# William’s Percentage Range – William’s %R

William’s percentage Range is a momentum oscillator developed by the trader Larry R. Williams in 1973. The concept behind this indicator is to demonstrate the price’s closing range in reaction to the high price for a specific period. Based on this concept it would be logical that prices will close at higher ranges in an uptrend and vice versa during a downtrend. The equation for calculating William’s %R includes the high, low, and close of the period under subject. William’s %R formula is as follows:

### William’s %R = (Highest high- close)/ (Highest high-lowest low) X -100%

Based on the above formula, William’s %R is a bounded momentum line oscillator between zero and -100% where -100% is bounding the oscillator at the bottom and zero is bounding the oscillator on top. When the oscillator is between zero and -20% then the security is trading near the highest price of the assigned period, when the oscillator is between -80% and -100% then the security is trading at the lower side of the high-low range of the selected period. The default setting for the oscillator’s period is 14 however, the trader can adjust the period to the desired settings.

1- Oversold/overbought zones:
As stated by the indicator developer, buy the instrument when the indicator is breaking up the -90 zone since the instrument is rallying up from an oversold zone, and sell when the indicator is breaking the -20 zone since conceptually the security will rally down from an overbought area (Fig.1). However, it is not a rule that the indicator should go to the oversold zone by default once it reaches an overbought state as it would stay there for a long time (fig.2).

Fig. 1

Fig. 2

Moreover, traders can open or add to a long trading position when the indicator crosses the -50 mid-zone level. As demonstrated in (Fig.3) the trader can enter a long position once William’s %R crosses above the oversold zone (that’s when the price action starts an upward move as well) and add to the long position once William’s %R crosses above the -50% zone (which is almost 50% of the upward price movement). The same applies in the opposite direction, the trader can enter a short position once William’s %R crosses below the overbought zone (that’s when the price action starts a downward move as well) and add to the short position once William’s %R crosses below the -50% zone.

Fig. 3

2-Reversal signals: Traders can figure out trade reversal when William’s %R trades in an overbought zone between 0 and -20 followed by heading to the oversold zone however can’t push over above the -50% mid-zone. This would signal trend reversal as demonstrated in Fig.4. Silver stayed below the 50% range from November 2012 till November 2015.

Fig. 4

3- Divergence:
Divergence is one of the much-appreciated signals indicators can provide. Divergence occurs when the indicator moves in the opposite direction of the price trend, signaling weakness in the current trend or that a trend reversal is underway. There are two types of divergence, positive and negative.

A negative divergence occurs in an uptrend meaning that, while prices are recording higher lows and higher highs, William’s %R is demonstrating lower highs. In February 2018, the Euro/USD pair (EURUSD) recorded a higher low and higher high compared to September 2017 low/high while William’s %R negatively diverted to a lower high signaling trend weakness, followed by a downtrend that lasted from October 2018 until March 2020, (Fig.5)

Positive divergence occurs in a downtrend meaning that, while prices are recording lower highs and lower lows, William’s %R is recording higher lows. In June 2006, the New Zealand dollar/USD pair (NZDUSD) recorded a lower low compared to March 2006 while William’s %R positively diverted to a higher low signaling a potential ending for the current trend, followed by an uptrend that lasted almost one month, (Fig.6)

Fig. 5

Fig. 6

This concept capitalizes on the idea of relying on the trend of the higher time frame from which the trader acts in a lower time frame. If the major time frame is uptrend then the trader would enter a trade or adds to an existing position whenever there is a downward correction on the lower timeframe, this is called “buy on strength”. However, it is highly recommended to accompany lagging indicators like the moving average to confirm entries and exits. The following is an example for the timeframe trading strategy. In the figure below (Fig.7) the S&P 500 was in an uptrend on the monthly chart, prices were trading above the 50-month moving average and William’s %R oscillator was in the overbought zone near -20% indicating that the main timeframe or higher timeframe trend is upward. Looking at the same instrument (S&P500) on the weekly chart for the same period, the index performed a downward correction and tested the 50-week moving average, adding to that, William’s %R was at the oversold zone near -80%. This is the entry signal for a trader to enter a position or add to an existing long one since the 50-week moving average acted as a support zone on the lower time frame (weekly chart) from which the instrument rebounded to resume the uptrend given that the uptrend on the higher time frame (monthly chart) is strong acquiring strong bullish momentum.

S&P Monthly time frame (Fig. 7)