# Construction

The construction of trading bands is really quite straightforward.

You start with some measure of central tendency and build the bands above and below that measure.

What measure of central tendency should be used and what determines the interval?

For Bollinger Bands:

- The measure of central tendency is a simple moving average.

-  The interval is delineated by a measure of volatility, a moving standard deviation.

What does moving mean here?

It means that for each period the analysis is calculated anew.

For a moving average, each period's values are drawn from the immediately prior values.

For a 20-day average, the most recent 20 days are used.

The next day the oldest day's data is discarded and the newest included.

The same is true for volatility; for each period, the volatility is measured using the immediately preceding periods.

Bollinger's first interest in the securities world was options.

Since volatility seemed to be the key to many things in that area, he studied volatility in all its forms.

When it came to trading bands, it was clear for him that to achieve success, the bands would have to incorporate volatility.

Which volatility measure is better to use?

Once volatility was identified as the best way to set the width of trading bands, there were still a lot of choices.

Early in the decision process it became clear that the more adaptive the approach, the better it would work.

In all of the measures examined, standard deviation stood out in this regard.

We all know how standard deviation is calculated:

- calculate deviation from the mean

- squaring each deviation

- calculate average of this squared deviations

- take the square root of this average

While squaring the deviations has the benefit of allowing the rest of the computation to proceed, it also has a side effect:

--> The deviations are magnified --> the larger the deviation, the larger the magnification.

There lies the key!!!

For as prices surge or collapse and the deviations from the average grow, the squaring process magnifies them and the bands efficiently adapt to the new prices.

As a result, it almost seems as if the bands chase after price. Do not underestimate this quality!

It is the key to the bands' power to clarify patterns and maintain useful definitions of what is high and low.

The defaults for Bollinger Bands are a 20-day calculation and 2 standard deviations.

As you shorten the calculation period, you will need to reduce the number of standard deviations used.

As you lengthen the calculation period, you will need to widen the bandwidth.

The reason for the adjustment has to do with the standard deviation calculation itself.

Bollinger tested a number of markets and found the following results:

- At 20 periods and 2 standard deviations you get containment between 88 and 89 percent in most markets.

- To keep that % constant when you shorten the calculation period to 10 --> decrease the bandwidth from 2.0 to 1.9.

- To keep that % constant when you lengthen the calculation period to 50 days -->  increase the bandwidth from 2.0 to 2.1.

For calculation periods less than 10 or greater than 50, changing the periodicity of the bars is more appropriate.

Example: if you require a shorter calculation period than 10 days --> shift to hourly bars might be better.

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