8.3 Introduction to Bollinger Bands

Bollinger Bands are a volatility overlay: a middle average with upper and lower bands that breathe. They belong in the same Classical Techniques indicator cluster as moving averages, and they return in the later volatility unit. This OpenExamPrep section is independent study material for the CMT Level I introduction to the bands.

Bollinger’s major insight

Older envelopes, including the moving-average bands in the previous section, shift an average by a fixed percent. That width is constant in percent whether the market is asleep or exploding. John Bollinger’s major insight was that volatility is variable, so the bands that describe “how far is far” should widen when volatility expands and narrow when volatility contracts. The measuring stick is a standard deviation of price around the same middle average, recomputed each bar. The overlay then becomes a picture of price versus its own recent dispersion, not versus an arbitrary 2% collar.

If realized volatility doubles and you still plot ±2.5% envelopes, those envelopes will be tagged constantly—they no longer mean “unusual.” If you plot ±2 standard deviations, the collar gapes with the data and “unusual” still means unusual. That single substitution—percent offset out, standard deviation in—is the construction leap.

First principles

Hold these as the construction creed, not as trading slogans:

1. Choose a typical-price reference. The usual teaching middle band is an SMA of the close. The default length is 20 bars—the short-trend daily map from the moving-average unit. The middle band is a moving mean, not a forecast of value.
2. Measure dispersion in the same window. Compute the standard deviation (SD) of those same closes. When the last 20 closes are tightly bunched, SD is small. When they include a shock, SD jumps.
3. Offset the mean by k dispersions. The usual teaching k is 2. Upper band = middle + k·SD; lower band = middle − k·SD. Two standard deviations is a wide enough collar that most closes in a roughly mound-shaped sample sit inside, while still allowing tags.
4. Let the collar breathe. No extra rule is required: if SD doubles, band width doubles. That is the whole insight made mechanical.
5. Read location as relative, not moral. A tag of the upper band means “high relative to the last n bars’ volatility,” not “the asset is objectively expensive” and not “sell.”

Platforms differ on population SD (divide by n) versus sample SD (divide by n−1). Level I cares that width comes from SD of the window, not which denominator your vendor picked.

A tiny numeric sketch using the same five closes as the SMA example (10, 12, 11, 13, 14): mean 12. Deviations −2, 0, −1, +1, +2. Squared sum 10. Population SD = √(10/5) ≈ 1.41. A two-SD collar is about 12 ± 2.82, or 9.18 to 14.82. The last close (14) is inside, nearer the upper edge. Stretch the same mean with a wilder sample and the collar gapes; that is the plot you see in a selloff. (Five bars are for arithmetic only; the teaching default remains 20.)

If closes were drawn from a neat bell curve, the empirical rule would put about 95% of them within two standard deviations of the mean. Market closes are not that neat—fat tails and trends violate the textbook curve—yet the same geometry still explains why containment is the basic look: most prints live inside a 2-SD collar, so a tag is noteworthy as location, not as a mandatory reversal.

How the bands are calculated

Because SD is in price points, a $50 stock and a $500 stock are not comparable by raw band width. Percent measures such as BandWidth ((upper − lower) / middle) exist to compare across time; the introductory plot is still the three lines on price.

If you change 20 to 50, you are describing a slower mean and a slower volatility. If you change 2 to 1.5, tags become common; if you change 2 to 3, tags become rare. Defaults are conventions for communication, not laws of the tape. The middle band is an SMA in the standard recipe; swapping in Wilder’s 14-period smoother would be a different overlay and would no longer match the usual “Bollinger 20, 2” language.

Most basic application: containment, walking, squeezes

Containment. In ordinary conditions a large share of closes occurs between the bands. The overlay is a soft container of recent price given recent volatility. A touch of a band is therefore a relative high or low versus that window. It is not, by itself, a reversal signal. Many closes will tag a 2-SD band in a trending market; that is geometry, not a malfunction.

Walking the bands. In a persistent uptrend, price can ride the upper band for many bars while the middle SMA slopes up and the lower band trails. That is strength. Covering a long because a momentum oscillator is high and price is on the upper band is how traders fade a trend too early. The opposite walk—closes plastered to the lower band with a falling middle—is persistent weakness. Walking answers “is the move extended and still in force?” not “has the move ended?”

Squeezes. When SD collapses, the bands pinch. That low-volatility coil is the squeeze. Squeezes often precede a volatility expansion (a breakout or a fast directional run). The squeeze does not tell you the direction. Direction comes from a break of a band, a pattern, volume, or a trend filter. A squeeze that breaks down is as much a squeeze play as one that breaks up.

Combine the three reads: quiet containment → squeeze → expansion, versus trending containment → walking a band → later squeeze when the trend rests. A high ADX walk of the upper band and a low-ADX squeeze are different tapes that happen to use the same three lines.

What the bands graphically illustrate

Graphically, Bollinger Bands are a moving mean plus a moving volatility collar. At a glance you see:

• Whether price is high or low versus its recent average (distance from the middle band).
• Whether that distance is large or small versus recent volatility (distance versus the bands, which already embed SD).
• Whether volatility itself is expanding or contracting (band width).

They do not illustrate implied volatility from options (that is a later unit). They do not illustrate a fixed-percent envelope. They do not print a buy or sell arrow. %B (where price sits as a fraction of the collar) and BandWidth are companion statistics; the Level I introduction is the picture of relative high and low versus realized volatility on the price pane.

Keltner channels, covered in the later volatility chapter, typically offset an average by a multiple of average true range rather than by standard deviation of closes.

Exam traps

Fixed-percent envelopes versus SD bands. Defaults 20 and 2 as teaching conventions, not sacred constants. Upper-band tags in a trend as possible continuation (walking), not automatic shorts. Squeezes as volatility states, not directional signals. A low ADX and a Bollinger squeeze often describe the same coiled tape from two recipes. The middle band is an SMA of the close in the standard construction, not Wilder’s 14-period smoother, unless you deliberately change it.

With k = 2, full band width is about four times the window’s standard deviation. In the illustrative bars above, a squeeze at SD = 1 gives a collar about 4 points wide; a shock window at SD = 5 gives a collar about 20 points wide around the same 20-period SMA. The middle line did not have to change recipes—the data’s dispersion did.