# Technical Studies Reference

### 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.

$$\%R_t\left(X^{(High)}, X^{(Low)}, X^{(Last)}, n\right) = -100 \cdot \displaystyle{\frac{\max_t\left(X^{(High)},n\right) - X_t^{(Last)}}{\max_t\left(X^{(High)},n\right) - \min_t\left(X^{(Low)},n\right)}}$$

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.

$$\%R_t\left(X^{(High)}, X^{(Low)}, X^{(Last)}, n\right) = 100 \cdot \displaystyle{\frac{\max_t\left(X^{(High)},n\right) - X_t^{(Last)}}{\max_t\left(X^{(High)},n\right) - \min_t\left(X^{(Low)},n\right)}}$$