Average Directional Index (ADX)
Introduction
The Average
Directional Index (ADX), Minus Directional Indicator (-DI) and Plus Directional
Indicator (+DI) represent a group of directional movement indicators that form
a trading system developed by Welles Wilder. Wilder designed ADX with
commodities and daily prices in mind, but these indicators can also be applied
to stocks. The Average Directional Index (ADX) measures trend strength without
regard to trend direction. The other two indicators, Plus Directional Indicator
(+DI) and Minus Directional Indicator (-DI), complement ADX by defining trend
direction. Used 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 incredible detailed in their calculation and have
stood the test of time.
Directional Movement
Plus Directional
Movement (+DM) and Minus Directional Movement (-DM) form the backbone of the
Average Directional Index (ADX). Wilder determined directional movement by
comparing the difference between two consecutive lows with the difference between
the 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 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
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 cancel out each other. Negative values revert to zero. All inside days will
have zero directional movement.
Calculation
The calculation steps
for the Average Directional Index (ADX) are detailed in each step. Average True
Range (ATR) is not detailed because there is an entire ChartSchool article for
this. Basically, ATR is Wilder's version of the two period trading range.
Smoothed versions of Plus Directional Movement (+DM) and Minus Directional
Movement (-DM) are divided by a smoothed version Average True Range (ATR) to
reflect the true magnitude of a move. The example below is based on a 14-day ADX
calculation.
1. Calculate the True
Range (TR), Plus Directional Movement (+DM) and Minus Directional Movement
(-DM) for each period.
2. Smooth these
periodic values using the 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 Plus Directional Indicator (green
line) that is plotted along with ADX.
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 Minus Directional Indicator
(red line) that is plotted along with ADX.
5. The Directional
Movement Index (DX) equals the absolute value of +DI14 less - DI14 divided by
the sum of +DI14 and - DI14.
6. After all these
steps, it is time to calculate the Average Directional Index (ADX). 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.
Below is a
spreadsheet example with all steps involved. There is a 119 day calculation gap
because around 150 periods are required to absorb the smoothing techniques. ADX
enthusiasts can click here to download this spreadsheet and see the gory
details. The chart below shows an example of ADX using the Nasdaq 100 ETF
(QQQQ).
As seen in the ADX
calculation, 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 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
TR14
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
Subsequent ADX14 = (Prior ADX14 x 13) + Current DX Value
Interpretation
The Average
Directional Index (ADX) is used to measure the strength or weakness of a trend,
not the actual direction. Directional 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 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 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.
DI Crossover System
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 insures that prices are
trending. 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.
The chart above shows Medco Health Solutions with the three
directional movement indicators. The green dotted lines show the buy signals
and the red dotted lines shows the sell signals. Wilders 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
validate signals. Others occur to invalidate signals signals. As with 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.
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. Wilders 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 never moved below 20 to make
the signals possible.
Conclusions
The directional
movement indicator calculations are complex, interpretation is straight-forward
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 Indicators 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.
SharpCharts
SharpCharts users can
plot the directional movement indicators by selecting Average Directional Index
(ADX) from the indicator drop-down list. By default, ADX will be in black, the
Plus Directional Indicator (+DI) in green and the Minus Directional 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 indentify 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.
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.
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. An 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.
(Courtesy www.stockcharts.com)
ADX on Nifty Daily
Charts
Now let us watch it on Nifty Daily Charts for trading
signals. On 24.06.2011 watch the green line(+DI) cross the red(-DI) line
setting the uptrend for Nifty. Also watch the yellow line(for momentum) of the
uptrend. The momentum then turned sideways and the green line(+DI) turned
downwards early before the downtrend on Nifty(divergence).We got a huge spike
on 07.07.2011 with a low reading on green line(+DI) which was our signal for
change in trend. After that the price action on Nifty is sideways as indicated
by the green(+DI) and red(-DI) lines and the yellow line(momentum) coming down.
On 27.10.2011 we see the red(-DI) cross the green(+DI) which was the signal to
short the Nifty or ad to earlier positions. Watch the yellow line (momentum) and
red line(-DI) both moving sync with each other depicting the strength of the
move& correspondingly the green line(+DI) moving down also signifying the
down move. In all good 1000 points move very rarely seen. On 22.08.2011 the
momentum yellow line was signaling the move losing its strength(cover the
additional position of shorts on Nifty).On 29.08.2011 it signaled the end of
the move(cover all shorts on Nifty) with the green line(+DI) touching the red
line(-DI) first time( on 02.09.2011) after a gap of 21 trading days. The price
action is pretty side ways after that on Nifty the momentum yellow line shows
it clearly by decreasing in value. On 07.10.2011 we see the green line(+DI)
cross the red(-DI) a buy signal with gap up on Nifty. On 10.10.2011 the yellow
line starts rising & the red line is declining in value confirming the
trend.On 28.10.2011 the high marks the end of the move. After which the
momentum line starts decreasing in value & green line is in sync with it. So
longs On Nifty were to be sold on 31.10.2011.The move on Nifty was from 4900(open on 10.10.2011) to 5344(close on
31.10.2011) i.e. 444 points of Nifty.
Happy Trading!
