# 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]

## Calculation

MetaTrader EUR/USD chart showing ATR indicator (cyan line) with period 14.

The range of a day's trading is simply ${\displaystyle {\text{high}}-{\text{low}}}$. The true range extends it to yesterday's closing price if it was outside of today's range.

${\displaystyle {\text{TR}}={\max[({\text{high}}-{\mbox{low}}),\operatorname {abs} ({\text{high}}-{\text{close}}_{\text{prev}}),\operatorname {abs} ({\text{low}}-{\text{close}}_{\text{prev}})]}\,}$

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)

${\displaystyle ATR_{t}={{ATR_{t-1}\times (n-1)+TR_{t}} \over n}}$

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

${\displaystyle ATR={1 \over n}\sum _{i=1}^{n}TR_{i}}$

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

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

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

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