# Technical Studies Reference

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# Williams' %R

This study calculates and displays Williams' %R for the data specified by the **Input Data for High**, **Input Data for Low**, and **Input Data for Last** Inputs. Williams' %R is a momentum study that measures overbought/oversold levels. It was developed by Larry Williams.

Let \(X^{(High)}\), \(X^{(Low)}\), \(X^{(Last)}\) be random variables denoting **Input Data for High**, **Input Data for Low**, and **Input Data for Last**, respectively, and let \(X_t^{(High)}\), \(X_t^{(Low)}\), \(X_t^{(Last)}\) denote their respective values at Index \(t\). Let the **Length** Input be denoted as \(n\).

We denote the maximum value of \(X^{(High)}\) and the minimum value of \(X^{(Low)}\) over a moving window of \(n\) chart bars terminating at Index \(t\) as \(\max_t\left(X^{(High)},n\right)\) and \(\min_t\left(X^{(Low)},n\right)\), respectively. These are computed for \(t > n\) as follows.

\(\max_t\left(X^{(High)},n\right) = \max\left\{X_{t - n + 1}^{(High)},..,X_t^{(High)}\right\}\)\(\min_t\left(X^{(Low)},n\right) = \min\left\{X_{t - n + 1}^{(Low)},..,X_t^{(Low)}\right\}\)

We denote the value of **Williams %R** at Index \(t\) for the given Inputs as \(\%R_t\left(X^{(High)}, X^{(High)}, X^{(High)}, n\right)\), and we compute it for \(t > n\). The method of computation varies slightly depending on the setting of the **Invert Output** Input.

If **Invert Output** is set to Yes, then we compute \(\%R_t\left(X^{(High)}, X^{(Low)}, X^{(Last)}, n\right)\) as follows.

This is the usual formula for **Williams' %R**.

If **Invert Output** is set to No, then we compute \(\%R_t\left(X^{(High)}, X^{(Low)}, X^{(Last)}, n\right)\) as follows.

#### Inputs

- Length
**Invert Output**: This Input is used to toggle the sign of the output at each chart bar.- Input Data for High
- Input Data for Low
- Input Data for Last

#### Spreadsheet

The spreadsheet below contains the formulas for this study in Spreadsheet format. Save this Spreadsheet to the Data Files Folder.

Open it through **File >> Open Spreadsheet**.

*Last modified Monday, 03rd October, 2022.