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The Average True Range (ATR) is a technical indicator used in finance to measure the volatility of an asset, usually a stock or currency. It was introduced by J. Welles Wilder in his book, "New Concepts in Technical Trading Systems." The ATR measures the average range of price movements over a given period of time, typically 14 days.

The ATR indicator can also be used to set a stop-loss level, which is a predetermined price level at which a trader will exit a trade if the market moves against them. A trader might set a stop-loss at a level equal to the ATR value, as this will help ensure that the stop-loss level is proportionate to the level of market volatility.

Another common use of the ATR is to determine position sizing. A trader might use the ATR to calculate the appropriate size of a position, based on the level of volatility and the amount of capital they have available for investment.

The ATR can also be used to identify market trends. A rising ATR indicates that market volatility is increasing, which can indicate that a trend is developing. On the other hand, a declining ATR suggests that market volatility is decreasing, which could indicate that a trend is coming to an end.

The prime component of the ATR formula is the True Range (TR) value. The TR (Current TR) is the greatest of the following:

- Current high minus current low: (current high – current low)
- Current high minus previous (yesterday’s) close: absolute(current high – previous close)
- Current low minus previous (yesterday’s) close: absolute(current low– previous close)

TR = max [(high − low), abs(high − close_{prev}), abs(low – close_{prev})]

`=AVERAGE(TRUE RANGE) `

Where `TRUE RANGE`

is calculated as:

`=MAX(HIGH - LOW, ABS(HIGH - PREV_CLOSE), ABS(LOW - PREV_CLOSE)) `

Where:

`HIGH`

is the current period's high price`LOW`

is the current period's low price`PREV_CLOSE`

is the previous period's close price

The ATR is calculated by taking the average of the `TRUE RANGE`

over a specified number of periods, typically 14 days.

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`atr = avg(tr, 14) tr = max(high - low, abs(high - close[1]), abs(low - close[1])) `

Where:

`atr`

is the Average True Range`tr`

is the True Range`high`

is the current period's high price`low`

is the current period's low price`close[1]`

is the previous period's close price`14`

is the number of periods over which the ATR is calculated

The ATR can be plotted as a line on a price chart and is typically used to help traders identify market trends, potential reversal points, and stop-loss levels. The higher the ATR, the greater the volatility, and vice versa.