# Technical Studies Reference

### Arms Ease of Movement

This study calculates and displays the Arms Ease of Movement Value (EMV) for the Price and Volume data, as well as a Moving Average of the EMV. It was developed by Richard W. Arms, Jr.

Let $$H$$, $$L$$, and $$V$$ be random variables denoting the High Price, Low Price, and Volume, and let $$H_t$$, $$L_t$$, and $$V_t$$ be their respective values at Index $$t$$. Let $$k$$ be the Volume Divisor Input. We then calculate the Midpoint Move and the Box Ratio as follows.

Midpoint Move:

$$\displaystyle{\frac{H_t + L_t}{2} - \frac{H_{t - 1} + L_{t - 1}}{2}}$$

Box Ratio:

$$\displaystyle{\frac{V_t}{d(H_t - L_t)}}$$

The Ease of Movement is essentially a ratio of these two quantities. We denote the Arms Ease of Movement at Index $$t$$ as $$EMV_t(k)$$, and we compute it for the given Input as follows.

For $$t = 0$$: $$EMV_0(k) = 0$$

For $$t > 0$$:

$$\displaystyle{EMV_t(k) = \left\{ \begin{matrix} \left. \left(\frac{H_t + L_t}{2} - \frac{H_{t - 1} + L_{t - 1}}{2}\right) \middle/ \left(\frac{V_t}{d(H_t - L_t)}\right)\right. & V_t \neq 0 \space and \space H_t \neq L_t \\ 0 & V_t = 0 \space or \space H_t = L_t \end{matrix}\right .}$$

Let $$n$$ be the Length Input. We denote the Moving Average of the EMV as $$\overline{EMV}_t(k,n)$$, and we compute it for $$t \geq n - 1$$ for the given Inputs in terms of a Simple Moving Average as follows.

$$\overline{EMV}_t(k,n) = SMA_t(EMV(k),n)$$

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.