  probability of up or down is assumed here variable which explains the escalation process, and we may assume that at the beginning as the market is at a support-resistance the probability of up or down is very close to 50%.    As the probability of up or down increases we increase also the position size. This may include both the classical moyen or the classical pyramiding. Some people like the psychology of moyen as it  starts always in opposite direction to the movements of the market and closes following the direction of the market. Let us say that with pattern recognition we have a success rate of 65% and the reward-to-risk ratio is 70% , then by the Kelly formula we must not exceed risking (0.7*0.65-0.35)/0.7=15% If it was a pattern recognition with 70% success rate (something very difficult) then the Kelly exposure would be 39% ! With the CORRECTIVE ESCALATION let us say that we start say with risking 1%, and then we correct in the opposite direction with  2% and then we re-correct in the initial direction with  5% (in total 1%-2%+5%=4% in the correct direction or -1%+2%-3%+5%=3%),then  we continue pyramiding  with 4%, then 3%, then 2% and no more. Thus in total 4%+4%+3%+2%=13% thus less than the Kelly exposure.Such sequences of trades are called excursions, and permit the definition of hierarchical sampling, where while at the level of trades the success rate may be say 55% at the sample layer of excursions it may be 75% or higher. With the CORRECTIVE ESCALATION we have the chance, even if the probability of an up or down move to be 50% to increase the success rate of the trades, to 70% - 75% with the above sequence (given of course the average momentum conservation).
Although we start with an assumed probability of success rate of the individual trades close to 50%, and we start with exposure (that is % of risked funds from 1% ) , after some trades (preferably about 30) we have a sample to measure it!. If e.g. the sampled measured success rate of the individual trades is 65% , (and e.g. a binary options broker gives us reward to risk ratio 70%, or our particular non-binary options trading with stop loss and take profit gives us reward-to-risk ratio 70%) then the Kelly criterion formula calculates for us an optimal exposure of (0.7*0.65-0.35)/0.7=15%. This would be the upper limit of exposure for us , starting from 1% and escalating to 15%. In other words the success rate for the Kelly criterion is practically measurable (from the history of trading of the back-office and not from the charts of the front office)! This is very important for the corrective escalation method! And at the beginning till the 30 trades, we have not a reliable method to measure it, this is another reason , why we start with very small and safe exposure of 1%. Also at the beginning of an excursion of trades, we may have not assessed well the market, while after some tardes we know it better, and thus we may calculate the success rate. This also filters out some weird situations of markets, where they are not well predictable and the low success rate at the excursion , suggest to us to abandon trading for that particular time, and come back again another time. 

The trading method may apply very well to binary options. For practical reasons, and in order that trading does not ruin other daily activities of life, it is best to , apply the corrective escalation on binary options on daily only frequency not faster. Then an excursion of trades, would be say for options expiring in a few days, or weekly expiration. Then the corrections and escalation are done not on equal  grid-distances but on equal time intervals, which are days. The Kelly criterion applies very well as the reward-to-risk ratio is directly given by the broker, and the success rate of past trades is also not very difficult o calculate from the list of expired positions in the account. Finally the percentages of exposure is also directly apparent from the amount bet each time relative to the size of the funds of the account.

The method is called interpolation because, it is not really necessary to know the exact bounds of a  channel, but rather its average middle line only, and all other levels of positions are somehow equally spaced, as grid around the middle channel line. In this way we substitute exact bounds of the trades with a random distribution of positions (grid-trading or interpolation) , that copies the random distribution of the flow of the prices movements. Only a massive random flow of positions can handle the random flow of price movements. The uncertainty of the future movements of the prices is reflected, in the massive distribution of smaller positions, that continuously re-adjust. In this way also the bad psychology of " I made a mistake opening this positions" or "Ï should open it in another place of the prices" or "I should open position in the opposite direction"   becomes weaker and weaker.  The rules of the interpolation are the next.

1) FOR FLAT CHANNELS , above the middle channel line (or also a support resistance level) we sell, and bellow the middle channel line we buy. The channel may be a Bollinger Bands of two standard deviations and of number of periods half the period of the closest active price cycle in the time scale we trade. We prefer non-decreasing width channels, for this method. The size also of buying increases as we get away from the middle line (according to a rule we decide)  This is the adjustment part (or moyen) of the corrective interpolation. We consult charts at two more slower time frames at least 5 times slower than the fastest and focus time frame, to assess the quality of the probability  or risk of the forecasting. We may have open positions simultaneously in opposite direction if e.g. the channel break out. The statistical quantities 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 , and Eliot-waves but also the spikes. 
2) FOR NON-FLAT BUT SKEW CHANNELS  we apply the Elliot waves. In the Elliot sub-waves of a trending channel we escalate (or pyramid) the volumes of the positions so that in the average per sub-wave the position increases according the numbers 5,4,3,2,1 ,for the first, second, third, fourth and fifth Eliot sub-wave correspondingly. Opening positions at break-outs of a channel is good only for non-waving trends, if we can predict that. But as in corrective escalation the opening of the position is grid-based and gradual we may open with a small size at a breakout and increase at he 3rd wave if the trend is after all waving or pyramid of it is not waving. We consult charts at two more slower time frames at least 5 times slower than the fastest and focus time frame, to assess the quality of the probability  or risk of the forecasting. This has been applied essentially by Bill Williams in his older books. We may have open positions simultaneously in opposite direction if e.g. the channel turns unexpectedly from a trend to a flat continuation pattern. 
3) FOR SPIKES and during the spike , we only escalate , we do not adjust , with the numbers 5,4,3,2,1 . And after the spike and during the reaction of the spike, in direction according to if the spike is initial or terminal. We consult charts at two more time frames at least 5 times slower than the fastest and focus time frame, to assess the quality of the probability  or risk of the forecasting , in other words if the spike is terminal or initial. We may have open positions simultaneously in opposite direction if e.g. the market continues in an expected way to the opposite direction.
4) FOR LONG TERM STABLE TRENDS.  When in the market there is a long term stable trend, a very good starting point to open a position is at a terminal spike opposite to the trend . We open at the opposite direction  of the terminal spike, thus in the direction of the long term trend. Due to the terminal spike, we may exceptionally put a very tight stop loss. We consult charts at two more time frames at least 5 times slower than the fastest and focus time frame, to assess the quality of the probability  or risk of the forecasting of the trend.This is essentially the basic way of the Bill Williams trading in his more recent books. We may have open positions simultaneously in opposite direction if e.g. the market continues in an expected way to the opposite direction.
5)THE ONLY CERTAINTY IN TRADING WITH MARGIN.  FIRST PRIORITY IS TO BOUND LOSSES WITH THE KELLY CRITERION. At each state of the multiple positions usually there is an expected move in some direction of the market. It is of primary priority that we have set opposite direction orders ,playing the role of stop loss, of doubling each of the open positions, at some critical level that signifies move of the market in the opposite of the expected direction . In this way  at a worst case scenario, we have bound  the losses , according to the size of the total position , and be sure that are never larger in the percentage from the accepted limits, that are e.g. 1%-6%, or  as the Kelly criterion defines. It is the only certainty that we can have in trading. 
6) THE CLOSING OF THE EXCURSION OF POSITIONS.  We may apply all-group-take profit or partial-group take profit of the positions, while opening at the opposite direction as stop-loss, according to the pattern action. In other words the first time all the open positions gaining or losing have in total a predetermined profit, we close all positions.
7) ONE SIDED DIRECTION CASE.  If we want to apply the corrective escalation improvisational interpolation method to one sided,  up only trading on stock indexes , at short time scale (e.g. 5 minutes or hourly bars) we start the excursion at up ward only cases. But if the short time scale market moves surprises us by turning from trend to stationary channel or from stationary channel to downward trend etc, the instead of closing the position by a stop loss, we correct it with opposite direction positions as above , till we close with a group-positions total profit of the excursion of positions. 
8)  CONSTANT RATIO WITHDRAWAL RULE . We may divide the funds to 2/3 of them that we trade, and 1/3 that we do not trade. The exact percentage should be defined by the ratio (f=R/a^2) (that we mention in posts 13, 1nd 33 from the book  "Stochastic Differential equations" by B. K. Oksendal (Springer editions) page 223, example 11.5)    where R is the average per period rate o return of the trading on the used funds, measured on a sample of periods and a^2 is the variance of this rate of return on this sample of  periods.  E.g. of the rate of return is 10% per period and the standard deviation a of it is 34%, then the percentage f is 2/3. Each period we re-adjust the total funds so that this ratio f applies as division of the funds. As the sample of measurement of this ratio is not small, usually it remains rather constant. We withdraw e.g. from the 1/3 non-trading funds ,each period never more than  half of the average profits per period of the other 2/3 of the funds that are traded. The current  withdrawal rule that e.g. has been applied for many years by professor Michael LeBoeuf in his investments (see https://en.wikipedia.org/wiki/Michael_LeBoeuf and http://www.nightingale.com/beat-time-money-trap-mp3.html ))


The back-office statistical quantities 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.

The general psychological feeling of the corrective escalated improvisational interpolation, is that it is the simplicity with which we may deal with the chaos of the randomness  of the short scale stationary  markets. We must not have an attitude that we "possess" the market, because it will spoil our psychology. We must keep a psychological  distance from the market , but also have a keen awareness of its observable moves.  In the successful conduction, it is required a correct balance between changing MENTAL IMAGES of a changing  forecasting, FEELINGS and beliefs from what we see in the market and our positions and our ability for faster response by positions, than the moves of the markets, and successful ACTION  of adjusting and opening and closing positions. And  It is important to feel that we are able to adjust faster our positions than the speed with which the market moves. And it is important to be aware that what we feel and believe during such fast and short time scale trading is not enforced without our consent by a possible discrepancy of our  choice of some open position and direction that the market moves. In fact in this method of trading it holds that we FOLLOW THE MARKET rather than we predict the market. Because we continuously correct our position. Eventually  because there is something that may be called "statistical conservation of the momentum of the moves of the market", we end up being successful. We may very often start against the market, but what ever the market does we respond continuously and in a rather improvisational  way, till we close following the market. And although   we  are never very exact at forecasting the market or level where we open positions ,  we are almost always, and in more than 80%  of the excursions, gaining! 

If there was in the market a constant on-going trending channel only, the escalation should not apply, and only the adjusting is the optimal trading as it has been proved mathematically (see post 3). But if the trend has a finite duration following the Pareto distribution , then the escalation too is optimal trading (see post 25). 

The automated trading as in the post 56, is a simplified example of the corrective escalated adjusting interpolation, where we do not apply channel pattern recognition, but only blind escalation and adjusting interpolation.