Bollinger Bands vs Keltner Channels: Standard Deviation vs ATR

Bollinger Bands and Keltner channels both draw an upper and a lower line around a moving average, but they size the gap differently. Bollinger Bands use the standard deviation of recent closes; Keltner channels use the Average True Range (ATR), which measures daily highs, lows and gaps. Vyreon reports Bollinger Bands (20, 2) and Keltner channels of EMA 20 ± 2 × ATR(10).

Bollinger Bands Formula

Over the last 20 sessions:

Middle = 20-day simple moving average (SMA) of the close
Upper = middle + 2 × sd
Lower = middle − 2 × sd

where sd is the population standard deviation of the same 20 closes (dividing by 20, as in John Bollinger's definition). See Bollinger Bands.

Keltner Channel Formula

Middle = 20-day exponential moving average (EMA) of the close
Upper = middle + 2 × ATR(10)
Lower = middle − 2 × ATR(10)

ATR(10) is Wilder's average of the true range over 10 sessions, where true range is the largest of high − low, |high − previous close| and |low − previous close|. See ATR and price channels.

Standard Deviation Vs ATR

The two widths respond to different things.

Standard deviation measures how far the 20 closes are spread around their average. Only closes count; intraday highs and lows do not.
ATR measures the typical size of each session's range, including overnight gaps. It does not depend on where the closes sit relative to each other.

This leads to the main practical difference. In a steady trend, the closes in the window spread out along the trend, so standard deviation and the Bollinger Bands widen even if each day's range is small. ATR, and so the Keltner channel, reflects only the daily ranges and widens only when those ranges grow.

A single large close also behaves differently: it raises the standard deviation sharply for exactly 20 sessions and then drops out. In ATR it is smoothed in with weight 1/10 and fades gradually.

Illustrative example: over 20 sessions a stock rises 0.50 a day from 90.50 to 100.00, with a true range of 1.00 every day. The closes average 95.25 with a population sd of about 2.88, so the Bollinger Bands sit near 89.5 and 101.0, about 12% wide. ATR(10) is 1.00, so the Keltner channel is 2 × 2.00 = 4.00 wide, about 4% of the price. (If the trend has run long enough, the 20-day EMA is also about 95.25: on a steady trend it lags as far as the SMA.)

Bollinger Bands Inside Keltner Channels

Some traders compare the two directly. When the Bollinger Bands fall inside the Keltner channel, closes have been tightly bunched relative to the typical daily range. This comparison is known in trading literature as a "squeeze". It describes a quiet stretch; it says nothing about the direction or timing of any later move.

How Vyreon Calculates Them

Bollinger (20, 2): upper, middle and lower bands with the population standard deviation, plus %B (where the close sits between the bands) and bandwidth (band width ÷ middle).
Keltner: EMA(20), seeded with the simple average of its first 20 closes and smoothing factor 2 ÷ 21, ± 2 × Wilder ATR(10).
Both use daily bars adjusted for splits and dividends, so a split does not appear as a giant move.

What They Do Not Tell You

Both describe recent prices and ranges. Neither forecasts.
A close at or beyond a band or channel line describes where the price is. Reading it as a breakout or as stretched is a convention, not a rule.
The windows (20 and 10) and multipliers (2) are conventions; other settings draw other lines.

Sources

John Bollinger, Bollinger on Bollinger Bands (2001): the bands, %B and bandwidth, with the population standard deviation.
Chester W. Keltner, How to Make Money in Commodities (1960): the original channel, a 10-day average of the typical price with lines set by the 10-day average daily range. The EMA ± ATR form used here is a later variant commonly attributed to Linda Bradford Raschke.
J. Welles Wilder Jr., New Concepts in Technical Trading Systems (1978): true range and Wilder's ATR.
John F. Carter, Mastering the Trade (2006): popularized the "squeeze" comparison of Bollinger Bands with Keltner channels.