Price Channels, Envelopes, and Bands

The simple moving average (SMA) represents the trend of a stock, but actual prices fluctuate about this average. There are various methods to quantify how much the prices tend to fluctuate by constructing either price channels, or envelopes or bands around the moving average. Traders then use the upper and lower limits to either trade price extremes, especially in a sideways market, or to detect breakouts. Also, prices that are strongly trending tend to hung one of the boundaries. In an uptrend, prices tend to hug the upper boundary, in a downtrend, the lower boundary.

Price Channels

The price channel consists of 2 lines on price chart. The upper line is set at the highest high within a past period, called the n-period, and is usually 20 days. The lower line is formed by the lowest low within the n-period. The trading signals created by the price channel are simple — when there is a breakout above the upper line, buy it; when there is a breakout below the lower line, sell or sell short.

1-year price chart for Citigroup, Inc. showing the 20-day price channel. Note that even though there are some false signals to buy here, the price action is hugging the lower band.
1-year price chart for Citigroup, Inc. showing the 20-day price channel.
BigCharts - Interactive Charting

Percentage Envelopes

One simple way of constructing an envelope is by taking a percentage of the simple moving average, then both adding and subtracting it from the SMA to create an envelope around most of the price fluctuations. The boundaries of the envelope from the SMA are fixed. The percentages chosen should be great enough to eliminate a lot of noise and to reduce the number of trading signals to what the trader prefers, but small enough to generate at least some signals.

The percentages used should be tested, since even small changes can result in a large difference in profits or losses.


The disadvantage of envelopes is that their boundaries do not expand or contract with volatility. Hence, if volatility increases, then the envelopes will not encompass most of the price variations, and generate too many false signals for a swing trader; if volatility decreases, then the boundaries will be too far away from prices, generating few, if any, signals.

To accommodate volatility, bands, which are distinguished from envelopes by their variable widths, are constructed around the moving average, using some measure of the volatility of prices. The most common measure of volatility is the standard deviation, and the most common band that makes use of the standard deviation is Bollinger bands.

Bollinger Bands

Created by John Bollinger in the early 1980's, Bollinger bands typically consists of a 20-day simple moving average with lines both above and below the SMA representing 2 standard deviations of the SMA that expand and contract with volatility. The number of days or the number of standard deviations can be varied to suit your trading objectives and methods.

The SMA is the middle band, the upper line, the upper band, and the lower line, the lower band. The interval between the upper band and lower band widens as volatility increases and narrows as it decreases. The standard deviation is calculated using the same prices to calculate the moving average.

In statistics, with truly random data, 2 standard deviations would encompass 95% of all data. However, in the financial markets that are trending, the upper and lower bands encompass fewer prices than would be the case for truly random prices. In an uptrend, prices tend to hug the upper band, while in a downtrend, prices hug the lower band.

1-year price chart of Citigroup, Inc. showing the Bollinger Bands. Note how, in this downtrend, the price action tends to hug the lower band.
1-year price chart of Citigroup, Inc. showing the Bollinger Bands.
BigCharts - Interactive Charting

Keltner Bands (ATR Bands)

Chester Keltner created another type of band that varies according to the volatility of the market. First, daily prices are averaged according to the following formula:

Average Price = (Close + High + Low) / 3

Then a 10-day simple moving average is calculated for these prices. The bands are created by calculating a 10-day moving average for the average true range (ATR) of the same prices, then this SMA is added and subtracted from the SMA for prices.