# Bollinger Bands

Bollinger Bands are plotted (typically) two standard deviations above and below a simple moving average of the price series. Since standard deviation is a measure of volatility, the Bollinger Bands widen during periods of volatility

# Bollinger Bands

Bollinger Bands are plotted (typically) two standard deviations above and below a simple moving average of the price series. Since standard deviation is a measure of volatility, the Bollinger Bands widen during periods of volatility and contract during calm markets.

## Calculation of Bollinger Bands

Bollinger Bands consist of a moving average and two outer bands.  The moving average displayed in the middle is (typically) a 20 day Simple Moving Average (SMA).  Sometimes an Exponential Moving Average is used in place of the SMA. The upper band is calculated as the moving average plus (typically) 2 standard deviations.   The lower band is calculated as the moving average minus (typically) 2 standard deviations.

Middle Band = SMA(n)

Upper Band = SMA(n) + D * StdDev(n)

Lower Band = SMA(n) - D * StdDev(n)

Where:

• n is the number of time periods and is typically 20.
• D is the number of standard deviations the upper and lower bands are shifted by.  D is typically set to 2.
• StdDev(n) is the standard deviation of Stock Price - SMA() calculated over n periods
Bollinger Bands are 2 standard deviations about a moving average.

## Application of Bollinger Bands

The spacing between the Bollinger Bands varies based on stock price volatility.  During periods of extreme volatility, the bands widen.  During periods of low volatility, the bands narrow.  The stock price tends to be contained within the upper- and lower-band.

Bollinger Bands are generally not used to create trading signals by themselves but are rather combined with other indicators such as the Relative Strength Index (RSI) or the Money Flow Index (MFI).

## Issues With Bollinger Bands

Standard deviations are a statistical unit of measure describing the dispersal pattern of a data set.  By definition, one standard deviation includes about 68% of all data points from the average in what is referred to as a normal distribution pattern, while two standard deviations include about 95% of all data points.

Unfortunately, this unit of measure does not apply to financial time series as they generally do not follow a normal distribution pattern, but tend to have a so-called fat-tail.  Therefore two standard deviations do not actually include 95% of all data points.  Using standard deviation may not be the most appropriate measure of volatility.