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

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.

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 5^th , 10^th ,15^th  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):

For the 1—day timeframe (D1):

The combination of reversal signals and the MACD indicator

For the 1—hour timeframe (H1):

For the 1—day timeframe (D1):

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):

For the 1—day timeframe (D1):

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

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 

Summing up all the results with the following diagrams:

Detailed results are shown in the Appendix:

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