# Freedom of Movement

This study calculates and displays a Freedom of Movement Indicator for the Price and Volume Data. It is frequently used in conjunction with the Relative Volume Standard Deviation study. Both studies were created by Melvin E. Dickover.

Let the Input Data, Length, and Number of Standard Deviations Inputs be denoted as $$X$$, $$n$$, and $$N_{\sigma}$$, respectively.

We denote the Percent Move at Index $$t$$ as $$\%\Delta X_t$$, and we compute it as follows.

$$\displaystyle{\%\Delta X_t = \frac{X_t - X_{t - 1}}{X_{t - 1}}, \space X_{t - 1} \neq 0}$$

We then normalize the Percent Move to have values between $$1$$ and $$10$$. We denote the Normalized Percent Move as $$\%\Delta X^{(N)}_t$$, and we compute it as follows.

$$\displaystyle{\%\Delta X^{(N)}_t(n) = 1 + 9\cdot\frac{\%\Delta X_t - \min_t(\%\Delta X,n)}{\max_t(\%\Delta X,n) - \min_t(\%\Delta X,n)}}$$

For an explanation of the functions $$\max_t()$$ and $$\min_t()$$, refer to our descriptions of the Moving Maximum and Moving Minimum.

We then compute the Relative Volume Standard Deviation $$RV_t(n)$$, and we normalize it to values between $$1$$ and $$10$$ just as we did with the Percent Move. The Normalized Relative Volume Standard Deviation is denoted as $$RV^{(N)}_t$$, and we compute it as follows.

$$\displaystyle{RV^{(N)}_t(n) = 1 + 9\cdot\frac{RV_t(n) - \min_t(RV_t(n),n)}{\max_t(RV_t(n),n) - \min_t(RV_t(n),n)}}$$

Next we compute the ratio $$\frac{RV^{(N)}_t(n)}{\%\Delta X^{(N)}_t(n)}$$, $$\left(\%\Delta X^{(N)}_t(n)\right) \neq 0$$, as well as the Simple Moving Average and Standard Deviation of that ratio.

We denote the Freedom of Movement at Index $$t$$ as $$FOM_t(X,n)$$, and we compute it as follows.

$$\displaystyle{FOM_t(X,n) = \frac{\frac{RV^{(N)}_t(n)}{\%\Delta X^{(N)}_t(n)} - SMA_t\left(\frac{RV^{(N)}(n)}{\%\Delta X^{(N)}_t(n)}, n\right)}{\sigma_t\left(\frac{RV^{(N)}(n)}{\%\Delta X^{(N)}_t(n)}, n\right)}, \space \left(\sigma_t\left(\frac{RV^{(N)}(n)}{\%\Delta X^{(N)}_t(n)}, n\right) \neq 0\right) }$$

Note: Depending on the setting of the Moving Average Type Input, the Simple Moving Average in the above formula could be replaced with an Exponential Moving Average, a Linear Regression Moving Average, a Weighted Moving Average, a Wilders Moving Average, a Simple Moving Average - Skip Zeros, or a Smoothed Moving Average.

By default, $$FOM_t(X,n)$$ is displayed as a histogram. If $$FOM_t(X,n) > N_{\sigma}$$, then the Primary Color (green by default) is used. Otherwise, the Secondary Color (red by default) is used.