ANALYTICAL TOOLBOX: Average True Range and Directional Movement

The Directional Movement Indicator [DMI] and Average Directional Index [ADX] are technical tools developed by Welles Wilder Jr. and described in his 1978 classic, New Concepts in Technical Trading Systems. In order to apply these unique tools, some background information is required. This article uses weekly charts and looks at Average True Range and two components of Directional Movement as an introduction to the ADX.

Average True Range

The Average True Range [ATR] uses a True Range [TR] value to identify a better price range vale for a specific period. The TR uses the previous week’s close to calculate three different range values and as a result, weekend gaps (up or down) are incorporated into the price ranges. The highest absolute value for the three calculations is used as the True Range for the week. Figure 1 provides the three weekly range calculations and bar chart examples of each one as the greatest TR for the period.

Figure 1: Weekly True Range Calculations and Display
(click here for larger view) 

The ATR uses each period’s TR value to obtain an average that represents a common range for the period. Welles Wilder, the developer of the indicator often used a value that approximated a 27-period exponential moving average to smooth the data. A strong move in the ATR incorporates price gaps and provides traders with important information about price volatility that can be missed by other smoothed indicators.

The ATR uses historical price information plus a smoothing process to construct a line, so it’s a lagging indicator. Although price volatility cannot be predicted using this line, it provides an objective view of volatility. A sharp move in the ATR will likely be accompanied by an increase in the implied volatility [IV] component of the option’s premium.

Figure 2 provides a weekly chart for QQQQ, the Nasdaq 100 exchange traded fund [ETF], along with a 10-week and 40-week exponential moving average [EMA] and a 14-week ATR. The two-month consolidation in QQQQ ending in early July 2007 is accompanied by a dip in the ATR. Since that time, price volatility in the ETF is at levels not seen since early 2003. If you’ve been trading these markets, you probably didn’t need the ATR to tell you volatility has gone up, but comparing the relative values does put the current volatility into perspective.

Figure 2: Weekly Chart of QQQQ with EMA and Average True Range

Flat movement in the ATR often accompanies consolidation phases, while strong moves suggest a potential change in direction. It remains to be seen whether the recent ATR rise accompanying higher QQQQ prices confirms a return to the long-term uptrend in the ETF. It’s important to note that the ATR is note a directional tool, a rising ATR line does not suggest rising prices, just increased volatility.

Major tops and bottoms are often associated with strong moves in the ATR. Since volatility won’t increase indefinitely, the ATR is expected to decline after a sharp move and return to a relatively normal range. The trader should use other technical tools to ascertain whether a new trend has been initiated given a sharp rise in ATR or if the action was a temporary change in conditions.

Directional Movement Indicator

The Directional Movement Indicator [DMI] is created using two other oscillators: upward directional movement (+DI) and downward directional movement [-DI]. The +DI and -DI lines can be used separately to generate trade signals or as part of the DMI calculation.

It takes a little effort to arrive at the +DI and –DI calculations, and slightly more for the DMI. The calculations include: ATR (average true range), +DM (plus directional movement), -DM (minus directional movement), +DI (plus directional indicator) and -DI (minus directional indicator). This derivation is provided for reference purposes¹ since it’s not commonly found with ADX discussions. It’s okay to skim through or skip it.

+DM, –DM, +DI, –DI (assumes a 14-week setting)

+DM = Current High – Previous High (over 14-weeks)
-DM = Current Low – Previous Low (over 14-weeks)

+DI = +DM x (100 / ATR)
–DI = –DM x (100 / ATR)

DMI = (+DI – –DI) / (+DI + –DI)

¹ The formula detail is courtesy of the Market Technicians Association [MTA].

There are occasions when the +DM or –DM is set to zero, but that detail is not provided here. So we have two of three referenced calculations completed (+DI and –DI).

The Directional Movement Indicator attempts to provide useful information on how the current move relates to the recent trading range for the security. In terms of this particular indicator, it’s not sufficient to simply note upward movement; it’s important to quantify the extent of that upward movement.

Figure 3 displays the same weekly QQQQ chart with +DI (solid green line) and –DI (dotted red line). When +DI is above –DI price is generally trending upward and when -DI is above +DI price is generally trending downward.

Figure 3: Weekly Chart of QQQQ with EMA, Average True Range and +DI, -DI

Although +DI is currently above –DI, both are currently moving downward. Consider monitoring these indicators over the next week through the next Fed meeting.

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Clare White, CMT 
Contributing Writer and Options Strategist 
Optionetics.com ~ Your Options Education Site 
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