# 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.

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

The oscillator is on a negative scale, from −100 (lowest) up to 0 (highest), obverse of the more common 0 to 100 scale found in many technical analysis oscillators. A value of −100 means the close today was the lowest low of the past N days, and 0 means today's close was the highest high of the past N days. (Although sometimes the %R is adjusted by adding 100.)

Note

The original formula from his book multiple the % with 100 instead of −100. Maybe he has another book/magazine printed it incorrectly and spread out. Nowadays, many software already implemented it as −100.

${\displaystyle \%R={high_{Ndays}-close_{today} \over high_{Ndays}-low_{Ndays}}\times 100}$ [2]

Book reference: Williams, Larry. How I Made One Million Dollars… Last Year… Trading Commodities. Windsor Books. ISBN 978-0930233105.

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 drops 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

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

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