Bollinger bands

Bollinger bands are an indicator, developed by John Bollinger, based on the concept of volatility, defined as standard deviation. The standard deviation is calculated as the square root of the variance

Specifically, Bollinger bands are placed around a moving average, usually at 20 day period. The upper Bollinger band is obtained by adding to the moving average twice the standard deviation, while the lower Bollinger band is obtained by subtracting the standard deviation twice the moving average.

A wider Bollinger band determines high price volatility, while by getting closer to each other, the Bollinger band suggests a lower price volatility:

From an operational point of view, some rules state that:

• if the Bollinger bands shrink it is likely that there will soon be a strong explosion of volatility,
• if the price exceeds a Bollinger band, the trend is likely to continue,
• If the price exceeds a Bollinger band and an inversion figure is formed then a trend reversal is likely to be expected.

Bollinger % B indicator

With Bollinger bands, we have almost 95% certainty that all price movements that will happen within the bands. Hence, it is understood that when price levels exceed these levels, such moves would be very exceptional.

Band violations can be quickly seen by looking at the chart however this can be achieved in a better way using the Bollinger % B indicator.

The Bollinger %B is an indicator usually between 0 and 1 depending on the price position compared to the Bollinger bands.

The Bollinger %B can be:

> 1 if prices exceed the upper band,
= 1 if prices are at the upper band,
= 0.5 if prices are in the median band,
= 0 if the prices are at the lower band,
<0 if prices exceed the lower band.

The Bandwidth indicator

The bandwidth is an indicator that is constructed starting from the Bollinger Bands and is given by the ratio between the difference of the upper band with the lower band and the median band.

The bandwidth measures the width of the Bollinger bands and has the function of identifying cycles of volatility to confirm the approach of a directional movement.

In the following graph it can be clearly seen how this indicator is characterized by a cyclic movement that defines the phases of contraction and expansion of the volatility of the Bollinger bands.