Williams %R: the formula, and how it relates to the stochastic

1. 01

   Find the highest high and lowest low of the last N bars.

   N is usually 14, and the latest bar is included.

2. 02

   Measure down from the top.

   Distance = highest high − close.

3. 03

   Express it as a share of the range, with a minus sign.

   %R = −100 × (highest high − close) ÷ (highest high − lowest low).

Some programs show the scale as 0 to 100 without the minus sign, or plot it reversed; the line is the same. If the highest high equals the lowest low the formula divides by zero; this page shows −50 for such a bar, as it shows 50 for the stochastic.

Four bars, written high / low / close: 10 / 8 / 9, then 12 / 9 / 11, then 11 / 9 / 10, then 13 / 10 / 12. Length 3. They are the bars of the stochastic page.

1. Bar 3: highest high of bars 1 to 3 = 12; lowest low = 8
2. %R = −100 × (12 − 10) ÷ (12 − 8) = −100 × 2 ÷ 4 = −50
3. Bar 4: highest high of bars 2 to 4 = 13; lowest low = 9
4. %R = −100 × (13 − 12) ÷ (13 − 9) = −100 × 1 ÷ 4 = −25
5. The stochastic page found %K = 50 and 75 for the same bars: 50 − 100 = −50, and 75 − 100 = −25

The last bar closed a quarter of the way down from the top of its three-bar range, which is the same fact as three quarters of the way up.

The numbers in this example were chosen to be easy to add up. They are not prices of anything.

• The −20 and −80 lines. By convention a reading above −20 is called overbought and one below −80 oversold: the close is near the top, or the bottom, of its recent range.
• The −50 line. Above it the close is in the upper half of the range; below it, the lower half.
• Failure to reach an extreme. Readers note when the price makes a new high but %R stops short of its earlier peak, a form of divergence.
• Together with the trend. In a steady rise the line spends most of its time near zero; its dips then get the attention, not its peaks.

• It cannot say a turn is due. A market that closes near its high bar after bar keeps %R above −20 throughout.
• It cannot add anything to a stochastic oscillator on the same chart. It is the same sum, and two copies of one fact are not two pieces of evidence.
• It cannot tell you how big the range is. A reading of −10 in a range of 0.50 and in a range of 50 look identical.
• It cannot hold still. When an old high or low leaves the window the reading can jump although the price has barely changed, and without smoothing it jumps more than the stochastic does.

• Reading the scale the wrong way up: −90 is a low close, not a high one.
• Reading above −20 as ‘sell’ and below −80 as ‘buy’. In a trend that reading repeats for a long time.
• Counting agreement between %R and the stochastic as confirmation.
• Shortening the length to catch every wiggle. A short window makes the line swing from 0 to −100 on ordinary noise.

Why is Williams %R negative?

Because it measures down from the top of the range: the distance from the highest high to the close, written with a minus sign. A close on the highest high reads 0, and a close on the lowest low reads −100. Some charting programs drop the sign, which changes the labels and not the line.

What is the difference between Williams %R and the stochastic oscillator?

Only the end they measure from, and the smoothing. The stochastic’s raw %K is the close’s height above the lowest low as a share of the range; %R is its depth below the highest high. %R equals raw %K minus 100. The stochastic is usually smoothed and given a second line, %D; %R is usually shown raw.

What does a Williams %R above −20 mean?

That the latest close is in the top fifth of the range between the lowest low and the highest high of the bars it looks back over. The convention is to call that overbought. It describes position in a recent range and does not mean a fall is due.

• Overbought
• Oversold
• Momentum
• Range
• Indicator