Uncommon Theory-Mathod

Chaos Theory'

A mathematical concept that explains that it is possible to get random results from normal equations. The main precept behind this theory is the underlying notion of small occurrences significantly affecting the outcomes of seemingly unrelated events. Chaos theory has been applied to many different things, from predicting weather patterns to the stock market. Simply put, chaos theory is an attempt to see and understand the underlying order of complex systems that may appear to be without order at first glance. 

Related to financial markets, proponents of chaos theory believe that price is the very last thing to change for a stock, bond, or some other security. Price changes can be determined through stringent mathematical equations predicting the following factors:
1) A trader's own personal motives, needs, desires, hopes, fears and beliefs are complex and nonlinear.
2) Volume changes
3) Acceleration of the changes
4) Momentum behind the changes
Chaos theory is highly controversial and extremely complicated.

 The science of chaos has given us a couple of principles that are applicable in the financial markets:

• You, your nails, your market orders follow the path of least of resistance

• The path of least resistance is determined by the always underlying (and typically unseen) structure

Let us say you have a river running down the mountain. The behavioural decisions that the river makes does not depend on the mind of the river but the riverbed itself. So if you have a riverbed that is shallow and narrow that river is going to go down in rapids. If you have a riverbed that is wide and deep you are going to have a calm pond. So if you want to change the flow of that river you can get buckets and start a bucket brigade or go up to the start of the river where the force of the water is still so slow that it only takes replacing a few rocks to change the direction and it will change everything.

Then there is this thing called the butterfly effect.

That theory simply says that somewhere in South America there is this little Monarch butterfly that flaps its wings as it is flying around looking for some pollen and it sees a flower over here and as he is going there he sees a better flower somewhere else and decides to change its path. As he changes his mind, that is a fractal. The change in his path sets up a little air current and that air current sets up another air current that sets up another air current that keeps the high level winds off of the Antarctica which causes a hurricane like the El Niño, which causes a drought next year in the bean belt and we are going to have beans in the teens because of this little Monarch butterfly that changed his mind.

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So how do we trade fractals and what do they look like on a chart? 

• A fractal is a trend change
• A swing top or a swing bottom is a fractal
• The end of every Elliot wave is a fractal
• A fractal requires a minimum of five bars
• Fractals show the path of least resistance
• A fractal trading system works in all time frames

In the example below you have the market going up as evident by the highs. All we care about here is the highs and not the open, high, low and close. Any time you have a sequence of five bars where you have one bar that has two preceding lower highs followed by two preceding lower highs you have a fractal.

If you have a fractal whose middle finger is parallel to the top, the second one does not count. They both count as one (as in the case below where you have two candles whose highs are identical). In the chart below you see how the market started trading up, changed its mind and now it is going down. Coming up, the left leg must be longer than the right leg for a buy fractal to be valid.

 

After the buy fractal triggers a long position, the sell fractal is negated. For a new sell fractal to set up you will need to see a high, followed by three lower lows and two higher lows, none of which can trade through the high of the first bar. When you have a fractal in one direction which is followed by a fractal in the other direction you have an Elliot wave of one degree or another.

 

So this market started trading up the page, changed its mind (like the Monarch butterfly) and traded down the page. It then changed its mind again and traded through the previous high, just following the path of least resistance. By religiously taking trades only when fractals break, we effectively rule out fighting the market. The challenge, of course, is to avoid double tops/bottoms and not get caught long on up thrusts and short on springs.

 You always hear that what goes up must come down but one of the things that chaos teaches us is that Newton's laws of motions do not apply universally. They apply to man-made things. Market fundamentalists have a fundamentally flawed conception of how financial markets operate. They believe that financial markets tend toward equilibrium.

Equilibrium theory in economics is based on a false analogy with physics. Physical objects move the way they move irrespective of what anybody thinks but financial markets attempt to predict a future that is contingent on the decisions people make in the present. Instead of just passively reflecting reality, financial markets are actively creating the reality that they, in turn, reflect. There is a two-way connection between present decisions and future events, which George Soros calls reflexivity.

So having said all that; when do I want to be in a trade?

• when I can make the most amount of money in the least amount of time
• when volatility explodes and ranges expand
• when odds increase of a directional move
• when risk:reward is favourable

You do not want to put your hard earned cash at risk in a market that just moves about randomly but get onboard a market that has clearly signalled that it is done consolidating and now ready to move.

Look for inside candles (range contraction) and then a break uptown or downtown (range expansion). As a rule of thumb, the longer the timeframe the rarer the trade but the more powerful the signal will be.

Also the more inside candles within inside candles the more powerful the signal will be. The reason is that the more time traders have to build positions the bigger the effect as these positions are unwound.

Below is a great example of how just by looking at candles you can pinpoint the most opportune time to get in.

Only imagine how many traders looking at overbought indicators either sold out too early or faded the move.

 

Fractals 

 Many people believe that the markets are random. In fact, one of the most prominent investing books out there is "A Random Walk Down Wall Street" (1973) by Burton G. Malkiel, who argues that throwing darts at a dartboard is likely to yield results similar to those achieved by a fund manager (and Malkiel does have many valid points). However, many others argue that although prices may appear to be random, they do in fact follow a pattern in the form of trends. One of the most basic ways in which traders can determine such trends is through the use of fractals. Fractals essentially break down larger trends into extremely simple and predictable reversal patterns. This article will explain what fractals are and how you might apply them to your trading to enhance your profits.

What Are Fractals? When many people think of fractals in the mathematical sense, they think of chaos theory and abstract mathematics. While these concepts do apply to the market (it being a nonlinear, dynamic system), most traders refer to fractals in a more literal sense. That is, as recurring patterns that can predict reversals among larger, more chaotic price movements. These basic fractals are composed of five or more bars. The rules for identifying fractals are as follows:

• A bearish turning point occurs when there is a pattern with the highest high in the middle and two lower highs on each side.
• A bullish turning point occurs when there is a pattern with the lowest low in the middle and two higher lows on each side.

The fractals shown in Figure 1 are two examples of perfect patterns. Note that many other less perfect patterns can occur, but the basic pattern should remain intact for the fractal to be valid.

Figure 1

The obvious drawback here is that fractals are lagging indicators - that is, a fractal can't be drawn until we are two days into the reversal. While this may be true, most significant reversals last many more bars, so most of the trend will remain intact (as we will see in the example below). Applying Fractals to Trading Like many trading indicators, fractals are best used in conjunction with other indicators or forms of analysis. Perhaps the most common confirmation indicator used with fractals is the "Alligator indicator", a tool that is created by using moving averages that factor in the use of fractal geometry. The standard rule states that all buy rules are only valid if below the "alligator's teeth" (the center average), and all sell rules are only valid if above the alligator's teeth.

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Figure 2 is an example of such a setup:

Figure 2

The obvious drawback here is that fractals are lagging indicators - that is, a fractal can't be drawn until we are two days into the reversal. While this may be true, most significant reversals last many more bars, so most of the trend will remain intact (as we will see in the example below). Applying Fractals to Trading Like many trading indicators, fractals are best used in conjunction with other indicators or forms of analysis. Perhaps the most common confirmation indicator used with fractals is the "Alligator indicator", a tool that is created by using moving averages that factor in the use of fractal geometry. The standard rule states that all buy rules are only valid if below the "alligator's teeth" (the center average), and all sell rules are only valid if above the alligator's teeth.

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Figure 2 is an example of such a setup: 

Figure 3

Here is a basic rule setup that is used when using a chart with a four-hour time frame:

• Initiate a position when the price has hit the farthest Fibonacci band, but only after a daily (D1) fractal takes place.
• Exit a position after a daily (D1) fractal reversal takes place.

Notice how the fractals pinpoint meaningful tops and bottoms? This helps to take the guesswork out of deciding at which Fibonacci level to trade - all we have to do is check to see if the daily fractal occurred. We should also note that the trend strength began increasing at the sell fractal, and topped at the buy fractal. Although we lose some pips with the confirmation, it saves us from losing out on mere market noise - 139 pips certainly isn't bad for three days!

Things to Consider Here are a few things to remember when using fractals:

• They are lagging indicators. They are best used as confirmation indicators to help confirm that a reversal did take place. Real-time tops and bottoms can be surmised with other techniques.
• The longer the time period (i.e. the number of bars required for a fractal), the more reliable the reversal. However, you should also remember that the longer the time period, the lower the number of signals generated.
• It is best to plot fractals in multiple time frames and use them in conjunction with one another. For example, only trade short-term fractals in the direction of the long-term ones. Along these same lines, long-term fractals are more reliable than short-term fractals.
• Always use fractals in conjunction with other indicators or systems. They work best as decision support tools, not as indicators on their own.

Conclusion As you can see, fractals can be extremely powerful tools when used in conjunction with other indicators and techniques, especially when used to confirm reversals. The most common usage is with the "Alligator indicator"; however, there are other uses too, as we've seen here. Overall, fractals make excellent decision support tools for any trading method. Resources These are the two main charting packages that contain fractals:

• MetaTrader 
• TradeStation for equities (via plug-in)

If you want to know more about chaos theory and its applications in the marketplace, an excellent book on the topic is "Profiting From Chaos" (1994) by Tonis Vaga.

Chaos Theory Market Fractals - By-Nadeem Walayat's.

Are Elliott Wave's Chaos Theory?

Whilst there are many elements to chaos theory, my focus that grew out of studying the Julia and Mandelbrot sets was fractals. In that clearly the stock and other market price action resembles fractal structures as the same structure appears to repeat on ALL time frames. At the time it seemed that Elliott Wave and Chaos theory were very similar of not the same thing, in that Elliott Waves are the fractals for market price action that appear to on ALL time frames as discovered in the 1930's by RN Elliott which was decades before Mandelbrot appeared on the scene.
However on spending many, many years going down this path I concluded that Elliott Waves and Chaos Theory are NOT the same. Elliott Wave theory is something ELSE, yes, it resembles Chaos Theory i.e. Fractals, but it is not Chaos theory Fractals.
Again they look very similar but in a way Chaos Theory is Elliott Waves without having to know the WAVES! That may sound confusing but that is actually how it is. In Chaos Theory all one would know is What is Impulse and What is Corrective, and that is it! None of the 5th of the 5th of the 5th or ABC or the rest matter, just Impulse or Corrective. Which is probably what many experienced elliotticians eventually conclude without ever having ventured into chaos theory that at the end of the day the only thing that matters is Impulse or Corrective and not What Elliott Wave implies i.e. that Stocks 1987 peak was the final 5th of the 5th of the 5th and then so were each of the subsequent bull market peaks right into the present days bull market.

Fractal Theory

In a way Chaos Theory should really have been called Fractal Theory, because rather than chaos i.e. randomness it actually implies order and structure, and that structure is found in fractals.
The point about Fractals is that they give you a window into probabilities for price action on ALL market levels, i.e. hourly, daily, weekly, monthly, even yearly. I.e. fractals are akin to flexible pattern recognition, simple patterns that repeat and result in high probabilities given certain conditions which in themselves are flexible, so it unlike traditional chart patterns such as Head and Shoulders, the interpretation of market fractals is dependant upon changing conditions, such as trend, cycles, and volume.

What are Market Fractals ?

Simply put Market fractals are trend changes. A trend change is either a reversal of the Impulse trend or an end of the Corrective trend on ANY time frame.

Fractal Patterns

Fractal patterns are not complicated, you already know the more common ones, such as spike, double and triple tops and bottoms that occur on ALL time frames, what you don't know or have not studied are the conditions that increase their probabilities for particular markets at particular points in time, such as volume, preceding trend, and momentum oscillators (I use the MACD) once you factor these into the equation amongst your TRIGGER (Fractal) increases in probability exponentially, as it reduces the instances of its occurrence. Still it does requires HARD WORK for the market one trades to identify the current TRIGGERS (Fractals), especially when one starts going down the path of fractals of fractals i.e. in this example, a double top plus double top fractal. 

Trading Fractals

It all boils down to practice, knowing current fractal patterns and having them engrained in your mind, and then you WAIT for the FRACTAL TRIGGERS, and REACT in real time, just as as you trade traditional price patterns such as double and triple tops as identified in real time. Fractal triggers are not limited to Bar charts, as you can use other types of charts, my preference is for swing charts as illustrated in "How to Trade Commodities" by WD Gann (not to confuse with the rest of his work which in my opinion is a red herring).
Once you understand that Chaos Theory comprises fractals that give a high probability of an outcome given x, y,z condition then one starts to see fractals EVERYWHERE, for fractals ARE Nature. It is how our universe is constructed on every level, we are living in an unfolding fractal universe, nothing is fixed, everything is in motion, if you understand this then you will now know more truth than anything you will find in any ancient superstition.
The bottom line is this, that there is no black or white, no holy grail, everything has its basis in how we interpret the world around us is be it markets or the wider environment, fractals appear to offer the best window into a better interpretation of the world in our time, until the next innovation comes along.