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# Arms Ease of Movement

### Description

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.

**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.

#### Inputs

**Volume Divisor:**The value that the volume is divided by.- Length
- Moving Average Type

#### 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 Sunday, 29th January, 2023.