Technical Studies: Bollinger Bands

Bollinger Bands—named for John Bollinger, their creator—are a lagging upper chart indicator that plots three lines:

• a Simple Moving Average (SMA)
• an upper band that sits above the moving average
• a lower band that sits below the moving average

The upper band and lower band adjust in accordance with the standard deviation levels of the security. The upper band is plotted at two standard deviations above the SMA. The lower band is plotted at two standard deviations below the SMA.

According to John Bollinger, periods of low volatility often precede periods of high volatility, or relatively large price swings. Because standard deviation measures price volatility, Bollinger Bands are useful for identifying periods of low and high volatility. When the price contracts, or becomes less volatile, the two bands narrow. When the price expands up or down, and becomes more volatile, the two bands widen.

As well, price moves that pierce the bands may imply a continuation of the current uptrend or downtrend. Trend reversals, on the other hand, may be signaled when bottoms and tops made outside the bands are followed by bottoms and tops made inside the bands. Bollinger also believes that a price move originating at one band tends to extend to the other band.

Customizing Bollinger Bands: Bollinger Bands, by default, are plotted at two standard deviations above and below a 20-period SMA. Periods are based on the selected frequency (minutes/hours/days/weeks/months). To customize the Bollinger Bands on a chart, select Bollinger Bands as a study. To change the parameters of the bands, click the "Edit" button to modify the parameters. In the popup screen, select the SMA period in the first text box and the number of standard deviations (one or two) from the SMA in the second text box.

For longer moving average lengths, such as 50, some technical analysts plot Bollinger Bands at 2.5 standard deviations above and below the SMA. For shorter moving average lengths, such as 10, some analysts plot the bands at 1.5 standard deviations above and below the SMA.

How the bands are calculated: Here are the various steps:

1. Calculate the SMA for the period:
   SMA = Sum of the last n closing prices / n
   Where the default value for n is 20, but can be customized. The SMA is the average price for the security during that period.
   
   
2. Calculate the upper band and lower band. Start by finding the Variance:
   Variance = Sum of all deviations from the mean, squared, for last n closing prices / n
   Where the default value for n is 20, but can be customized. The SMA is the average price for the security during that period.
   
   For a 20-day SMA, for example, the SMA might be 40.90 while the fifth day's closing price is 38.90. The deviation from the moving average for the fifth day is -2. The square of -2 is 4. Add that number to the square of the deviation for all 19 remaining periods and divide the sum by 20 to arrive at the variance.
   
   Then calculate the standard deviation:
   Standard Deviation = Square root of Variance
   
   Standard Deviation is the amount a security's price has varied from its mean over a specified period. Therefore, it is a measure of a security's volatility. The higher the standard deviation, the more the security's price fluctuates from its average price.
   
   Next, since the default parameter is 2× the standard deviation, the upper band is plotted at two standard deviations above the SMA and the lower band is plotted at two standard deviations below the SMA:
   Upper Band = SMA + (2 × Standard Deviation)
Lower Band = SMA - (2 × Standard Deviation)