Trading Strategies That Changed the World: Trading Chaos-2 by Bill Williams (part 4)

Trading Strategies That Were a Revolution: Trading Chaos-2 by Bill Williams (part 4)

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Welcome back to our blog!

As of yet, we’ve managed to describe the market behavior and how most of the traders behave there. We’ve considered Trading Chaos as a more effective interpretation paradigm of the way of existence and development of the market and the market crowd. Today’s post is meant to finish the analysis of Bill Williams’ ideas and approaches in accordance with the Chaos Theory. We will find out about new indicators, a system to search for buy/sell signals, signals to add positions, methods to optimize protection and minimize risks. Also, we’ll consider Williams’ “Reverse pyramid” as an aggressive money management model for skilled and experienced traders who follow the rules of the Trading Chaos strategy.

The Stairway To Profits

Just like in his first book, Bill Williams insists on the idea that there is a universal five-step progression from first interest or novice to becoming an expert in any field of endeavor.

The function of the novice level is to enable you to trade in the market and not lose money while you gain experience.

The advanced beginner has become a quality producer of profits.

The competent trader is more like a craftsman who uses tools in their everyday work that leads to planned results. In other words, the competent trader increases their total ROI for every deal by varying both instruments and volumes.

The proficient trader trades at the same pace the market lives. On this stage, a trader creates both mentally and physically their underlying structure based on the market’s structure.

For the expert trader at Level Five, trading is a low-stress way of living. You feel as though you are floating down a river that is providing you with any desire you name. Your nice fantasy has become completely achievable by following the Profitunity approach.

The Mighty Alligator

In this early part of the twenty-first century, we have a choice to either be a part of the last generation of traders and investors using linear (ineffective) techniques, or the first generation using effective nonlinear (chaotic) techniques

The Alligator serves as a compass to keep us trading in the appropriate direction regardless of which way the immediate price is moving.

Alligator’s tasks

  1. Provide an integrated approach to monitoring the market’s momentum on three different time frames in one chart.
  2. Provide a simple indicator to know when a trend starts and stops.
  3. Create a protection device so as to not lose money during a bracketed, range-bound market.

What is the alligator?

Basically, the Alligator is a combination of balance lines using fractal geometry and nonlinear dynamics. The blue line that is called the Alligator’s jaw is the balance line for whatever time frame is on the chart. The (blue) balance line is where the market would be if there were no new incoming information. The distance between this line and the current price is an indication of how the traders interpret this new incoming information. The red line (the Alligator’s teeth) is the balance line for one significant time frame lower.

Significant in this case is approximately one-fifth of the time frame on the chart. So, roughly, if the time frame on the current chart is daily and refers to the Blue Line, the Red Line would approximate an hourly chart. The green line (the Alligator’s lips) is the balance line for still another significant time frame lower. Again, it would be approximately one-fifth of the time frame of the red line. So, if the chart we are examining is daily, the red line would approximate the hourly chart and the green line would approximate a 5 to 10-minute chart.

Alligator - Trading Chaos

Putting this another way, the blue line is where the market would be on the daily chart, the red line is where the market would be on an approximately a one-hour chart, and the green line is where the market would be on an approximately 5- to 10-minute chart. Remember these time values are approximate and not connected to clock time. New incoming information would first affect the green line, followed by the red line and finally by the blue line.

Construction of the Alligator

  • Blue Line—a 13-bar smoothed moving average offset 8 bars into the future
  • Red Line—an 8-bar smoothed moving average offset 5 bars into the future
  • Green Line—a 5-bar smoothed moving average offset 3 bars into the future
Alligator settings - Trading Chaos

When the Alligator’s lines are intertwined, it is asleep, which means that the market is range-bound. The longer he sleeps the hungrier he gets.

When he awakes from a long sleep, he is very hungry and chases the price (Alligator food) much farther because it takes more prices to fill his stomach.

Alligator move - Trading Chaos

Bill Williams didn’t recommend to trade while the Alligator is sleeping, but believed that traders should look for signals when it awakes. Hunting Alligator is the finest hour for traders to increase profits.

The first wise man

The first wise man is the best tool for entering the market; it’s the first countertrend signal. The first wise man is the bullish/bearish divergent bar.

The bearish divergent bar

The bearish divergent bar is a bar that has a higher high and closes in the lower half of that bar.

The bearish divergent bar - Trading Chaos

The bullish divergent bar

A bullish divergent bar is a bar that has a lower low and closes in the top half of the bar.

The bullish divergent bar - Trading Chaos
The first wise man - Trading Chaos


Angulation - Trading Chaos

When the price is moving at a steeper angle than the Alligator, it is called angulation. Angulation is an additional argument when looking for a divergent bad to enter a deal or a series of deals.

Rules for angulation

  1. The price bars cross or go through the Alligator’s mouth (jaw, teeth, and lips).
  2. Draw or imagine a line that follows the Alligator’s mouth but pay attention to the jaw and teeth more than the lips.
  3. Draw or imagine another line that basically follows the edges of the price bars. You would look at the bottom edge of the prices in an up move and the top edge of the prices on a down move.
  4. If those two lines show clearly that they are moving away from each other, you have angulation.

Entrance strategy

On a bullish divergent bar, we place the buy stop 1-2 pips above the top of the bullish divergent bar and on the bearish divergent bar, we place our sell stop 1-2 pips below the bottom of the bearish divergent bar.

A very important moment: if the order fails (a signal bar isn’t broken) through the next two bars, you should delete a pending order and consider the bar false. Also, if the signal wasn’t broken, then the opposite bar was broken instead of it (low/high, depending on a signal bar, bullish or bearish).

Exit strategy

Once our buy or sell stop is hit, we need a protective stop. The first protective stop would be placed just below the bullish divergent bar or just above the top of a bearish divergent bar.

Once that signal is hit, we place a stop and reverse on the following bar. In the case of a bullish reverse, sell stop is placed below the bottom of the bar. In the case of a bearish reverse, buy stop is placed above the top of the bar.

The second wise man: adding on with momentum

Awesome Oscillator

The second entry signal is based on the Awesome Oscillator (AO). Basically, it is a 34-bar simple moving average that is subtracted from a 5-bar simple moving average. The Awesome Oscillator is an improved Market Facilitation Index (MFI). Assume that you have entered a trade at the direction of the first wise man (the bullish/bearish divergent bar), and the market is now moving in your direction. The next question should be, do I add on and if so where would be the most appropriate place?

The second wise man buy signal is formed after the buy signal in the form of a bullish reverse. It looks like the third straight green histogram bar. Buy stop should be placed 1-2 pips above the top of the signal bar.

The second wise man sell signal is formed after a bullish reverse. It looks like the third straight red histogram bar. Sell stop should be placed 1-2 pips below the bottom of the signal bar.

Two signals - Trading Chaos

The third wise man: trading the fractal breakaway trade

The Fractal signal is usually the third entry point, although if an appropriate fractal appears before the wise men 1 and 2, we would still place a trade on that Fractal.

We’ve already talked about models and forms of fractals in previous articles, but only buy and sell fractals are interesting for us in trading.

DownFractal - Trading Chaos
Upfractal - Trading Chaos

Once a Fractal signal is formed and is valid in relation to its position outside the Alligator’s mouth. The Alligator helps to distinguish true fractals from false. A true buy fractal is the one with the signal bar formed and closed above or at the Alligator’s teeth. A true sell fractal is the one with the signal bar formed below or at the Alligator’s teeth.

Buy stop should be placed 1-2 pips above the top of the signal bar of the true buy fractal. Sell stop should be placed 1-2 pips below the bottom of the signal bar of the true sell fractal. Every new true buy or sell fractal requires moving the pending order to a more favorable level.

What happens when the wise men get together?

All signals - Trading Chaos

Now that we understand all the three wise men, let us go a bit deeper and learn how to respond most profitably to various setups that the market gives us. A classic First we examine the pristine setup, where we enter the market in the following order of market-generated signals:

  1. Bullish/bearish divergent bar
  2. Super AO—three consecutive bars of the same color
  3. A Fractal signal

All orders are equal in volume (for example, 1 lot).


All signals - Trading Chaos
  • The first wise man (bearish divergent bar) was formed after a strong impulse to the upside with good angulation. The AO histogram was green. Sell signal was hit at 1.4185.
  • The second wise man (the third red bar of the AO histogram) was formed on the fifth day after the first wise man. Sell signal was hit at 1.4020.
  • The third wise man (fractal) appeared in the trend several ties: the third sale was at 1.3312, the fourth – 1.3025, the fifth – 1.2763.

If we participated in such a series of orders and moved Stop Loss along fractal highs (it’s the key exit strategy according to the Trading Chaos strategy), then our exit would be at 1.3172.


  • The first wise man profit – 1,013 pips or 10,130$;
  • The second wise man profit – 848 pips or 8,480$;
  • The third wise man profit: the 1st fractal – 140 pips or 1,400$;
  • The third wise man loss: the 2nd fractal – 147 pips or 1,470$;
  • The 3rd fractal – 409 pips or 4,090$.


This is how much money we can make if reading the market’s hints correctly and respond to them timely.

Reverse Pyramiding – money management at maximums

Reverse Pyramiding is a pretty aggressive way to manage your funds and Bill Williams didn’t recommend it to novices. However, if you’re not, it’s one of the best ways to maximize your profit. So, what’s the point? Williams recommends to open the first position using the minimum amount, 1-2% of your capital because it’s the moment when you risk the most and try to check our hypothesis about future market behavior. As soon as the first position becomes profitable, the second wise mand appears and we can increase aggressively. The position volume for the second signal should be four times bigger than the previous deal. In case the third wise man (fractal) appears, the position volume will be three times more than the first one. When another fractal appears (the fourth deal), the position volume should be increased twice in comparison with the first deal.

Such a “jump-ramp”-like model allows one to receive the most from the market movement in the very beginning and cover possible losses from the last deals in the case of a reverse. Let’s get back to our example, but reshape it based on the Reverse Pyramiding principle.

For example, the volume of our first deal is 1 lot.

  • The first wise man profit – 1,013 pips or 10,130$;
  • The second wise man profit – 4*848 pips or 8,480$;
  • The third wise man profit: the 1st fractal – 3*140 pips or 1,400$;
  • The third wise man loss: the 2nd fractal – 2*147 pips or 1,470$;
  • The 3rd fractal – 1*409 pips or 4,090$.


The final result of using the Reverse Pyramiding principle is several-fold larger than the previous one.


All books, ideas, and reflections of Bill Williams influenced not only me, but a lot of other traders, and provided us with the opportunity to trade on the market and get profit with pleasure and without stress. I believe his works are “must read and learn” for all beginners.

I hope that articles from our blog will reveal the market novices and motivate them to read the books written by this outstanding person.

On May 24th, 2019, Bill Williams passed away. However, he not only made a mark on the world but left an excellent legacy and a great number of disciples.

Thanks a lot, master!

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