Name, Sometimes Called:
Average Directional Movement Index
Abbreviated ADX
Not to be confused with the Average Directional Movement Index Rating
(ADXR)
See also Directional Movement (DM) and the Directional
Movement Index (DMI) under History below.
Brief Description:
ADX is an n-period exponential smoothing indicator
developed by Wilder, one of a set of indicators he developed. ADX
is derived from two other Wilder-developed indicators called the
Positive Directional Indicator, sometimes written +DI, (here we
write that as DI(plus)) and the Negative Directional Indicator or
–DI (here, DI(minus)).
ADX is used to determine the existence and strength of the current
environment. Is it trending or non-trending? If trending, is the
trend strong or weak?
Definitions, Formulas:
ADX is an n-period exponential
smoothing indicator, used to determine the strength of the current
trend. Whether it is trending
or
non-trending is important both for market entry and to see whether
other indicators’ results may be useful.
ADX is based on two other directional movement indicators: DI(plus)
and DI(minus):
DI(plus) = HTODAY - HYESTERDAY
DI(minus) = LYESTERDAY - LTODAY
where
HTODAY = today's high price
HYESTERDAY = yesterday's high
price
LYESTERDAY = yesterday's low price
LTODAY = today's low price
We then make these adjustments:
If DI(plus) is less than DI(minus), then DI(plus) = 0
If DI(minus) is less than DI(plus), then DI(minus) = 0
If DI(plus) is negative, then DI(plus) = 0
If DI(minus) is negative, then DI(minus) = 0
It is possible that both DI(plus) and DI(minus) may be set to zero.
We then calculate a value called the True Range (TR), which is
the largest of three differences:
TR = max[(HTODAY – LTODAY),
(HTODAY - CYESTERDAY),
CYESTERDAY - LTODAY)]
where CYESTERDAY = yesterday's
closing price
Next, calculate smoothed DI(plus), smoothed DI(minus), and smoothed
TR:
smoothed DI(plus) = EMA(27)(DI(plus))
smoothed DI(minus) = EMA(27)(DI(minus))
smoothed TR = EMA(27)(TR)
For smoothing, we use a 27-day EMA
(the standard form for this TAI) which equates to a non-standard
“14-day” EMA (used by Wilder, who calculates the EMA
using 1/14 of today's data + 13/14 of yesterday's average). See
the extended explanation under History section
below.
Then
PDI = smoothed DI(plus) / smoothed TR
MDI = smoothed DI(minus) / smoothed TR
and
DX = 100 x | PDI – MDI | / (PDI + MDI)
(where | PDI – MDI | means the absolute value of PDI –
MDI)
We then compute the ratio of positive to negative (scaled by 100
times):
DX = 100 x | PDI – MDI | / (PDI + MDI)
Let’s examine this for a moment. If PDI (upward pressure)
and MDI (downward pressure) are equal, then DX is zero, and there
is no trend direction. If PDI is huge with respect to MDI (that
is, PDI is much larger than MDI), then DX is near 100. If MDI
is much larger than PDI, then DX is also near 100. So it does
not matter whether the major pressure is upward or downward: the
DX value approaches 100 as the absolute value of the ratio of
the two pressures. This is why ADX cannot indicate direction.
Finally
ADX = smoothed DX = EMA(27)(DX)
ADX has values in the range 0 to 100. However, readings above 60
are relatively rare.
- An ADX value below 20 indicates a weak trend, or a non-trending
environment. In such markets, oscillators
may have more predictive value.
- An ADX value above 20 indicates a trend. In such markets, moving
averages (see the variety of moving
averages in the glossary) may have more predictive value.
- An ADX value above 30 indicates a strong trend. Some prefer
to use values above 40 to indicate a strong trend.
As a reminder, ADX was designed to indicate the strength of the
current trend, not its direction. So a reading above 30 can indicate
either a strong downtrend or a strong uptrend.
Positive Development Calculation:
ADX has no positive
developments. It indicates the presence (or absence) of a trend
and the strength (or weakness) of the trend.
History:
J. Welles Wilder, Jr., in his book New Concepts
in Technical Trading Systems (Trend Research, PO Box 128, McLeansville,
NC 27301, 1978), asserts that markets exhibit strong trends only
about 30 percent of the time. To determine when such strong trends
occur, Wilder created a set of indicators, among them ADX. ADX is
valuable in guiding the use of other indicators, which give more
useful results depending on whether the market is trending or not.
Wilder suggests that high and rising levels of ADX indicate a healthy
and forceful major trend (either up or down). Low and falling levels
of ADX indicate a non-trending market.
If you use the ADX TAI, be aware that Wilder uses a non-standard
EMA construction.
Under Wilder's EMA computation, a parameter of “14 days”
would be 1/14 of today's data plus 13/14 of yesterday's EMA.
However, the standard
EMA construction generates the same value using a 27-day parameter,
as follows.
The smoothing constant k for a 27-day period is
k = 2 / (27 + 1) = 2 / 28 = 1/14
and today's EMA is
EMATODAY = (Today's Value x k)
+ EMAYESTERDAY x (1 - k)
Substituting:
EMATODAY = (Today's Value x
1/14) + EMAYESTERDAY x (1 - 1/14)
or
EMATODAY = (Today's Value x
1/14) + EMAYESTERDAY x (13/14)
which is what Wilder uses.
We use the standard EMA for consistency in presentation. It produces
the same result as Wilder's calculation.
Directional Movement (DM) and the Directional Movement
Index (DMI)
DM is a family of indicators that Wilder created to
help determine if a security is trending. The DM family of indicators
has also been called the Directional Movement Index (DMI). This
confuses the family of indicators with the single indicator called
the Directional Movement Indicator
(sometimes confusingly abbreviated DX).
The indicators and their abbreviations are:
Plus Directional Indicator or Positive Directional Indicator
(+DI or DI(plus))
Minus Directional Indicator or Negative Directional Indicator
(-DI or DI(minus))
Directional Movement Indicator (DX)
Average Directional Movement Indicator (ADX)
Average Directional Movement Index Rating (ADXR)
This chart has the ADX indicator showing the rise to a very strong
trend, the weakening of that trend, eventually leading to a non-trending
environment.
|
