Signed midpoint range oscillator from stochastic and Williams

Shared range, different origins

A five-period stochastic oscillator locates the latest close above the lookback low, divides that distance by the lookback range, and scales the ratio onto a 0-100 range. The lookback range is the span between the highest high and the lowest low over the chosen sampling window.

A five-period Williams %R reading uses the same lookback range as that stochastic construction but measures the distance from the lookback high down to the latest close. Both readings therefore place the close inside one shared high-low span and differ only in which extreme is treated as the origin.

Measuring from the range midpoint

Substituting the range midpoint for a range extreme, and scaling by half the lookback range, produces a signed midpoint oscillator that fluctuates between 100 and -100. The range midpoint is the average of the lookback high and the lookback low, and it is the zero reference of that signed reading.

After reduction, the signed reading equals 100 times (twice the close minus the lookback high minus the lookback low) divided by the lookback range.

When both classic oscillators share the same lookback high and lookback low, the signed midpoint reading equals the stochastic reading minus the Williams reading. If the close equals the lookback low, the signed midpoint reading equals -100.

Action bands and a slower confirmation line

Action bands may be placed at +70 and -70, at +50 and -50, or near one standard deviation of the series. A weekly large-cap index sample of the signed reading had a standard deviation of 66.

The same construction can be slowed by lengthening the lookback. One illustration used 26 weeks with a nine-week exponentially smoothed confirmation line and bands near 67. Exponential smoothing here is a recursively weighted average of the oscillator series, used as a slower confirmation line on the same lookback.

After a severe overbought or oversold extreme, the signed reading can remain stretched for several weeks, and a first crossing of an action band is often followed by a move in the opposite direction.