# Williams %R

Williams %R, or just %R, is a technical analysis oscillator showing the current closing price in relation to the high and low of the past N days (for a given N). It was developed by a publisher and promoter of trading materials, Larry Williams. Its purpose is to tell whether a stock or commodity market is trading near the high or the low, or somewhere in between, of its recent trading range.

$\%R = { high_{Ndays} - close_{today} \over high_{Ndays} - low_{Ndays} } \times -100$ [1]

The oscillator is on a negative scale, from -100 (lowest) up to 0 (highest), considered unusual since it is the obverse of the more common 0 to 100 scale found in many Technical Analysis oscillators. Although sometimes altered (by simply adding 100), this scale needn't cause any confusion. A value of -100 is the close today at the lowest low of the past N days, and 0 is a close today at the highest high of the past N days.

Williams used a 10 trading day period and considered values below -80 as oversold and above -20 as overbought. But they were not to be traded directly, instead his rule to buy an oversold was

•  %R reaches -100%.
• Five trading days pass since -100% was last reached
•  %R rises above -95% or -85%.

or conversely to sell an overbought condition

•  %R reaches 0%.
• Five trading days pass since 0% was last reached
•  %R falls below -5% or -15%.

The timeframe can be changed for either more sensitive or smoother results. The more sensitive you make it, though, the more false signals you will get.

## Notes

Due to the equivalence

${ (close_{today} - low_{Ndays}) - (close_{today} - high_{Ndays}) = high_{Ndays} - low_{Ndays} }$

the %R indicator is arithmetically exactly equivalent to the %K stochastic oscillator, mirrored at the 0%-line, when using the same time interval.