# The Effectiveness of the “Profitunity” TS by Bill Williams

23 march 2022 117 4

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
Hypothesis

The «Profitunity» trading system by Bill Williams is profitable.

#### Method for Event Detection

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:

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:

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:

StopLoss = Low[1] - 5

f2 > TEETH

Parameters for opening a position:

StopLoss = Low[2] - 5

f3 > TEETH

Parameters for opening a position:

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 5th bar after the market entry;
• At the closing of the 10th bar after the market entry;
• At the closing of the 15th bar after the market entry.
Data used

The set of financial instruments and timeframes which will be tested the trading signal against:

• 25 currency pairs (Forex);
• 6 commodity futures (Commodities);
• 2 US stock indices (US indices);
• 30 US stocks (US stocks);
• 58 RF stocks (RF stocks);
• 1 RF stock index (RF index).

Timeframes used:

• H1 (1 hour): the history covers the 5-years period,
• D1 (1 day): the history covers the 10- years period.

Total: 1 979 015 bars.

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 5th bar position when setting the 1-hour timeframe;

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

«H1/15»: closing the 15th 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 5th bar position when setting the 1-day timeframe;

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

«D1/15»: closing the 15th 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)

 Timeframe Indicator Forex Commodities US indices RF index US stocks RF stocks All Н1 Number of signals 38074 5741 3002 638 11007 25034 83496 Momentum -0.055 -0.092 -0.050 -0.077 -0.164 -0.594 -0.340 SPP 27.2 28.6 30.9 32.6 31.3 26.9 28.2 Volatility coefficient 1.02 1.02 1.02 1.00 1.01 1.07 1.04 D1 Number of signals 4319 934 363 163 4171 6613 16563 Momentum -0.218 -0.444 -0.226 -0.189 -0.498 -1.009 -0.674 SPP 31.2 33.8 31.3 36.0 31.3 30.2 30.9 Volatility coefficient 1.01 1.00 0.98 1.02 1.01 1.05 1.03

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)

 Timeframe Indicator Forex Commodities US indices RF index US stocks RF stocks All Н1/OS Number of events 28020 4345 1980 644 12070 20031 67090 Momentum 0.001 0.078 0.023 0.077 0.166 0.174 0.129 SPP 19.0 22.4 19.4 23.9 28.2 27.0 25.2 Volatility coefficient 1.03 1.01 1.05 1.02 1.05 1.11 1.07 H1/5 Number of events 28026 4347 1982 644 12078 20052 67129 Momentum -0.006 0.024 0.011 0.014 0.062 -0.180 -0.070 SPP 49.1 49.6 51.3 53.3 51.6 45,1 47,9 Volatility coefficient 1.03 1.01 1.05 1,02 1.05 1.11 1.07 Н1/10 Number of events 28019 4344 1980 644 12073 20047 67107 Momentum -0.003 0.027 -0.005 0.021 0.062 -0.217 -0.087 SPP 49.4 49.3 50.2 51.9 51.7 46.7 48.7 Volatility coefficient 1.03 1.01 1.05 1.02 1.05 1.11 1.07 H1/15 Number of events 28007 4340 1980 644 12060 20035 67066 Momentum -0.008 0.046 0.001 -0.026 0.041 -0.240 -0.104 SPP 49.1 50.4 50.0 50.3 51.0 46.6 48.5 Volatility coefficient 1.03 1.01 1.05 1.02 1.05 1.11 1.07

 Timeframe Indicator Forex Commodities US indices RF index US stocks RF stocks All D1/OS Number of events 3223 730 247 142 3640 5674 13656 Momentum 0.039 0.084 0.230 0.142 0.262 -0.465 -0.137 SPP 19.0 19.4 19.0 19.0 20.7 23.6 21.6 Volatility coefficient 1.02 1.02 0.98 1.02 1.01 1.08 1.05 D1/5 Number of events 3224 732 247 142 3650 5691 13686 Momentum -0.043 -0.052 0.222 0.290 0.185 -0.312 -0.107 SPP 47.6 47.9 50.3 56.3 50.5 45.9 47.6 Volatility coefficient 1.02 1.02 0.98 1.02 1.01 1.08 1.05 D1/10 Number of events 3219 730 247 142 3640 5682 13660 Momentum -0.043 -0.085 0.078 0.655 0.235 -0.488 -0.178 SPP 48.6 47.4 44.9 54.9 51.3 47.4 48.6 Volatility coefficient 1.02 1.02 0.98 1.02 1.01 1.08 1.05 D1/15 Number of events 3215 729 247 142 3634 5670 13637 Momentum -0.006 0.123 0.565 0.523 0.107 -0.536 -0.208 SPP 50.6 50.9 49.4 51.4 50.2 48.9 49.7 Volatility coefficient 1.02 1.02 0.98 1.02 1.01 1.08 1.05

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)

 Timeframe Indicator Forex Commodities US indices RF index US stocks RF stocks All Н1/OS Number of events 42434 6830 3325 616 12192 30621 96018 Momentum 0.012 0.083 0.021 0.036 0.161 -0.090 0.004 SPP 26.9 26.7 26.5 29.1 33.0 28.1 29.0 Volatility coefficient 1.01 1.00 03 0.99 1.01 1.04 1.02 H1/5 Number of events 42438 6831 3327 616 12204 30633 96049 Momentum 0.010 0.057 -0.007 0.061 0.093 -0.110 -0.024 SPP 49.6 51.7 47.6 54.4 50.9 44.5 47.6 Volatility coefficient 1.01 1.01 1.03 0.99 1.01 1.04 1.02 Н1/10 Number of events 42423 6828 3323 616 12195 30617 96002 Momentum 0.009 0.069 -0.011 0.022 0.101 -0.140 -0.036 SPP 49.3 51.6 49.4 49.0 50.7 45.3 47.9 Volatility coefficient 1.01 1.00 1.03 0.99 1.01 1.04 1.02 H1/15 Number of events 42419 6828 3321 615 12184 30592 95959 Momentum 0.007 0.085 0.002 0.010 0.102 -0.135 -0.034 SPP 49.6 52.5 49.8 48.3 50.8 45.4 48.1 Volatility coefficient 1.01 1.00 1.03 0.99 1.01 1.04 1.02

 Timeframe Indicator Forex Commodities US indices RF index US stocks RF stocks All D1/OS Number of events 4457 1033 357 173 4659 7244 17923 Momentum 0.023 0,370 0.041 0,729 0,131 0,042 0,082 SPP 29.0 29.7 27.4 37.6 29.0 28.5 28.8 Volatility coefficient 0.99 0.98 1.05 0.99 1.02 1.01 1.01 D1/5 Number of events 4458 1035 357 173 4665 7259 17947 Momentum 0.011 0.273 0.142 0.752 0.063 0.086 0.080 SPP 50.5 52.6 48.7 60.1 50.0 48.8 49.7 Volatility coefficient 0.99 0.98 1.05 0.99 1.02 1.03 1.01 D1/10 Number of events 4451 1030 357 173 4658 7247 17916 Momentum -0.029 0.245 -0.052 0.831 0.027 -0.017 0.011 SPP 50.3 50.4 46.5 62.4 49.3 49.3 49.6 Volatility coefficient 0.99 0.98 1.05 0.99 1.01 1.03 1.01 D1/15 Number of events 4448 1029 356 173 4642 7241 17889 Momentum 0.007 0.521 -0.078 0.962 -0.035 -0.078 -0.012 SPP 50.2 53.2 47.2 59.0 49.6 49.5 49.9 Volatility coefficient 0.99 0.98 1,05 0,99 1,01 1,03 1,01

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

 Timeframe Indicator Forex Commodities US indices RF index US stocks RF stocks All Н1/OS Number of events 38103 6203 3062 533 10732 24845 83478 Momentum -0.036 -0.089 -0.019 -0.054 -0.076 -0.034 -0,048 SPP 23.4 24.1 24.3 26.8 28.3 26.6 26,2 Volatility coefficient 1.03 1.03 1.01 1.00 1.03 1.11 1,07 H1/5 Number of events 38111 6208 3062 533 10756 24848 83518 Momentum -0.009 -0.026 -0.016 0.059 0.054 0.031 0,025 SPP 46.9 48.0 48.4 53.3 49.2 44.7 46,6 Volatility coefficient 1.03 1.03 1.01 1.00 1.03 1.11 1,07 Н1/10 Number of events 38102 6204 3062 533 10739 24839 83479 Momentum -0.010 -0.035 -0.009 0.024 0.018 0.299 0.143 SPP 47.2 47.4 47.8 51.0 49.4 45.3 46.9 Volatility coefficient 1.03 1.03 1.01 1.00 1.03 1.11 1.07 H1/15 Number of events 38090 6204 3062 533 10727 24825 83441 Momentum -0.010 -0.044 0.004 -0.005 0.039 0.256 0.127 SPP 48.0 47.3 48.4 50.1 49.6 45.4 47.1 Volatility coefficient 1.03 1.03 1.01 1.00 1.03 1.11 1.07

 Timeframe Indicator Forex Commodities US indices RF index US stocks RF stocks All D1/OS Number of events 3990 870 309 140 3888 6108 15305 Momentum -0.165 -0.376 -0.211 -0.373 -0.384 -0.784 -0.526 SPP 24.8 24.5 25.9 28.6 24.7 27.4 26.1 Volatility coefficient 1.01 1.02 0.94 0.99 1.02 1.09 1.05 D1/5 Number of events 4013 870 309 140 3895 6122 15349 Momentum -0.019 0.156 -0.012 -0.064 -0.068 -0.198 -0.107 SPP 50.2 50.5 57.0 52.1 50.4 46.9 48.8 Volatility coefficient 1.01 1.02 0.94 0.99 1.02 1.11 1.06 D1/10 Number of events 4001 869 309 140 3888 6107 15314 Momentum -0.062 -0.020 -0.152 -0.149 -0.110 0.025 -0.033 SPP 48.5 49.7 56.9 52.9 51.6 47.8 49.2 Volatility coefficient 1.01 1.02 0.94 0.99 1.02 1.11 1.06 D1/15 Number of events 3989 865 309 140 3884 6094 15281 Momentum -0.068 -0.164 -0.066 -0.179 -0.157 0.025 -0.052 SPP 47.9 46.3 56.4 49.3 49.5 48.7 48.7 Volatility coefficient 1.01 1.02 0.94 0.99 1.02 1.11 1.06

Summary of the Results using the following diagram:

Conclusion

Momentum

According to the study results, the «Profitunity» trading system yields an explicit loss-making of signals.

The momentum of the TS «Profitunity» is negative on both timeframes. Especially, its value modulo exceeds the minimum significant value of 0.15% for the hourly timeframe and 0.3% for the daily timeframe (- 0.340% and – 0.674% respectively).

The Н1 timeframe:

The highest momentum of separate signals is observed with the “Fractal” signal of 0.143% when closing a position on the 10th bar.

The lowest momentum of separate signals is observed with the “bar of the Bullish/Bearish reversal” signal of 0.104% when closing a position on the 15th bar.

The D1 timeframe:

The highest momentum of separate signals is observed with “the AO indicator” signal of 0.082% when closing a position with an opposite signal of the AO indicator.

The lowest momentum of separate signals is observed with the “Fractal” signal of 0.526 % when closing a position with an opposite fractal signal.

The momentum of the fractal signal exceeds the minimum significant value of 0.3% modulo on the daily timeframe.

The momentum of other signals on the daily timeframe does not reach the minimum significant value of 0.3%.

SPP

The share of profitable positions of the «Profitunity» TS on the hourly timeframe is 28.2 %, and 30.9 % on the daily timeframe.

The share of profitable positions of separate signals on the hourly timeframe varies between 25.2 % and 48.7 %; on the daily timeframe it varies between 21.6 % and 49.9 %.

Volatility

Volatility rises by more than 5% after the “bar of the Bullish/Bearish reversal” signal appears on the hourly timeframe and after the ”Fractal” signal appears on the daily and hourly timeframes.

The volatility remains unchanged after other signals appear.

The effectiveness of the «Profitunity» TS aimed at market forecasting has not been identified.

The effectiveness of separate system signals by Bill Williams aimed at market forecasting has not also been identified.

A loss proved by the «Profitunity» and the «Fractals» TS may induce traders to trade in the opposite direction from the obtained signals.

However, using built-in stop loss in the system will not give the same results with the opposite sign.

Detailed results are shown in the Appendix:

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