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Index (ADX)

Introduc on Outline
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 Average Directional Index
(ADX)
The Average Directional Index (ADX), Minus Directional Indicator (-
Introduction
DI) and Plus Directional Indicator (+DI) represent a group of Calculation
Indicator Calculation
directional movement indicators that form a trading system
Wilder's Smoothing
developed by Welles Wilder. Although Wilder designed his Techniques
Interpretation
Directional Movement System with commodities and daily prices in Trend Strength
mind, these indicators can also be applied to stocks. Trend Direction and
Crossovers
Conclusions
Positive and negative directional movement form the backbone of Using with SharpCharts
Suggested Scans
the Directional Movement System. Wilder determined directional
Overall Uptrend with
movement by comparing the difference between two consecutive +DI Crossing above -DI
Overall Downtrend
lows with the difference between their respective highs. with -DI Crossing above
+DI
Additional Resources
The Plus Directional Indicator (+DI) and Minus Directional
Stocks & Commodities
Indicator (-DI) are derived from smoothed averages of these Magazine Articles

differences, and measure trend direction over time. These two

indicators are often referred to collectively as the Directional
Movement Indicator (DMI).

The Average Directional Index (ADX) is in turn derived from

the smoothed averages of the difference between +DI and -DI, and
measures the strength of the trend (regardless of direction) over
time.

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 Using these three indicators together, chartists can determine both
the direction and strength of the trend.

Wilder features the Directional Movement indicators in his 1978

book, New Concepts in Technical Trading Systems. This book also
includes details on Average True Range (ATR), the Parabolic SAR
system, and RSI. Despite being developed before the computer age,
Wilder's indicators are incredibly detailed in their calculation and
have stood the test of time.

Calcula on
Directional movement is calculated by comparing the difference
between two consecutive lows with the difference between their
respective highs.

Directional movement is positive (plus) when the current high

minus the prior high is greater than the prior low minus the current
low. This so-called Plus Directional Movement (+DM) then equals
the current high minus the prior high, provided it is positive. A
negative value would simply be entered as zero.

Directional movement is negative (minus) when the prior low

minus the current low is greater than the current high minus the

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 prior high. This so-called Minus Directional Movement (-DM) equals
the prior low minus the current low, provided it is positive. A
negative value would simply be entered as zero.

The chart above shows four calculation examples for directional

movement. The first pairing shows a big positive difference between
the highs for a strong Plus Directional Movement (+DM). The second
pairing shows an outside day with Minus Directional Movement (-
DM) getting the edge. The third pairing shows a big difference

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 between the lows for a strong Minus Directional Movement (-DM).
The final pairing shows an inside day, which amounts to no
directional movement (zero). Both Plus Directional Movement
(+DM) and Minus Directional Movement (-DM) are negative and
revert to zero, so they cancel each other out. All inside days will have
zero directional movement.

Indicator Calculation
The calculation steps for the Average Directional Index (ADX), Plus
Directional Indicator (+DI), and Minus Directional Indicator (-DI)
are based on the Plus Directional Movement (+DM) and Minus
Directional Movement (-DM) values calculated above, as well as the
Average True Range. Smoothed versions of +DM and -DM are
divided by a smoothed version of the Average True Range to reflect
the true magnitude of the move.

Note: Average True Range (ATR) is not described because there is an

entire ChartSchool article for this. Basically, ATR is Wilder's version
of the two-period trading range.

The calculation example below is based on a 14-period indicator

setting, as recommended by Wilder.

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 1. Calculate the True Range (TR), Plus Directional Movement
(+DM) and Minus Directional Movement (-DM) for each period.
2. Smooth these periodic values using Wilder's smoothing
techniques. These are explained in detail in the next section.
3. Divide the 14-day smoothed Plus Directional Movement (+DM)
by the 14-day smoothed True Range to find the 14-day Plus
Directional Indicator (+DI14). Multiply by 100 to move the
decimal point two places. This +DI14 is the green Plus Directional
Indicator line (+DI) that is plotted along with the ADX line.
4. Divide the 14-day smoothed Minus Directional Movement (-DM)
by the 14-day smoothed True Range to find the 14-day Minus
Directional Indicator (-DI14). Multiply by 100 to move the
decimal point two places. This -DI14 is the red Minus Directional
Indicator line (-DI) that is plotted along with the ADX line.
5. The Directional Movement Index (DX) equals the absolute value
of +DI14 less -DI14 divided by the sum of +DI14 and -DI14.
Multiply the result by 100 to move the decimal point over two
places.
6. After all these steps, it is time to calculate the Average Directional
Index (ADX) line. The first ADX value is simply a 14-day average
of DX. Subsequent ADX values are smoothed by multiplying the
previous 14-day ADX value by 13, adding the most recent DX
value, and dividing this total by 14.

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 Above is a spreadsheet example with all the calculations involved.
There is a 119-day calculation gap because approximately 150 periods
are required to absorb the smoothing techniques. ADX/DMI
enthusiasts can click here to download this spreadsheet and see the
gory details. The chart below shows an example of ADX with +DI
and -DI using the Nasdaq 100 ETF (QQQQ).

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 Wilder's Smoothing Techniques
As seen in the ADX, +DI, and -DI calculations, there is a lot of
smoothing involved and it is important to understand the effects.
Because of Wilder's smoothing techniques, it can take around 150
periods of data to get true ADX values. Wilder uses similar
smoothing techniques with his RSI and Average True Range
calculations. ADX values using only 30 periods of historical data will

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 not match ADX values using 150 periods of historical data. ADX
values with 150 days or more of data will remain consistent.

The first technique is used to smooth each period's +DM1, -DM1, and
TR1 values over 14 periods. As with an exponential moving average,
the calculation has to start somewhere so the first value is simply the
sum of the first 14 periods. As shown below, smoothing starts with
the second 14-period calculation and continues throughout.

First TR14 = Sum of first 14 periods of TR1

Second TR14 = First TR14 - (First TR14/14) + Current TR1
Subsequent Values = Prior TR14 - (Prior TR14/14) + Current TR1

The second technique is used to smooth each period's DX value to

finish with the Average Directional Index (ADX). First, calculate an
average for the first 14 days as a starting point. The second and
subsequent calculations use the smoothing technique below:

First ADX14 = 14 period Average of DX

Second ADX14 = ((First ADX14 x 13) + Current DX Value)/14
Subsequent ADX14 = ((Prior ADX14 x 13) + Current DX Value)/14

Interpreta on
The Average Directional Index (ADX) is used to measure the
strength or weakness of a trend, not the actual direction. Directional

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 movement is defined by +DI and -DI. In general, the bulls have the
edge when +DI is greater than -DI, while the bears have the edge
when -DI is greater. Crosses of these directional indicators can be
combined with ADX for a complete trading system.

Before looking at some signals with examples, keep in mind that

Wilder was a commodity and currency trader. The examples in his
books are based on these instruments, not stocks. This does not
mean his indicators cannot be used with stocks. Some stocks have
price characteristics similar to commodities, which tend to be more
volatile with short and strong trends. Stocks with low volatility may
not generate signals based on Wilder's parameters. Chartists will
likely need to adjust the indicator settings or the signal parameters
according to the characteristics of the security.

Trend Strength
At its most basic, the Average Directional Index (ADX) can be used
to determine if a security is trending or not. This determination helps
traders choose between a trend-following system or a non-trend-
following system. Wilder suggests that a strong trend is present
when ADX is above 25 and no trend is present when below 20. There
appears to be a gray zone between 20 and 25. As noted above,
chartists may need to adjust the settings to increase sensitivity and

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 signals. ADX also has a fair amount of lag because of all the
smoothing techniques. Many technical analysts use 20 as the key
level for ADX.

The chart above shows Nordstrom (JWN) with the 50-day SMA and
14-day Average Directional Index (ADX). The stock moved from a
strong uptrend to a strong downtrend in April-May, but ADX
remained above 20 because the strong uptrend quickly changed into
a strong downtrend. There were two non-trending periods as the

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 stock formed a bottom in February and August. A strong trend
emerged after the August bottom as ADX moved above 20 and
remained above 20.

Trend Direc on and Crossovers

Wilder put forth a simple system for trading with these directional
movement indicators. The first requirement is for ADX to be trading
above 25. This ensures that prices are trending. Many traders,
however, use 20 as the key level. A buy signal occurs when +DI
crosses above -DI. Wilder based the initial stop on the low of the
signal day. The signal remains in force as long as this low holds, even
if +DI crosses back below -DI. Wait for this low to be penetrated
before abandoning the signal. This bullish signal is reinforced
if/when ADX turns up and the trend strengthens. Once the trend
develops and becomes profitable, traders will have to incorporate a
stop-loss and trailing stop should the trend continue. A sell signal
triggers when -DI crosses above +DI. The high on the day of the sell
signal becomes the initial stop-loss.

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 The chart above shows Medco Health Solutions with the three
directional movement indicators. Note that 20 is used instead of 25
to qualify ADX signals. A lower setting means more possible signals.
The green dotted lines show the buy signals and the red dotted lines
show the sell signals. Wilder's initial stops were not incorporated in
order to focus on the indicator signals. As the chart clearly shows,
there are plenty of +DI and -DI crosses. Some occur with ADX above
20 to validate signals. Others occur to invalidate signals. As with

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 most such systems, there will be whipsaws, great signals, and bad
signals. The key, as always, is to incorporate other aspects of
technical analysis. For example, the first group of whipsaws in
September 2009 occurred during a consolidation. Moreover, this
consolidation looked like a flag, which is a bullish consolidation that
forms after an advance. It would have been prudent to ignore bearish
signals with a bullish continuation pattern taking shape. The June
2010 buy signal occurred near a resistance zone marked by broken
support and the 50-62% retracement zone. It would have been
prudent to ignore a buy signal so close to this resistance zone.

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 The chart above shows AT&T (T) with three signals over a 12-month
period. These three signals were pretty good, provided profits were
taken and trailing stops were used. Wilder's Parabolic SAR could
have been used to set a trailing stop-loss. Notice that there was no
sell signal between the March and July buy signals. This is because
ADX was not above 20 when -DI crossed above +DI in late April.

Conclusions
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 The Directional Movement System indicator calculations are
complex, interpretation is straightforward, and successful
implementation takes practice. +DI and -DI crossovers are quite
frequent and chartists need to filter these signals with
complementary analysis. Setting an ADX requirement will reduce
signals, but this uber-smoothed indicator tends to filter as many
good signals as bad. In other words, chartists might consider moving
ADX to the back burner and focusing on the Directional Movement
Indicators (+DI and -DI) to generate signals. These crossover signals
will be similar to those generated using momentum oscillators.
Therefore, chartists need to look elsewhere for confirmation help.
Volume-based indicators, basic trend analysis, and chart patterns
can help distinguish strong crossover signals from weak crossover
signals. For example, chartists can focus on +DI buy signals when
the bigger trend is up and -DI sell signals when the bigger trend is
down.

Using with SharpCharts

SharpCharts users can plot these three directional movement
indicators by selecting Average Directional Index (ADX) from the
indicator dropdown list. By default, the ADX line will be in black, the
Plus Directional Indicator (+DI) in green and the Minus Directional

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 Indicator (-DI) in red. This makes it easy to identify directional
indicator crosses. While ADX can be plotted above, below or behind
the main price plot, it is recommended to plot above or below
because there are three lines involved. A horizontal line can be added
to help identify ADX moves. The chart example below also shows the
50-day SMA and Parabolic SAR plotted behind the price plot. The
moving average is used to filter signals. Only buy signals are used
when trading above the 50-day moving average. Once initiated, the
Parabolic SAR can be used to set stops. Click here for a live example
of ADX.

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 Suggested Scans

Overall Uptrend with +DI Crossing above -DI

This scan starts with stocks that average 100,000 shares daily
volume and have an average closing price above 10. An uptrend is
present when trading above the 50-day SMA. A buy signal is possible
when ADX is above 20. This signal materializes when +DI moves
above -DI.

[type = stock] AND [country = US]

AND [Daily SMA(20,Daily Volume) > 100000]
AND [Daily SMA(60,Daily Close) > 10]

AND [Daily ADX Line(14) > 20]

AND [Daily Plus DI(14) crosses Daily Minus DI(14)]
AND [Daily Close > Daily SMA(50,Daily Close)]

Overall Downtrend with -DI Crossing above +DI

This scan starts with stocks that average 100,000 shares daily
volume and have an average closing price above 10. A downtrend is
present when trading below the 50-day SMA. A sell signal is possible
when ADX is above 20. This signal materializes when -DI moves
above +DI.

[type = stock] AND [country = US]

AND [Daily SMA(20,Daily Volume) > 100000]

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 AND [Daily SMA(60,Daily Close) > 10]

AND [Daily ADX Line(14) > 20]

AND [Daily Minus DI(14) crosses Daily Plus DI(14)]
AND [Daily Close < Daily SMA(50,Daily Close)]

For more details on the syntax to use for Average Directional Index,
Plus DI and Minus DI scans, please see our Scanning Indicator
Reference in the Support Center.

Addi onal Resources

Stocks & Commodities Magazine Articles
The Average Directional Movement Index (ADX) by Thom
Hartle
Feb 1991 - Stocks & Commodities V. 9:3 (101-102)

How the Pros Use Average Directional Index by Barbara

Star, PhD.
Sep 1999 - Stocks & Commodities

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