Bollinger Bands

Volatility has a shape

Moving averages smooth price. RSI measures speed. MACD measures the gap between two speeds. None of them tell you how wide the market's range is — how volatile the tape is right now compared to the recent past.

That's what Bollinger Bands do. John Bollinger popularized them in the 1980s, and they've been a default overlay on almost every charting platform since. The idea is disarmingly simple: wrap a standard-deviation envelope around a moving average, and let the envelope breathe with volatility.

The formula

where $\sigma_N$ is the population standard deviation of the last $N$ closes.

Canonical defaults: $N = 20$, $k = 2$.

Kaufman's key clarification on why 2σ does not mean 95%:

Because the standard deviation represents a confidence level, and prices are not normally distributed, the choice of two standard deviations equates to an 87% confidence band (if prices were normally distributed, two standard deviations would contain 95.4% of the data). — Trading Systems and Methods

This is the single most misunderstood stat about Bollinger Bands. Every intro video says "95% of price action falls within the bands." In reality, because market returns have fat tails and skew, ~87% of closes land inside the bands, not 95%. The 13% of closes that land outside are the interesting ones.

And a rigid definition from Kaufman:

If it's not a 20-day average and 2 standard deviations, it's not a Bollinger band.

You can modify the parameters — they're just sliders — but then you've built a generic standard deviation band, not Bollinger Bands per se. The naming convention matters: when someone says "Bollinger Bands," they mean 20/2.

Two sub-indicators

Bandwidth measures how wide the bands are relative to the middle:

Low bandwidth = quiet market. High bandwidth = volatile market. The transition from low to high is the squeeze — one of the most actionable setups Bollinger Bands produce.

%B normalizes where the close sits within the bands:

At the lower band, %B = 0. At the upper band, %B = 1. Above the upper band, %B > 1. Below the lower band, %B < 0. Think of %B as "how far into the envelope is the close?" — it turns the bands into an oscillator.

Play with it

Three things to try:

1. Switch between up / sideways / down. In a trend, notice how price walks along one band — hugging the upper in uptrends, the lower in downtrends. Murphy's description is exact: "In a strong uptrend, prices will usually fluctuate between the upper band and the 20-day average."

2. Crank the period down to 5. The bands become hyperactive, constantly whipping around. Crank it up to 50 — the bands become so smooth they're almost useless for short-term reads. Just like MAs: shorter = more noise, longer = more lag.

3. Toggle %B and Bandwidth on. Watch bandwidth compress, then expand. That's the volatility cycle Bollinger called "extreme seeking": very low volatility forecasts high volatility, and very high volatility forecasts low volatility.

The squeeze

This is the setup traders care most about. From Kaufman:

Bollinger band squeeze is a variation on compression but measures the narrowing of the Bollinger bands. Wait until the Bollinger band compresses to some percentage of the average, for example, 50%, then buy or sell a new breakout through the bands. — Trading Systems and Methods

The logic:

1. Volatility contracts (bandwidth narrows)
2. Price coils inside an ever-tighter range
3. Eventually, volatility must expand — the bands blow out
4. The direction of the first breakout through a band after a squeeze is the trade

Kaufman adds a critical qualification:

Compression has a history of success as a filter and trading on the same side as the trend often shows an improvement in performance.

Translation: the squeeze tells you when something is about to happen, not what. You still need a directional bias — a higher-timeframe trend, a volume confirmation, an oscillator divergence — to decide which band the breakout will pierce.

One enhancement Kaufman documents: use Keltner Channels (a band based on ATR instead of σ) as a reference. When Bollinger Bands narrow so far that they fit entirely inside the Keltner Channel, that's an extreme squeeze. Then wait for the Bollinger Bands to re-expand outside the Keltner Channel — that's the breakout confirmation.

The band walk

Murphy:

In a strong uptrend, prices will usually fluctuate between the upper band and the 20-day average. In that case, a crossing below the 20-day average warns of a trend reversal to the downside. — Technical Analysis of the Financial Markets

Beginners look at a candle touching the upper band and think "overbought — sell." But in a trend, touching the band is normal — it's the trend asserting itself. The upper band isn't a ceiling; it's a moving goalpost that rises with volatility.

Kaufman confirms the same phenomenon:

Once the price moves outside either the upper or lower band, it remains outside for a number of days in a row. This type of pattern was typical of what used to be called high momentum. — Trading Systems and Methods

This is why Bollinger Bands as a standalone reversal system are dangerous. When momentum is high, the band just keeps getting dragged along. The correct reading: touching a band in low-volatility environments is a reversal cue; touching a band in high-volatility environments is a continuation cue. Bandwidth tells you which regime you're in.

Using bands as targets

Murphy's simplest application:

The simplest way to use Bollinger Bands is to use the upper and lower bands as price targets. If prices bounce off the lower band and cross above the 20-day average, the upper band becomes the upper price target. — Technical Analysis of the Financial Markets

This mean-reversion framing works best in sideways / range-bound markets — when bandwidth is moderate and stable. Switch to the sideways market in the playground above and you'll see clean bounces between bands that respect this rule. In a trend, the same approach gets you crushed by the band walk.

What bands expand and contract on

Murphy's cleanest paragraph on the volatility mechanism:

Bollinger Bands differ from envelopes in one major way. Whereas the envelopes stay a constant percentage width apart, Bollinger Bands expand and contract based on the last 20 days' volatility. During a period of rising price volatility, the distance between the two bands will widen. Conversely, during a period of low market volatility, the distance between the two bands will contract. — Technical Analysis of the Financial Markets

The fixed-percentage envelope (e.g., ±3% from an SMA) treats all regimes as equal. Bollinger Bands don't — they breathe. A 2% band on a stock that normally moves 4% per day is meaningless; a 2σ band automatically adapts.

But Kaufman warns about the lagging response:

One of the significant problems with Bollinger bands, as well as any volatility measure based on historic data, is that the bands will expand after increasing volatility but are slow to narrow as volatility declines.

The "bubble" effect: after a spike in volatility, the bands stay wide for ~N days even as the market has already calmed down. This is the same lag-vs-smoothing tradeoff you saw with MAs — here it's just in the volatility dimension rather than the price dimension.

Combining with oscillators

Murphy's recommendation:

Bollinger Bands work best when combined with overbought/oversold oscillators. — Technical Analysis of the Financial Markets

And Bollinger himself:

To reduce [mean-reversion] risk, Bollinger recommends confirming a downside penetration using other indicators, primarily those based on volume and market breadth. — Kaufman, summarizing Bollinger

The textbook combination: price touches the lower band (potential bounce) + RSI divergence from the RSI lesson + volume drying up. That gives you three independent filters converging on one setup. Any one alone is weak; all three together is worth studying.

Quick check

What you now know

• Bollinger Bands = SMA(20) ± 2σ — a volatility-adaptive envelope.
• ~87% of closes fall inside (not 95%) — because markets have fat tails.
• The squeeze (bandwidth compression → breakout) is the highest-conviction setup, but tells you when, not which direction.
• Band walk = touching a band during a trend is continuation, not reversal.
• Use %B as a position-in-band oscillator and bandwidth for the volatility cycle.
• Always combine with an oscillator (RSI) and volume for confirmation.

Next: we've covered the four core indicators — MAs, RSI, MACD, Bollinger. The next unit looks at Dow Theory, the framework that ties all of this together.