Bollinger Bands (BOLL)

Bollinger Bands are a kind of trading envelope. They are lines plotted at an interval around a moving average. Bollinger Bands consist of a moving average and two standard deviations charted as one line above and one line below the moving average. The line above is two standard deviations added to the moving average. The line below is two standard deviations subtracted from the moving average. Traders generally use them to determine overbought and oversold zones, to confirm divergences between prices and indicators, and to project price targets. The wider the bands are, the greater the volatility is. The narrower the bands are, the lesser the volatility is. The moving average is calculated on the close.

Parameters:

• Period (20) - the number of bars, or period, used to calculate the study. John Bollinger, the creator of this study, states that those periods of less than ten days do not seem to work well for Bollinger Bands. He says that the optimal period for most applications is 20 or 21 days.
• Standard Deviation (2) - the percent of one standard deviation. John Bollinger suggests, if you reduce the number of days used to calculate the bands, you should also reduce the number of deviations and vise versa. For example, 200 percent of a standard deviation means two deviations above and two deviations below the moving average. If you use a period of 50, you may want to use 250 percent of a standard deviation. For a period of 10, you may want to use 150 or 100 percent.

Computation

1. Calculate the moving average. The formula is:
   
   
   • Pn the price you pay for the nth interval
   • n the number of periods you select
   
   
   
2. Subtract the moving average from each of the individual data points used in the moving average calculation. This gives you a list of deviations from the average. Square each deviation and add them all together. Divide this sum by the number of periods you selected.
   
   
   
   
3. Take the square root of d. This gives you the standard deviation.
   
   
   
   
4. Compute the bands by using the following formulas:
   
   
   • Pn is the price you pay for the nth interval
   • n is the number of periods you select