Building average directional index, the stochastic pair, and Williams percent R from highs, lows, and closes

Three recipes from the same inputs

Packaged oscillators can be rebuilt from highs, lows, and closes. The three recipes here are average directional index, the stochastic oscillator, and Williams percent R.

Each series uses those same inputs and then applies a different construction choice. Editorial reading: the choices that change what the plotted series can represent are true-range scaling, the lookback window, smoothing, and a reversed scale.

Rebuilding average directional index

Plus directional movement equals the current high minus the previous high. Minus directional movement equals the current low minus the previous low.

True range is the largest of the up-move, the down-move, and the close-to-close change on the bar. The plus directional indicator is that period's plus directional movement divided by the same-period true range. The minus directional indicator is that period's minus directional movement divided by the same-period true range.

The directional index is one hundred times the plus directional indicator minus the minus directional indicator, divided by the sum of those two indicators. Average directional index is a moving average of that directional index.

Average directional index is described as an oscillator spanning zero to one hundred, with higher values indicating a stronger trend.

The stochastic pair

The raw stochastic reading, percent K, compares the current close with the high-low range of the last n bars and scales that position by one hundred.

The companion line, percent D, is a moving average of the raw stochastic. Both the bar count and the averaging length are chosen by the user.

The stochastic oscillator is therefore a two-line construction: an unsmoothed range-position reading and a user-chosen average of that reading.

Williams percent R without smoothing

Williams percent R is presented as an unsmoothed stochastic that measures the close against an n-period price range in order to mark overbought and oversold conditions.

On a reversed Williams percent R scale running from zero to negative one hundred, values above negative twenty are treated as overbought and values below negative eighty as oversold.

What each construction choice can represent

Editorial reading: true-range scaling is what the directional indicators use. The lookback window is what percent K and Williams percent R use to place the close inside a high-low range. Smoothing is what turns the directional index into average directional index and percent K into percent D. A reversed scale from zero to negative one hundred is what carries the Williams percent R overbought and oversold marks.

The packaged names therefore describe different assemblies of the same three inputs: highs, lows, and closes.