J. Welles Wilder is one of the most innovative minds in the field of technical analysis. In 1978, he introduced the world to the indicators known as true range and average true range as measures of volatility. Although they are used less frequently than standard indicators by many technicians, these tools can help a technician enter and exit trades, and should be looked at by all systems traders as a way to help increase profitability.

## What Is the Average True Range?

A stock's range is the difference between the high and low price on any given day. It reveals information about how volatile a stock is. Large ranges indicate high volatility and small ranges indicate low volatility. The range is measured the same way for options and commodities - high minus low - as they are for stocks.

One difference between stocks and commodity markets is that the major futures exchanges attempt to prevent extremely erratic price moves by putting a ceiling on the amount that a market can move in a single day. This is known as a lock limit and represents the maximum change in a commodity's price for one day. During the 1970s, as inflation reached unprecedented levels, grains, pork bellies, and other commodities frequently experienced limit moves. On these days, a bull market would open limit up and no further trading would occur. The range proved to be an inadequate measure of volatility given the limit moves and the daily range indicated there was extremely low volatility in markets that were actually more volatile than they'd ever been.

Wilder was a futures trader at that time when those markets were less orderly than they are today. Opening gaps were a common occurrence and markets moved limit up or limit down frequently. This made it difficult for him to implement some of the systems he was developing. His idea was that high volatility would follow periods of low volatility. This would form the basis of an intraday trading system.

As an example of how that could lead to profits, remember that high volatility should occur after low volatility. We can find low volatility by comparing the daily range to a 10-day moving average of the range. If today's range is less than the 10-day average range, we can add the value of that range to the opening price and buy a breakout.

When the stock or commodity breaks out of a narrow range, it is likely to continue moving for some time in the direction of the breakout. The problem with opening gaps is that they hide volatility when looking at the daily range. If a commodity opens limit up, the range will be very small, and adding this small value to the next day's open is likely to lead to frequent trading. Because the volatility is likely to decrease after a limit move, it is actually a time that traders might want to look for markets offering better trading opportunities. (Related: A Simplified Approach To Calculating Volatility. )

## Calculating the Average True Range

The true range was developed by Wilder to address this problem by accounting for the gap and more accurately measuring the daily volatility than was possible by using the simple range calculation. True range is the largest value found by solving the following three equations:

﻿\begin{aligned}&1.\ \text{TR}\ =\ \text{H}\ -\ \text{L}\\&2.\ \text{TR}\ =\ \text{H}\ -\ \text{C.1}\\&3.\ \text{TR}\ =\ \text{C.1}\ -\ \text{L}\\&\textbf{where:}\\&\text{TR}\ =\ \text{the true range}\\&\text{H}\ =\ \text{today's high}\\&\text{L}\ =\ \text{today's low}\\&\text{C.1}\ =\ \text{yesterday's close}\end{aligned}﻿

If the market has gapped higher, equation #2 will accurately show the volatility of the day as measured from the high to the previous close. Subtracting the day's low from the previous close, as done in equation #3, will account for days that open with a gap down.

## Average True Range

The average true range (ATR) is an exponential moving average of the true range. Wilder used a 14-day ATR to explain the concept. Traders can use shorter or longer timeframes based on their trading preferences. Longer timeframes will be slower and will likely lead to fewer trading signals, while shorter timeframes will increase trading activity. The TR and ATR indicators are shown in Figure 1.

Figure 1: True range and average true range indicators

Figure 1 illustrates how spikes in the TR are followed by periods of time with lower values for TR. The ATR smooths the data and makes it better suited to a trading system. Using raw inputs for the true range would lead to erratic signals.

## Applying the Average True Range

Most traders agree that volatility shows clear cycles and relying on this belief, ATR can be used to set up entry signals. ATR breakout systems are commonly used by short-term traders to time entries. This system adds the ATR, or a multiple of the ATR, to the next day's open and buys when prices move above that level. Short trades are the opposite; the ATR or a multiple of the ATR is subtracted from the open and entries occur when that level is broken.

The ATR breakout system can be used as a longer-term system by entering at the open following a day that closes above the close plus the ATR or below the close minus the ATR.

The ideas behind the ATR can also be used to place stops for trading strategies, and this strategy can work no matter what type of entry is used. ATR forms the basis of the stops used in the famed "turtle" trading system. Another example of stops using ATR is the "chandelier exit" developed by Chuck LeBeau, which places a trailing stop from either the highest high of the trade or the highest close of the trade. The distance from the high price to the trailing stop is usually set at three ATRs. It is moved upward as the price goes higher. Stops on long positions should never be lowered because that defeats the purpose of having a stop in place. (For more, see Exit strategies: A key look.)

## Conclusion

The ATR is a versatile tool that helps traders measure volatility and can provide entry and exit locations. An entire trading system can be built from this single idea. It's an indicator that should be studied by serious market students.