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# Volatility - Historical

This study calculates and displays the Historical Volatility for the data specified by the **Input Data** Input.

Let \(X\) be a random variable denoting the **Input Data** Input. Then we denote the Logarithmic Return of the **Input Data** at Index \(t\) as \(LR_t(X)\), and we compute it for \(t > 0\) as follows.

Let \(LR(X)\) be a random variable denoting the Logarithmic Return of the **Input Data**, and let the **Length** and **Number of Bars per Year** Inputs be denoted as \(n\) and \(N\), respectively. Then we denote the **Volatility - Historical** at Index \(t\) for the given Inputs as \(HVol_t(X,n,N)\), and we compute it in terms of a Simple Moving Average for \(t \geq n\) as follows.

For an explanation of the Sigma (\(\Sigma\)) notation for summation, refer to our description here.

#### Inputs

- Input Data
- Length
**Number of Bars per Year**: In order for this study to calculate historical volatility correctly, it is necessary for you to enter the number of bars in your chart that make up a one-year time period.

#### 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.