Bollinger Bands is one of the commonly used technical indicators. It is also one of our favorite indicators because of its properties. It was introduced by John Bollinger back in the 1980s. Its purpose is to define how high or low the price is, compared to the previous periods. Bollinger Bands consists of three lines: a middle line which is nothing more but a simple moving average, an upper line and lower line placed at some distance from the middle line. Typical sample size or period of the indicator is 20 and deviations is usually 2. The deviations value determines the spacing of the upper and lower lines from the moving average.
They are calculated as this:
upper_band = μ + kσ
lower_band = μ – kσ
where μ is the mean or moving average and σ represents one standard deviation. In other words, the upper line is k standard deviations above the mean, and lower line is k standard deviations below the mean. Standard deviation measures how spread out the data points are. In normal distributions the data points are more concentrated around the mean. The further away we go from the mean the less the number of data points. This can be also expressed numerically using the Chebyshev’s inequality:
In simple words it states that the probability that a data point (X) lies beyond k standard deviations from the mean (μ) is no more than 1/k². If we apply the standard Bollinger Bands value of 2 deviations it turns out that no more than 25% of the price points will be outside the upper and lower band and 75% of the data points will be inside the bands. If we use 3 deviations in the Bollinger Bands indicator, then only 11.1% of the price points will lie outside the bands and 88.9% will be inside the bands. The following table gives a good idea of how the data points are distributed depending on the number of standard deviations:
| Deviations, k | Min % Inside Bands | Max % Outside Bands |
|---|---|---|
| 1.5 | 55.6% | 44.4% |
| 2 | 75% | 25% |
| 2.5 | 84% | 16% |
| 3 | 88.9% | 11.1% |
| 4 | 93.75% | 6.25% |
| 5 | 96% | 4% |
This law is usually used in mean reversion or price reversal strategies where the trader buys at the lower band or sells at the upper band and closes the trade at the mean. The law implies that the price is more likely to go back to the mean and inside the bands. This is more likely to happen if the slope of the bands is small. Care should be taken as there’s still some chance the price continue in same direction. That’s why Bollinger Bands is usually combined with other indicators, support/resistance lines, etc.
A period of low volatility is observed when the bands are close together. Conversely, when the bands expand a high volatility is indicated.
Bollinger Bands is also used as a breakout indicator and trade is opened in same direction when the price breaks any of the two bands.
No matter what strategy is used Bollinger Bands is a great tool to use.
Sofia
Forrest
Vida