The Effectiveness of the “Profitunity” TS by Bill Williams

In the present article, we estimate the effectiveness of the “Profitunity” trading system by Bill Williams. We will assess the effectiveness of the trading system both as a whole and its separate signals.

The «Profitunity» trading system or («Alligator») was developed and described by the famous trader, Bill Williams, in his book titled “Trading Chaos, 2nd edition”.

The Profitunity system consists of the following indicators: Alligator, Awesome Oscillator (AO), and Fractals, as well as the “Bar of the Bullish/Bearish reversal” pattern.

There are 3 signals for entry into the market. Williams called them "three wise men’’.

Alligator

The Alligator technical indicator is a combination of three smoothed moving averages with various time intervals shifted by a certain number of periods. When creating moving averages, the author uses the median price himself.

• The blue line or the 13-period smoothed moving average shifted by 8 bars represents the Alligator Jaw.
• The red line or the 8-period smoothed moving average shifted by 5 bars represents the Alligator teeth.
• The green line or the 5-period smoothed moving average shifted by 3 bars represents the Alligators lips.

The three moving averages comprise the Jaw, Teeth, and Lips of the Alligator mouth.

Alligators Jaw = SMMA (Median price, 13, 8)

Alligator Teeth = SMMA (Median price, 8, 5)

Alligator Lips = SMMA (Median price, 5, 3)

First wiseman is a bar of the Bullish/Bearish reversal

The next part of the system is a bar of the bullish or bearish reversal. This is the first signal for the market entry.

A bar of the bullish reversal shows a lower minimum relative to the preceding bar and closes above its middle.

Namely, the bears were at the helm first, but the bulls won then.

There is a bar of the bearish reversal opposite to the bullish. This bar shows a new maximum and closes in its lower part. It means, if the bulls were at the helm first, the bears won in the end. 

Bars of the bullish and bearish reversals must be at a substantial distance from the Alligator lines.

Second wiseman is Awesome Oscillator

The next stage of the system is the AO oscillator.

It defines the driving force behind the market. We measure it on the basis of the last 5 bars which are similar to the driving force of thirty-four bars.

The calculation method of the AO indicator is simple: it is enough to calculate the difference between moving averages and the median price with periods of 34 and 5:

AO = SMA (Median Price, 34) — SMA (Median Price, 5)

where  “SMA” is a simple moving average, “Median Price” is the median price.

Changes in the bar color (from green to red in the pic.) signals the second market entry (refilling) and the three consecutive bars of one color of the AO area chart.

If there is no reversal bar, the market entry is based on the AO indicator.

Third wiseman is Fractals

Fractals are used for the third signal of the «Profitunity» TS.

An ascending fractal is at least the five consecutive candlesticks with the highest High on both sides followed by lower Highs.

The same is true of the descending fractal with the lowest Low followed by four bars with higher Low value.

In the case of ascending fractals, we take notice only of bar maximums; in the case of descending fractals - only of bar minimums. 

Fractal is optional in its candlesticks (not only 5); the shapes may be different:

The key moment is when the fractal is executed, it places behind the red Alligator line (to buy above the red line; to sell below the red line).

When the fractal is executed, the entries are made on subsequent fractals until 5 entries are summed up.

Fractal is supposed to be the first system signal if there have been no signals on the reversal bar and the AO indicator before. 

Wisemen gather together

1. The first wiseman signal forms at a certain distance from Alligator. Waiting for a bar of a bullish or bearish reversal.
2. If the market continues to move in our direction, start calculating the bars in the AO bar chart. When the bar colors of the AO bar chart change and three consequent bars of one color (the green color is to buy; the red color is to sell) appear, a refilling is made to the main position according to the system of the reverse pyramid (more detailed information described below).
3. When the second signal is handled, start defining the point for the third entry, i.e. we wait for the condition for forming a fractal.
4. We continue to follow new signals until the position size does not reach its maximum (referring to the book written by Williams: in total of 5 entries).

Exit from the position 

Once an opposite signal appears, it’s time to exit from the position. Namely, when a reversal bar, three consequent bars of one color form after changes in bar colors in the AO bar chart or a fractal.

Reverse pyramid

To calculate the position size, Bill William recommends the following method which resembles a reverse pyramid:

1. The first entry under this system: the 1*X lot
2. The second entry under this system: the 5*X lot
3. The third entry under the system: the 4*X lot
4. The fourth entry under the system: the 3*X lot
5. The fifth entry under the system: the 2*X lot

Method for Event Detection

Formation of buy signals

1. Bullish reversal candlestick

• PS < TEETH
• TEETH < JAW
• Candlestick i: a candlestick of the bullish reversal:

1. Low[i] < Low[i-1]
2. Close[i] > 0.5*(High[i] - Low[i])

• High[i] < LIPS[i]
• LIPS[i] – High[i] > TEETH[i] – LIPS[i]
• LIPS[i] – High[i] > JAW[i] – TEETH[i]

Parameters for opening a position:

BuyStop = High[i] + 5

StopLoss = Low[i] – 5

The order execution is canceled when any of the three opposite signals appears: a reversal bar, three consequent bars of one color after changes in bar colors in the AO bar chart or a fractal.

2. АО indicator

• LIPS < TEETH
• TEETH < JAW
• AO[i-4] > AO[i-3] и
• AO[i-3] < АО[i-2] и
• АО[i-2] < AO[i-1] и
• AO[i-1] < AO[i]

Parameters for opening a position:

BuyStop = High[i] + 5

StopLoss = Low[i] – 5

The order execution is canceled when any of the three opposite signals appears: a reversal bar, three consequent bars of one color after changes in bar colors in the AO bar chart or a fractal.

3. Fractal

f1 > TEETH

Parameters for opening a position:

BuyStop = High[1] + 5

StopLoss = Low[1] - 5

f2 > TEETH

Parameters for opening a position:

BuyStop = High[2] + 5

StopLoss = Low[2] - 5

f3 > TEETH

Parameters for opening a position:

BuyStop = High[3] + 5

StopLoss = Low[3] – 5

The order execution is canceled when any of the three opposite signals appears: a reversal bar, three consequent bars of one color after changes in bar colors in the AO bar chart or a fractal.

Formation of sell signals



1. Bearish reversal candlestick

• LIPS > TEETH
• TEETH >JAW
• Candlestick i: a candlestick of the bearish reversal:

1. High[i] > High[i-1]
2. Close[i] < 0.5*(High[i] - Low[i])

• Low[i] > LIPS
• Low[i] – LIPS[i] > LIPS[i] – TEETH[i]
• LIPS[i] – High[i] > TEETH[i] – JAW[i]

Parameters for opening a position:

SellStop = Low[i] – 5

StopLoss = High[i] + 5

The order execution is canceled when any of the three opposite signals appears: a reversal bar, three consequent bars of one color after changes in bar colors in the AO bar chart or a fractal.

2. АО indicator

• LIPS > TEETH
• TEETH > JAW
• AO[i-4] < AO[i-3] и
• AO[i-3] > АО[i-2] и
• АО[i-2] > AO[i-1] и
• AO[i-1] > AO[i]

Parameters for opening a position:

SellStop = Low[i] – 5

StopLoss = High[i] + 5

The order execution is canceled when any of the three opposite signals appears: a reversal bar, three consequent bars of one color after changes in bar colors in the AO bar chart or a fractal.

3. Fractal

f1 < TEETH

Parameters for opening a position:

SellStop = Low[1] – 5

StopLoss = High[1] + 5

f2 < TEETH

Parameters for opening a position:

SellStop = Low[2] – 5

StopLoss = High[2] + 5

f3 < TEETH

Parameters for opening a position:

SellStop = Low[3] – 5

StopLoss = High[3] + 5

The order execution is canceled when any of the three opposite signals appears: a reversal bar, three consequent bars of one color after changes in bar colors in the AO bar chart or a fractal.

Closing a position:

1. Based on the «Profitunity» system, when any of the three opposite signals appears: a reversal bar, three consequent bars of one color after changes in bar colors in the AO bar chart or a fractal;

2. We take every signal separately for the analysis:

• When an opposite signal appears;
• At the closing of the 5^th bar after the market entry;
• At the closing of the 10^th bar after the market entry;
• At the closing of the 15^th bar after the market entry.

Having determined all the conditions and set the necessary parameters, we can start testing!

Analysis of the Results

First, we will estimate the results by the sample size. Let us draw them in the following diagrams:

Then, we will see the share of events in % in the total number of initial bars and in the timeframes:

Note that based on the Profitunity system the signals appear on average 5 times on the hourly timeframes and 6 times on the daily timeframes, the separate AO indicator signals appear on average 6 times in the hourly and daily charts; the remaining signals are less frequent.

Now, let us consider the results of the handled system..

We will assess the results with the two following criteria:

• Momentum (m) reflects an average change in quotes of financial instruments at the moment of the closing a position, in %. A positive momentum value indicates profitability of the handled signal; a negative momentum value indicates a loss.
• SPP, the share of profitable positions, %.

We take the following notations:

«Н1»: closing under the «Profitunity» trading system when setting the 1-hour timeframe;

«H1/OS»: closing when an opposite signal appears when setting the 1-hour timeframe;

«H1/5»: closing the 5^th bar position when setting the 1-hour timeframe;

«H1/10»: closing the 10^th bar position when setting the 1-hour timeframe;

«H1/15»: closing the 15^th bar position when setting the 1-hour timeframe;

«D1»: closing under the «Profitunity» TS when setting the 1-day timeframe;

«D1/OS»: closing when an opposite signal appears when setting the 1-day timeframe;

«D1/5»: closing the 5^th bar position when setting the 1-day timeframe;

«D1/10»: closing the 10^th bar position when setting the 1-day timeframe;

«D1/15»: closing the 15^th bar position when setting the 1-day timeframe;

Volatility coefficient:

• For the daily timeframe: a ratio of the average volatility of 5 bars after opening a position to the average volatility of 20 bars before opening a position;
• For the hourly timeframe: a ratio of the average volatility for 5 bars after opening a position to the average volatility of the same hours over the preceding 4 days.

The volatility with the coefficient more than 1 implies the higher volatility after the signal appears compared with volatility before the signal appears; if the coefficient is  less than 1, this is the opposite.

The Number of signals, the Momentum, the Share of profitable positions, and the Volatility coefficient in terms of timeframes and market segments (the «Profitunity» system)

The Number of signals, the Momentum, the Share of profitable positions, and the Volatility coefficient in terms of timeframes and market segments (A bar of the bullish/bearish reversal)

The Number of signals, the Momentum, The Share of profitable positions, and the Volatility coefficient in terms of timeframes and market segments (the АО indicator)

The Number of signals, the Momentum, The Share of profitable positions, and the Volatility coefficient in terms of timeframes and market segments (Fractal)

Summary of the Results using the following diagram:

Detailed results are shown in the Appendix:

XLSX (0.15 MB)Application to the article 'Performance of the TS 'Profitunity' by Bill Williams'.xlsx