Williams %R

A bounded momentum indicator, published by Larry Williams, computed from three numbers: the highest high and the lowest low over a lookback window, conventionally fourteen periods, and the current close. The highest high less the close is divided by the highest high less the lowest low, and the result is multiplied by minus one hundred. A close at the top of the window's range therefore reads zero, a close at the bottom reads minus one hundred, and a close halfway reads minus fifty. Because both ends are fixed by the calculation, the line cannot run away in either direction the way a price can.

The conventional reading calls the upper band overbought and the lower band oversold, with the thresholds set by habit rather than by the mathematics. One structural fact is worth more than any of those conventions: the indicator is arithmetically the fast line of the stochastic oscillator shifted onto a negative scale, so over the same lookback the two draw one shape, inverted. They are frequently presented on the same chart as though each confirmed the other, which is a restatement rather than a confirmation.

Two limits account for most misreadings. A bounded indicator pins at its extreme while a market keeps moving, so a reading held at minus one hundred through a long decline is reporting that each close is at the bottom of its recent range, which is what a sustained decline looks like, and not that the decline is ending. And the value depends on a window that keeps moving: when an old extreme drops out of the lookback, the denominator changes, and the reading can shift materially on a period in which the close barely moved. Practitioners disagree about whether the raw series should be smoothed before it is read, which is one reason two charts of the same indicator on the same instrument can disagree.