# How to calculate ATR

The Average True Range (ATR) of an asset is a historical volatility indicator that calculates the average of a number of previous True Range values. The True Range (TR) of an asset can be defined as follows:

ATRx = (TRt + … + TRt-x) / Opent-x

Where: ATRx – Rolling x-day Average True Range TRt – True Range in period t Opent – Open price in period t

The ATR and TR values allow us to understand historical volatilities; and when we compare these values across various periods we can gauge how volatility of an asset has changed with time. By understanding ATR as a historical volatility indicator we can use is to appreciate the trading opportunities inherit in the asset and the risk that come with it. In this example we calculate rolling one day ATRs for the S&P500, and compare averages of these rolling ATRs over different periods in time.

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