Bollinger Bands
Bollinger Bands, developed by John Bollinger of Bollinger Capital Management, are trading bands that vary in distance from the moving average as a function of a market’s volatility. Bollinger took mathematical formulas commonly used by statisticians to determine the standard deviation of a data series and adapted them to calculate the width of trading bands.
Bollinger Bands are usually plotted at an interval of two standard deviations above and two standard deviations below the moving average for the market studied. Bollinger suggests the optimal period for most applications is a 20-21 period average, but it is possible to go as high as 50. A Simple Moving Average is most commonly used, but both Exponential and Weighted Averages are used to assign a greater weight to newer prices.
Formula
The formula for computing Bollinger Bands is relatively simple:
- Calculate the moving average using the following formula
MA = (P1 + … + Pn)/n, where
Pn = Price at nth interval
n = Number of periods
- Subtract the Moving Average (MA) from each of the data points (p) used in the moving average calculation
This will give you a list of deviations (d) from the average
- Finally, compute the three Bollinger Bands using the following formulas
- Upper Band = MA + 2σ
- Middle Band = MA
- Lower Band = MA -2σ
Initially developed for use in the equities markets, Bollinger Bands are a highly versatile TA indicator. In contrast to most other TA tools, Bollinger Bands can be used in both range bound and trending markets. The image below
For instance, in the case of range-bound markets, traders will typically look to sell the market if prices touch the upper band or buy the market if prices touch the lower band. Traders would then look to take profit either at the middle band moving average or look to take profit at the opposite band before taking the opposite position.
In the case of trending markets, however, traders will first wait for the market to penetrate the upper band before buying or wait for the market to penetrate the lower band before selling. If correct, traders would look to remain in the trade until the market retraced either back up to the middle band moving average or alternatively back to the opposite band.
Width of Bollinger Bands
As with most TA tools, however, it is imperative for traders to accurately assess whether the market is likely to stay within a range or about to trend to make accurate trading decisions – and Bollinger Bands are no exception. However, since the width of Bollinger Bands indicates market volatility, they can also be used to make precisely this kind of assessment.
For example, with volatility being just as cyclical as price behaviour, a period of narrow Bollinger Bands implies low historical volatility. However, low volatility cannot last indefinitely – which means that a period of high volatility (usually associated with a directional, trending move) may be about to occur.
