Technical analysis Technical indicators

Bollinger Bands «Reversals»: Estimating the Effectiveness of the System

Elena Berseneva 16 march 2022 330 4

In the present article, we will talk about the John Bollinger’s indicator named Bollinger Bands.


This indicator was firstly described by Perry J. Kaufman in 1987 in the book titled “Commodity Trading Systems and Methods”. Later, the indicator became widespread thanks to John Bollinger. His book “Bollinger on Bollinger Bands” represents a detailed guidance of how to use it on its own as well as with other indicators.

 

In fact, Bollinger Bands (BB) can be used as a final trading signal.

 

John Bollinger suggests three trading methods in his book:

  1. Volatility breakout
  2. Following the trend
  3. Reversals

 

In this study, we will analyze the third trading option of Bollinger bands: reversals.

Hypothesis
To conclusion

Events on the ‘’Reversals’’ Bollinger trading system influence the market trend direction.

To conclusion
Data used

The set of financial instruments and their timeframes for testing against a trading signal:

  • 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 a 5-year period,
  • D1 (1 day): the history covers a 10-year period.


Total: 1,980,649 values.

Bollinger bands are made up of three lines (pic.1). An average band is a moving average. An upper band is also an average band moved upwards by a certain number of standard deviations (by two defaults). A lower band is an average band moved downwards by the same number of standard deviations.


The main rule when drawing Bollinger Bands is the following statement: about 5% of prices must be outside these bands and 95% inside.

Bollinger bands boundaries are positioned at distances which are equal to a certain number of standard deviations. As the value of a standard deviation depends on the volatility, bands regulate their own width. If there is a higher volatility in the market, for example, during news release, a band expands; when the market is calm, a band gets narrower.

 

To plot Bollinger Bands in a standard way, the following elements are used:

  • A simple moving average with the N period averaging out the SMA closing price (N, Close);
  • A standard deviation over the N period calculated by the StdDev closing price (N, Close).

 

A standard deviation represents a root-mean-square difference between closing prices and a moving average:

StdDev reflects the value of market noise. It increases when the instrument volatility gets higher.



The channel boundaries position is calculated as follows:


  • The upper boundary:

BBup = SMA (N, Close) + D * StdDev

 

  • The lower boundary:

BBdn = SMA (N, Close) – D * StdDev

 


D is an additional deviation coefficient aimed at adjusting the bandwidth; its standard constant: D = 2.

 

So, the bandwidth boundaries are shifted from the average band to the value exceeding the market noise value. Accordingly, most of the time price chart is within a given Bollinger bandwidth. The price approaches or goes beyond its boundaries in case of a strong movement.

 

The Bollinger Reversals strategy includes the Bollinger Bands (20, 0, 2) indicator or Percentage Bandwidths (%B). In addition, Accumulation/Distribution (AD) indicators or Moving Average Convergence/Divergence (MACD with 21, 100, 9 parameters) are also included.

 

 

Method for Event Detection


 

1. Buy if the Bollinger Bands %B indicator is below the 0.05 boundary and the AD indicator is positive:

  • %B (i) < 0.05
  • %B (i-1) > 0.05
  • AD > 0



2. Sell if the Bollinger Bands %B indicator is above the 0.95 boundary and the AD indicator is negative:

  • %B (i) > 0.95
  • %B (i-1) < 0.95
  • AD < 0



3. Buy if the Bollinger Bands %B indicator is below the 0.05 boundary and the MACD indicator is positive:

  • %B (i) < 0.05
  • %B (i-1) > 0.05
  • MACD > 0



4. Sell if the Bollinger Bands % B indicator is above the 0.95 boundary and the MACD indicator is negative:

  • %B (i) > 0.95
  • %B (i-1) < 0.95
  • MACD < 0



Now, let us stipulate the conditions of closing a trading position

 

Closing a position:

  • In all conditions, the position lifetime is set to the 5th , 10th ,15th  candlesticks.
  • Autor’s options of closing positions:

 

Long position

  • Option 1: High(i1) > BB(i1) and High(i1-1) < BB (i1-1)
  • Option 2: %B (i2) > 0.95 and %B (i2-1) < 0.95


Short position

  • Option 1: Low(i1) < BB(i1) and Low(i1-1) > BB (i1-1)
  • Option 2: %B (i2) < 0.05 and %B (i2-1) > 0.05


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




Analysis of the Results

 

Let us estimate the results based on the sample size.

 


The combination of reversal signals and the AD indicator

 

For the 1—hour timeframe (H1):


Market segment
Number of candlesticks
Number of events
Forex
655727
25326
Commodities
115947
4362
US indices
52779
1996
RF index
11419
404
US stocks
234486
8118
RF stocks
612999
22850
Total
1683357
63056



For the 1—day timeframe (D1):


Market segment
Number of candlesticks
Number of events
Forex
67473
2685
Commodities
15451
581
US indices
5451
178
RF index
2517
78
US stocks
71598
2486
RF stocks
134802
4972
Total
297292
10980




The combination of reversal signals and the MACD indicator



For the 1—hour timeframe (H1):


Market segment
Number of candlesticks
Number of events
Forex
655727
21664
Commodities
115947
3822
US indices
52779
1756
RF index
11419
334
US stocks
234486
7118
RF stocks
612999
18663
Total
1683357
53357



For the 1—day timeframe (D1):


Market segment
Number of candlesticks
Number of events
Forex
67473
2742
Commodities
15451
552
US indices
5451
223
RF index
2517
84
US stocks
71598
2565
RF stocks
134802
5048
Total
297292
11214



Then, we will see the share of events in % in the total number of initial candlesticks on the basis of timeframes:

 


For the 1—hour timeframe (H1):


Indicator
Forex
Commodities
US indices
RF index
US stocks
RF stocks
AD
3.9
3.8
3.8
3.5
3.5
3.7
MACD
3.3
3.3
3.3
2.9
3.0
3.0



For the 1—day timeframe (D1):


Indicator
Forex
Commodities
US indices
RF index
US stocks
RF stocks
AD
4.0
3.8
3.3
3.1
3.5
3.7
MACD
4.1
3.6
4.1
3.3
3.6
3.7



Next what we analyze the results of handled Bollinger reversal signals.


We will assess the results with two criteria:

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


Let us review the results in terms of holding positions, timeframes, indicators, and market segments.

 

Let us take the following notations:

«H1 / 5»: сlosing the 5th candlestick position when setting the hourly timeframe;

«H1 / 10»: closing the 10th candlestick position when setting the hourly timeframe;

«H1 / 15»: closing the 15th candlestick position when setting the hourly timeframe;

«D1 / 5»: closing the 5th candlestick position when setting the daily timeframe;

«D1 / 10»: closing the 10th candlestick position when setting the daily timeframe;

«D1 / 15»: closing the 15th candlestick position when setting the daily timeframe;

«ВВ»: closing a position when touching the opposite Bollinger bands price;

«%В»: closing a position when a percentage bandwidth (%В) crosses the opposite level;

SPP, the share of profitable positions, %;

AD, the Accumulation/Distribution indicator;

MACD, the Moving Average Convergence/Divergence indicator.



Volatility coefficient:

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


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



The combination of reversal signals and the AD indicator



The Number of reversal signals, the Momentum, the Share of profitable positions, and the Volatility coefficient in terms of holding positions, timeframes, and market segments


AD
Indicator
Forex
Commodities
US indices
RF index
US stocks
RF stocks
All
Н1/5
Number of signals
25326
4362
1996
404
8118
22850
63056
Momentum
0.006
-0.018
-0.006
-0.018
0.022
0.041
0.025
SPP
51.7
48.3
54.1
50.5
51.7
51.5
51.4
Volatility coefficient
1.06
1.04
1.18
1.10
1.20
1.15
1.14
Н1/10
Number of signals
25322
4361
1996
404
8115
22844
63042
Momentum
0.005
-0.022
0.005
0.064
0.115
0.049
0.052
SPP
51.5
48.6
54.6
55.5
54.9
51.8
52.4
Volatility coefficient
1.06
1.04
1.18
1.10
1.20
1.15
1.14
Н1/15
Number of signals
25317
4360
1996
404
8105
22842
63024
Momentum
0.005
-0.015
0.027
0.111
0.111
0.066
0.060
SPP
51.1
49.2
53.6
54.7
54.1
52.2
52.3
Volatility coefficient
1.06
1.04
1.18
1.10
1.20
1.15
1.14
H1/BB
Number of signals
25274
4346
1996
404
8096
22779
62895
Momentum
0.025
-0.032
0.038
0.342
0.395
0.240
0.218
SPP
63.4
61.8
67.4
72.8
69.1
65.5
65.9
Volatility coefficient
1.06
1.04
1.18
1.10
1.20
1.15
1.14
H1/%B
Number of signals
25250
4346
1996
404
8096
22775
62867
Momentum
0.033
-0.050
0.061
0.338
0.418
0.371
0.287
SPP
64.0
62.4
69.8
72.8
69.9
67.5
67.2
Volatility coefficient
1.06
1.04
1.18
1.10
1.20
1.15
1.14


AD
Indicator
Forex
Commodities
US indices
RF index
US stocks
RF stocks
All
D1/5
Number of signals
2685
581
178
78
2486
4972
10980
Momentum
0.051
-0.222
0.063
-0.172
0.276
0.190
0.157
SPP
52.1
46.4
58.4
53.9
56.3
50.6
52.2
Volatility coefficient
1.01
1.01
1.08
0.99
1.00
0.99
1.00
D1/10
Number of signals
2680
581
178
78
2483
4961
10961
Momentum
0.012
-0.236
0.160
-0.352
0.385
0.277
0.217
SPP
49.4
46.2
59.5
51.3
56.9
49.7
51.4
Volatility coefficient
1.01
1.01
1.08
0.99
1.00
0.99
1.00
D1/15
Number of signals
2677
579
178
78
2473
4954
10939
Momentum
0.011
-0.475
0.263
-0.266
0.460
0.455
0.310
SPP
49.5
46.8
63.6
52.6
56.8
50.6
51.9
Volatility coefficient
1.01
1.00
1.08
0.99
1.00
0.99
1.00
D1/BB
Number of signals
2644
575
176
78
2462
4911
10846
Momentum
0.165
-1.125
0.559
0.510
0.948
-0.263
0.100
SPP
68.4
63.6
78.3
61.5
74.5
64.0
67.7
Volatility coefficient
1.01
1.00
1.08
0.99
1.00
0.99
1.00
D1/%B
Number of signals
2608
570
178
78
2459
4872
10765
Momentum
0.165
-1.564
0.286
0.312
1.389
0.651
0.615
SPP
49.9
45.5
64.7
55.1
59.9
50.3
52.6
Volatility coefficient
1.01
1.00
1.08
0.99
1.00
0.99
1.00




The combination of reversal signals and the MACD indicator

 


The Number of reversal signals, the Momentum, the Share of profitable positions, and the Volatility coefficient in terms of holding positions, timeframes, and market segments 


MACD
Indicator
Forex
Commodities
US indices
RF index
US stocks
RF stocks
All
Н1/5
Number of signals
21664
3822
1756
334
7118
18663
53357
Momentum
0.001
-0.037
-0.012
0.008
-0.006
0.080
0.035
SPP
51.6
49.1
50.2
47.9
50.5
53.2
51.9
Volatility coefficient
1.02
1.04
1.00
1.02
1.07
1.11
1.08
Н1/10
Number of signals
21660
3821
1756
334
7114
18654
53339
Momentum
0.008
-0.044
0.011
0.021
0.030
0.063
0.037
SPP
51.6
48.3
51.8
50.3
52.0
52.6
52.0
Volatility coefficient
1.02
1.04
1.00
1.02
1.07
1.11
1.08
Н1/15
Number of signals
21658
3818
1756
334
7104
18648
53318
Momentum
0.010
-0.016
0.008
-0.042
0.029
0.071
0.042
SPP
51.0
49.1
50.6
47.6
51.6
52.8
51.9
Volatility coefficient
1.02
1.04
1.00
1.02
1.07
1.11
1.08
H1/BB
Number of signals
21645
3811
1756
334
7063
18594
53203
Momentum
0.016
0.022
0.018
-0.112
0.166
0.089
0.087
SPP
63.5
61.4
64.8
60.5
65.8
64.7
64.5
Volatility coefficient
1.02
1.04
1.00
1.02
1.07
1.12
1.08
H1/%B
Number of signals
21633
3811
1756
334
7062
18578
53174
Momentum
0.026
-0.009
0.039
-0.068
0.158
0.156
0.118
SPP
64,1
62,3
66.5
62.9
66.5
66.4
65.7
Volatility coefficient
1,02
1,04
1.00
1.02
1.07
1.12
1.08


MACD
Indicator
Forex
Commodities
US indices
RF index
US stocks
RF stocks
All
D1/5
Number of signals
2742
552
223
84
2565
5048
11214
Momentum
0.033
-0.379
-0.176
-0.466
0.022
0.288
0.124
SPP
51.8
45.3
51.6
44.1
52.0
51.3
51.2
Volatility coefficient
1.01
0.99
1.01
0.96
0.99
0.99
1.00
D1/10
Number of signals
2741
552
223
84
2565
5035
11200
Momentum
0.018
-0.635
-0.557
-1.027
0.025
0.443
0.172
SPP
49.4
43.4
46.2
44.1
52.6
50.7
50.4
Volatility coefficient
1.01
0.99
1.01
0.96
0.99
0.99
1.00
D1/15
Number of signals
2740
551
223
84
2559
5029
11186
Momentum
-0.005
-0.969
-0.561
-1.351
0.021
0.509
0.178
SPP
48.9
44.0
50.7
40.5
51.8
50.3
50.0
Volatility coefficient
1.01
0.99
1.01
0.96
0.99
0.99
1.00
D1/BB
Number of signals
2729
546
221
84
2545
4987
11112
Momentum
0.050
-0.630
0.026
-0.271
0.207
-0.271
-0.100
SPP
68.0
65.7
69.7
53.6
68.8
64.3
66.3
Volatility coefficient
1.01
0.99
1.01
0.96
1.00
0.99
1.00
D1/%B
Number of signals
2705
538
223
84
2543
4904
10997
Momentum
0.042
-1.429
-1.274
-1.605
0.097
0.790
0.304
SPP
48.7
42.3
48.9
42.9
52.0
51.2
50.4
Volatility coefficient
1.01
0.99
1.01
0.96
0.99
0.99
1.00




Summing up all the results with the following diagrams:

Conclusion

Momentum


The highest momentums of 0.615% and 0.287% are being observed with the Bollinger bands reversal signals on daily and hourly timeframes combined with the Accumulation/Distribution (AD) indicator when closing a position by percentage bandwidths (%В).


The combination with the Moving Average Convergence/Divergence (MACD) gives the results as follows: 0.304% and 0.118% respectively.


The lowest momentum of -0.100% is being observed with the signals combined with the MACD on the daily timeframe when closing a position by touching the opposite to the Bollinger band opening.



In general, the momentums of Bollinger reversal signals and author's market exits exceed the modular minimally significant value of 0.3% on the daily timeframe and the 0.15% modular value on the hourly timeframe.


A combination of Bollinger Bands %B and the Accumulation/Distribution (AD) indicator is more effective.



SPP


The share of profitable positions with the signals on the hourly timeframe ranges between 51.4% and 67.2%; between 50.0% and 67.7% on the daily timeframe.



Volatility


After signals have being handled, the volatility increases by more than 5% on the hourly timeframe; the volatility remains unchanged on the daily timeframe.




The effectiveness of the “Reversals” Bollinger trading system aimed at market forecasting has been confirmed.

Detailed results are shown in the Appendix:

XLSX (0.17 MB)Application to the article 'Bollinger u-turns. Evaluate the effectiveness of signals'.xlsx

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