Trading Bill Williams Chaos Theory

Bill Williams is a very well-known trader with decades of experience in several markets. He is known for his unconventional views on the market which are based on trading psychology and Chaos theory. As Bill Williams once stated, winners not only correctly interpret fundamental and technical information but also understand the underlying structure of the market.

In his opinion, market structure consists of these aspects:

  • Fractal dimension
  • Momentum dimension
  • Acceleration/Deceleration dimension
  • Zone dimension
  • Balance line dimension

He built a set of technical indicators which help to understand the current state of these market dimensions: Fractals, Alligator, Awesome Oscillator, Acceleration / Deceleration Oscillator and Balance Line.

Bill Williams’ tools are interesting because they can work independently but provide a clearer picture when used together. Let’s take a loot at the first tool in his kit – Fractals.

Williams Fractal

Bill Williams believes that human psychology has a huge impact on trading. Markets are always chaotic – there is a continuous flow of new information all the time, but the way people react to this information doesn’t change at all. If we saw a lion on the street our reaction would be exactly the same as thousands of years ago. This idea applies to the markets too – if people react to price action or fundamental events the same way again and again you can make a prediction of the future price movements even in chaotic systems.

Fractals can vary in size and structure – the most common fractals are widely known technical analysis patterns, for example flags and double-bottoms. These fractals can be seen on any timeframe and on any asset.

Bill Williams took a step ahead and generalized the idea of the fractal – he found a sequence of candles which form a short-term support or resistance, and the break of this structure means a probable stronger move in the direction of the break out.

An up fractal is a series of five consecutive bars where the highest high is preceded by two lower highs and is followed by two lower highs. The opposite structure is called a down fractal.

The general rule is to enter a long on the break above the last up fractal and enter a short on the break below the last down fractal.

Fractals help not only to spot the direction of a trade but also to place stop-losses. Usually stops are placed two fractals back in the opposite direction.

On time-frames above 4H it doesn’t make sense to use a stop on the second fractal – stops are getting way too wide. My personal rule is to look at the first fractal on a daily chart, first or second fractal (depending on how far they are from each other) on the 4H chart and a second fractal on the 1H and smaller timeframes.

Fractals are great because they provide a trailing stop-loss. Once the new subsequent fractal is created you move stops one fractal higher (if long) or one lower (if short).

Using a trading system based solely on fractals won’t yield a lot of profit because cryptocurrencies are very volatile – fractals are getting triggered right and left even in the ranging markets. But there is a tool which solves this exact problem. Meet the Alligator!

Williams Alligator

Alligator is a set of moving averages which are offset towards the future. It consists of:

  • Alligator’s Jaw (the blue line) – 13-period moving average at the mid price (High+Low)/2, which is offset 8 bars into the future
  • Alligator’s Teeth (the red line) – 8-period moving average at the mid price (High+Low)/2, which is offset 5 bars into the future
  • Alligator’s Lips (the green line) – 5-period moving average at the mid price (High+Low)/2, which is offset 2 bars into the future

It works as a very simple trend filter. Alligator can either be asleep (when all the lines are intertwined and are close to each other) or hunting (lines are untangled). You don’t want to enter trades when the Alligator is asleep – the market is range-bound and you will get chopped. But once the Alligator wakes up you can look for entries – the market is trending.

If the market is trending upwards you should only look for bullish signals from other Williams indicators, and the opposite for downward trends. If the market is range-bound and the Alligator is asleep don’t look for any trades at all, but be aware that the longer it sleeps the higher chance is that trend will occur very soon. It works the same way Bollinger Band squeezes do.

Now let’s get back to Fractals to see how it works in combination with Alligator.

There are two ways to filter out trades with these indicators. The first one is to look for break of up fractals in the uptrend and break of down fractals in the downtrend.

The second way is to divide fractals into two groups: valid and invalid. An up fractal is called valid if the close of the fractal’s candle is above the red line (alligator’s teeth). A down fractal is called valid if the close of the fractal’s candle is below the red line. All other fractals are called invalid.

On this chart I marked valid fractals with green rectangles and invalid fractals with red rectangles. To enter a trade we need a trigger of a valid fractal, so we discard invalid fractals completely.

Both ways of filtering work, it doesn’t really matter which style to choose, but it’s important to keep the rules consistent. Don’t jump from one way to another or you will eventually mess up.

The combination of Fractals and Alligator is the pillar of Bill Williams’ strategy. It creates the first and the main signal – every other indicator should be taken into consideration only after the first fractal signal was triggered.

It means that we enter our first position based solely on Fractal and Alligator and then if another indicator shows an entry we increase the size of our position. This way, if the trend is strong we get to enter in a good size.


The Oscillator is a very common trading tool which shows short-term overbought or oversold conditions and changes in the price momentum. This change of momentum is crucial because in the ranging market it might imply that the trading range will be broken soon and in a trending market it might show that the current trend is getting exhausted and a reversal is not far away.

Bill Williams’ tool kit provides two great oscillators: Awesome Oscillator and the Acceleration/Deceleration Oscillator.

Awesome Oscillator

Awesome Oscillator (AO) determines market momentum as a difference between the 34-period and 5-period moving averages of the bars’ midpoints: (High + Low) / 2. It is shown on a chart as a histogram with base value of 0. If the 5-period moving average is higher than 34-period moving average then AO is above 0, otherwise it’s below 0.

It provides three types of signals: crosses, saucers and divergences.

Crosses occur whenever AO value flips from positive to negative and vice versa.

On this chart the red line is a sell signal, and the green line is a buy signal. As you can see there was a period when AO flipped very frequently but we wouldn’t take these trades anyway. Why? Recall the main rule of the Bill Williams strategy – we use oscillators and everything else only after the signal comes from the Fractal and Alligator – in this case, the Alligator was sleeping.

The next signal, Saucer, occurs whenever AO takes shape of a saucer. The deeper this saucer the more reliable a signal is. A saucer is formed using three histogram bars with the middle one forming a higher low (or lower high for a bullish saucer) and the third bar switching color to the opposite one. Also, it helps if on the third bar we get a higher volume candle in the direction of the signal.

Here is a close-up of a bearish saucer on XCP/BTC chart. We get confirmation of a signal on the first red bar with lower low.

The last indicator is Divergence – a disagreement between a momentum indicator and a price. Usually it means that the current price of an asset or current momentum is irrational and will change its direction shortly.

Divergence occurs in four scenarios:

  • Price makes a higher high, oscillator makes a lower high (Bearish reversal)
  • Price makes a lower high, oscillator makes a higher high (Bearish continuation)
  • Price makes a lower low, oscillator makes a higher low (Bullish reversal)
  • Price makes a higher low, oscillator makes a lower low (Bullish continuation)

To spot a divergence you can use any momentum indicator including Awesome Oscillator. The general rule is: you need to connect two consecutive highs or lows on both price and oscillator and if divergence occurs on highs (lows) then it’s a bearish (bullish) indicator. Also keep in mind that it’s better to use divergence just as an indicator, not a sole signal to enter a trade because markets tend to stay irrational much longer than people expect.

Acceleration / Deceleration Oscillator (AC)

Acceleration/Deceleration (AC) is a third dimension of the market structure. As Bill Williams stated, before the price behaviour changes, the momentum changes, and even before the momentum, we see the change in the acceleration.

A/D Oscillator is a difference between Awesome Oscillator and 5-period moving average of Awesome Oscillator.

Acceleration / Deceleration Oscillator = AO – Moving Average(AO, 5)

It provides three signals all of which are pretty straight-forward:

  • Buy above the zero line (Sell below the zero line)
  • Buy below the zero line (Sell above the zero line)
  • Divergences

The rules are simple. To create a “buy above the zero line” an oscillator should have two consecutive green bars above the zero line. (other way around for the “sell below the zero line” signal). To create a “buy below the zero line” an oscillator should have three consecutive green bars below the zero line (same applies to the opposite signal).

It’s important to mention that unlike Awesome Oscillator, crosses of zero line are not considered signals.

The third signal, divergence, works exactly the same as it works on any other oscillator.

I’ve used this indicator only for two weeks but didn’t find the first two signals reliable. Probably I just need to dig deeper on lower timeframes. Right now I’m using A/D oscillator to spot divergences (they are sharper than on Awesome Oscillator).

Also, I’ve found an interesting relation between AO and A/D – whenever price crosses the zero line on Awesome Oscillator the signal can be trusted if A/D produces buy signal at the same time. I’ve backtested it on tens of 1D altcoin charts and it works more often than it doesn’t.

On this LINK/BTC chart green vertical lines indicate a “cross of zero line” signal on AO and a simultaneous “buy above the zero line” signal on A/D. A red vertical line is a cross on AO without a signal on A/D.

Trading in the Zone

The fourth dimension of Bill Williams market structure is the zone. The zone is created using two indicators mentioned above: Awesome Oscillator and Acceleration/Deceleration Oscillator. When both momentum indicators share the same direction this means that momentum is accelerating in the right direction.

A long signal is generated when two consecutive green bars appear on both histograms and the other way around for short signal. Important: the signal is valid if and only if there was a fractal & alligator signal in the same direction.

Let’s take a look at current BTC/USD 1H chart.

There are three zone signals we would take based on this strategy. First, a short around $8583 after a bearish alligator cross and break of the fractal (which are excluded from the chart for clarity). Up until the second signal Alligator was bearish or asleep so we discarded all bullish signals. But once Alligator turned bullish we got our long zone signal around $8221. The last signal appeared literally an hour ago (at time of writing) telling us to short at $8380.

Also, Bill Williams mentions that we should stop adding to the position based on the zone after the fifth or sixth consecutive bar of the same color – usually it’s a time to tighten up a stop-loss because markets rarely create 7-8 bars of the same color. I’ve found that in case of cryptocurrencies this rule tends to be broken (on 4H+ timeframes).

Balance Line

Balance line is the last market dimension according to Bill Williams. Action in this dimension should be taken only if there was an earlier signal from dimensions 1 & 2.

The Balance Line is the line where the price would be if there was no new incoming information (chaos) affecting the market. In this case the balance line is at high of candle “a”. New information pushed the price lower (candle “b”) and candle “c” broke the balance line.

Sellers were stronger than buyers on “b” bar but since “c” bar pushed price higher than a’s high we might assume that balance is changing and it’s a good time to make a deal.

In case of this candle structure bar “b” is called a base bar.

The first three principles of Balance Line trades:

  • Read the chart from right to left
  • If you are looking for longs, look at the highs. If you are waiting for shorts look at the lows
  • Establish the base bar

If the “base” bar is breached and price makes a lower low (or higher high in case of bearish balance line) trader should wait for two more lower lows (or higher highs) to establish the next base bar.

Here is a balance line trade on EOS/BTC 4H chart.

We enter our first short trade based on break of down fractal in bearish Alligator setup and start to look for trades based on other dimensions. Candle 2 forms a higher low relative to Candle 1 so we’ll consider it a base bar. Now we wait  – either for two more candles closing higher than Candle #2 (to create a new base bar) or for a break of Candle #1’s low. Candles #3 and #4 stay in the range formed by Candles #1 and #2 so we don’t take any action. Candle #5 successfully breaks the balance line and we increase our short position.

Final Notes

I’ve found Chaos Theory to be very complex. Bill Williams built this system from scratch and made a killing with it, but for an average guy who tries to get into trading it might be too much to handle.

It’s known that simpler strategies yield better results because even a good trader might have trouble following rules. Traders always act in the moment of uncertainty – it’s easy to backtest strategies and see where they perform and where they don’t but when it’s time to take action the game becomes much more complex because emotions become part of the equation.

I’ve tried to follow several setups using all five dimension but usually the cleanest setups are built with usage of Fractals, Alligator and Awesome Oscillator. For me everything else just adds unnecessary noise.

I’ve also found that the strategy works better on lower timeframes, using fractals on 5 min and 15 min charts on Bitmex was pretty profitable and fun (even though I rarely day-trade). 

Implementing this strategy as my go-to would take a lot of time and practice but a lot of principles mentioned by Bill Williams look great to become a part of scalping bot and I’m going to test it out.

Thank you for reading and good luck in the markets!



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