# Average true range

**Average true range** (**ATR**) is a technical analysis volatility indicator originally developed by J. Welles Wilder, Jr. for commodities.^{[1]} The indicator does not provide an indication of price trend, simply the degree of price volatility.^{[2]}^{[3]}
The average true range is an N-day smoothed moving average (SMMA) of the **true range** values. Wilder recommended a 14-period smoothing.^{[4]}

## Contents

## Calculation[edit]

The range of a day's trading is simply . The **true range** extends it to yesterday's closing price if it was outside of today's range.

The **true range** is the largest of the:

- Most recent period's high minus the most recent period's low
- Absolute value of the most recent period's high minus the previous close
- Absolute value of the most recent period's low minus the previous close

The ATR at the moment of time *t* is calculated using the following formula:^{[5]} (This is one form of an exponential moving average)

The first ATR value is calculated using the arithmetic mean formula:

The idea of ranges is that they show the commitment or enthusiasm of traders. Large or increasing ranges suggest traders prepared to continue to bid up or sell down a stock through the course of the day. Decreasing range suggests waning interest.

## Applicability to futures contracts vs. stocks[edit]

Since true range and ATR are calculated by subtracting prices, the volatility they compute does not change when historical prices are back-adjusted by adding or subtracting a constant to every price. Back-adjustments are often employed when splicing together individual monthly futures contracts to form a continuous futures contract spanning a long period of time. However the standard procedures used to compute volatility of stock prices, such as the standard deviation of logarithmic price ratios, are not invariant (to addition of a constant). Thus futures traders and analysts typically use one method (ATR) to calculate volatility, while stock traders and analysts typically use another (SD of log price ratios).

## Use in position size calculation[edit]

Apart from being a trend strength gauge, ATR serves as an element of position sizing in financial trading. Current ATR value (or a multiple of it) can be used as the size of the potential adverse movement (stop-loss distance) when calculating the trade volume based on trader's risk tolerance. In this case, ATR provides a self-adjusting risk limit dependent on the market volatility for strategies without a fixed stop-loss placement.^{[6]} A less volatile market has a larger trading position in comparison to a more volatile market in a portfolio.

## References[edit]

**^**J. Welles Wilder, Jr. (June 1978).*New Concepts in Technical Trading Systems*. Greensboro, NC: Trend Research. ISBN 978-0-89459-027-6.**^**ATR Definition - investopedia.com**^**Joel G. Siegel (2000).*International encyclopedia of technical analysis*. Global Professional Publishing. p. 341. ISBN 978-1-888998-88-7.**^**This is by his reckoning of SMMA periods, meaning an α=1/14.**^**Average True Range calculation**^**http://www.earnforex.com/blog/position-sizing-rules/#atr-based-position-sizing

## External links[edit]

*Measure Volatility With Average True Range*at investopedia.com*Enter Profitable Territory With Average True Range*at investopedia.com- Average True Range (ATR) at stockcharts.com