Study guide
8.3 Introduction to Bollinger Bands
CMT Level I Chartered Market Technician
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1 Introduction and Exam Overview
1.1 Current CMT Level I Exam Facts 1.2 Charter Path and Study Plan
2 Theory and History Foundations
2.1 A Brief History of Technical Analysis 2.2 The Dow Theory 2.3 Markets, Instruments, Data, and the Technician
3 Market Hypotheses and Fibonacci
3.1 The Efficient Markets Hypothesis 3.2 The Fibonacci Sequence and the Golden Ratio
4 Chart Types and Construction
4.1 An Overview of Charting 4.2 The X Axis 4.3 The Y Axis 4.4 Charting Volume and Open Interest
5 Trend Analysis
5.1 What Is a Trend 5.2 A Trend's Four Phases 5.3 Trend Identification and Following
6 Volume, Open Interest, and Internals
6.1 Introduction to Volume Analysis 6.2 Volume, Open Interest, and Price 6.3 Market Internals
7 Chart Pattern Analysis
7.1 Classical Chart Patterns 7.2 Introduction to Candlesticks 7.3 Introduction to Candlestick Patterns 7.4 Basics of Point-and-Figure Charting
8 Internal and External Technical Indicators
8.1 Moving Averages 8.2 Technical Indicator Construction 8.3 Introduction to Bollinger Bands
9 Statistics for Technicians
9.1 Introduction to Statistics, Part 1 9.2 Introduction to Statistics, Part 2 9.3 Introduction to Probability
10 Behavioral Finance and Sentiment
10.1 Behavioral Finance 10.2 Market Sentiment and Technical Analysis 10.3 Sentiment Measured from Market Data 10.4 Sentiment Measured from External Data
11 Cycle Analysis
11.1 Foundations of Cycle Theory 11.2 Common Cycles
12 Equities, Indexes, and Fixed Income
12.1 Equities 12.2 Indexes 12.3 Fixed Income and Bonds
13 Futures, ETPs, and Currencies
13.1 Futures 13.2 Exchange-Traded Products 13.3 Foreign Exchange
14 Digital Assets and Options
14.1 Digital Assets 14.2 Options
15 Relative Strength
15.1 Introduction to Relative Strength 15.2 Relative Strength and Its Uses
16 Volatility Analysis
16.1 The Meaning of Volatility to a Technician 16.2 Measuring Historical Volatility 16.3 Options-Derived Volatility
17 Systematic Methods and Ethics
17.1 Introduction to Quantitative Methods 17.2 Code of Ethics 17.3 Standards of Professional Conduct
8.3 Introduction to Bollinger Bands
Key Takeaways Explain This Topic AI
John Bollinger’s construction insight is that volatility is variable, so band width should expand and contract with a volatility measure rather than use a fixed-percent envelope.
Teaching defaults: middle band = 20-period SMA of the close; upper and lower bands = that SMA plus and minus k standard deviations, with k typically 2.
The most basic application is containment: most closes sit between the bands, so a tag is a relative high or low versus the recent window’s volatility—not an automatic reversal.
Walking the bands describes a strong trend riding one band; a squeeze describes unusually narrow bands after volatility has fallen and often precedes a volatility expansion without naming direction.
Graphically the overlay shows where price sits versus its recent mean and versus recent realized volatility; Keltner channels (later volatility unit) typically use ATR around an average instead of standard deviation.
Last updated: September 2026
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 ExamFinch 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:
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.
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.
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.
Let the collar breathe. No extra rule is required: if SD doubles, band width doubles. That is the whole insight made mechanical.
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
- Piece Teaching default Meaning
- Middle band 20-period SMA of the close Short-term mean; same length as the SD window
- Width unit Standard deviation of those 20 closes Realized volatility of the window, in price units
- Multiplier k 2 Upper = SMA + 2·SD; lower = SMA − 2·SD
- Full width About 4·SD (upper minus lower) The quantity that pinches in a squeeze
- Interval Same as the chart A 20-bar band on weekly bars is not a 20-day band
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.
Illustrative 20-bar standard deviation (price points) that sets band width
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.