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Technical analysis Technical indicators

The Effectiveness of the “Profitunity” TS by Bill Williams

Елена Берсенева 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
To conclusion

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

To conclusion

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 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:

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


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