Constructing volatility-scaled bands with relative strength index confirmation

What a price envelope locates

Price envelopes locate whether a reading is relatively high or low. Contact with a rail is not specified as an absolute buy or sell signal.

The moving average is the envelope centerline. Volatility-scaled bands sit a stated number of moving standard deviations away from a simple moving average computed on the same lookback, so width expands and contracts with realized dispersion.

Choose a centerline that describes the trend

The length of the moving average is chosen to describe the intended trend rather than to optimize crossover signals.

That length is judged by the first pullback after a low. A break of the average implies the length is too short. A miss implies it is too long. A well-chosen average is reached more often than it is broken.

Scale the rails from the same lookback

A fixed-percent envelope is built by multiplying a simple moving average by one plus a chosen percent for the upper rail and by one minus that percent for the lower rail. One illustrated specification used a 21-day average and a 4 percent shift.

A containment construction keeps a stated fraction of recent prices inside the envelope. A proposal around a 21-day average kept 85 percent of prices inside over about a year and allowed the upper and lower displacements to differ as an advance or decline persists.

Volatility-scaled bands use the same-lookback simple moving average plus and minus two standard deviations of that same series. The rails widen and contract with realized dispersion around the intermediate-term mean. Band-width expresses that envelope width as a fraction of the moving-average centerline and is used to observe those contractions and expansions.

Default lookbacks and deviation multipliers

A 20-period lookback is given as the default intermediate specification, with 10 periods for short-term work and 50 for long-term work. The deviation multiplier is raised toward 2.5 at 50 periods and lowered toward 1.5 at 10 periods.

A typical-price spreadsheet construction

Typical price is a bar summary equal to the high, low, and close averaged together. It is an optional input for the mean and the deviation.

One spreadsheet construction uses typical price, a 20-day simple moving average of that series, the population standard deviation over the same 20 days, and rails at the average plus and minus twice that deviation.

Require a non-colinear companion

Several close-only oscillators that share a similar span recount the same information. That recounting is multicolinearity: several indicators built from one series and similar spans. The relative strength index is a close-based momentum oscillator listed as a usable companion to the bands when it is not paired with other colinear close-derived measures.

A relative strength index reading that confirms a tag of the upper band is treated as continuation rather than a sell setup. A tag without that confirmation is treated as a sell setup. The same confirmation-versus-divergence test is applied at the lower band.

Compare extremes with percent-b

Percent-b is a location statistic that maps price onto the interval between the lower and upper rails. The measure places price at 100 on the upper band and 0 on the lower band and can print outside that range when price is outside the envelope. Successive extremes can then be compared with the relative strength index without requiring the second extreme to be higher or lower than the first.