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FIGURE 4: Bollinger Bands are plotted two standard deviations above and below a simple moving average. The data used to calculate the standard deviation are the same data as those used for the simple moving average. In essence, you are using moving standard deviations to plot bands around a moving average. The time frame for the calculations is such that it is descriptive of the intermediate-term trend. For the mathematically inclined, the middle band is the n-day mean. The upper band is the n-day mean plus twice the root mean squared deviation from that mean, while the lower band is the n-day mean minus twice the root mean squared deviation from that mean where n is chosen such that it describes the intermediate-term trend.

FIGURE 5: Here is the DJIA ,this time with Bollinger Bands. Note the bands ' responsiveness to changing market conditions. The width of the bands varies by more than three times from point A to point B, note also that many reversals occur near the bands and that the average provides support and resistance in many cases.

FIGURE 6: The easiest way to identify the proper average is to choose one that provides support to the correction of the first move up off a bottom. U the average is penetrated by the correction, then the average is too short. If, in turn, the correction falls short of the average, then the average is too long. An average that is currently chosen will provide support far more often than it is broken.

There is great value in considering different measures of price. The typical price, (high + low + close) / 3, is one such measure that I have found to be useful. The weighted close, (high + low + close + close) / 4, is another. To maintain clarity, I will confine my discussion of trading bands to the use of closing prices for the construction of bands. My primary focus is on the intermediate term, but short- and long-term applications work just as well. Focusing on the intermediate trend gives one recourse to the short and long-term arenas for reference, an invaluable concept.

For the stock market and individual stocks, a 20-day period is optimal for calculating Bollinger Bands. It is descriptive of the intermediate-term trend and has achieved wide acceptance. The short-term trend seems well served by the 10-day calculations and the long-term trend by 50-day calculations.

The average that is selected should be descriptive of the chose; time frame. This is almost always a different average length than the one that proves most useful for crossover buys and sells. The easiest way to identify the proper average is to choose one that provides support to the correction of the first move up off a bottom. If the average is penetrated by the correction, then the average is too short. If, in turn, the correction falls short of the average, then the average is too long. An average that is correctly chosen will provide support far more often than it is broken. (See Figure 6.)

Bollinger Bands can be applied to virtually any market or security. For all markets and issues, I would use a 20-day calculation period as a starting point and only stray from it when the circumstances compel me to do so. As you lengthen the number of periods involved, you need to increase the number of standard deviations employed. At 50 periods, two and a half standard deviations are a good selection, while at 10 periods one and a half do the job quite well.

In most cases, the nature of the periods is immaterial; all seem to respond to correctly specified Bollinger Bands. I have used them on monthly and quarterly data, and I know many traders apply them on an intraday basis.