Average directional movement index

The average directional movement index (ADX) was developed in 1978 by J. Welles Wilder as an indicator of trend strength in a series of prices of a financial instrument. ADX has become a widely used indicator for technical analysts, and is provided as a standard in collections of indicators offered by various trading platforms.

Calculations

The ADX is calculated from two indicators developed by Wilder: the positive directional indicator (${\displaystyle DI^{+}}$) and the negative directional indicator (${\displaystyle DI^{-}}$).

Let ${\displaystyle H_{t}}$, ${\displaystyle L_{t}}$, and ${\displaystyle C_{t}}$ denote the high, low, and closing prices in period ${\displaystyle t}$, respectively. Define the upward and downward movements as

${\displaystyle U_{t}=H_{t}-H_{t-1},\qquad D_{t}=L_{t-1}-L_{t}.}$

The positive and negative directional movements are

${\displaystyle DM_{t}^{+}={\begin{cases}U_{t},&{\text{if }}U_{t}>D_{t}{\text{ and }}U_{t}>0,\\0,&{\text{otherwise}},\end{cases}}}$

and

${\displaystyle DM_{t}^{-}={\begin{cases}D_{t},&{\text{if }}D_{t}>U_{t}{\text{ and }}D_{t}>0,\\0,&{\text{otherwise}}.\end{cases}}}$

For a sequence ${\displaystyle X_{t}}$, write ${\displaystyle S_{n}[X]_{t}}$ for Wilder's ${\displaystyle n}$-period smoothed moving average. It is initialized with the arithmetic mean of the first ${\displaystyle n}$ available observations and subsequently calculated recursively as

${\displaystyle S_{n}[X]_{t}={\frac {(n-1)S_{n}[X]_{t-1}+X_{t}}{n}}.}$

Wilder originally used ${\displaystyle n=14}$ periods.

The true range is

${\displaystyle TR_{t}=\max \left\{H_{t}-L_{t},\,\left|H_{t}-C_{t-1}\right|,\,\left|L_{t}-C_{t-1}\right|\right\},}$

and the average true range is

${\displaystyle ATR_{t}=S_{n}[TR]_{t}.}$

The directional indicators are

${\displaystyle DI_{t}^{+}=100\,{\frac {S_{n}[DM^{+}]_{t}}{ATR_{t}}},\qquad DI_{t}^{-}=100\,{\frac {S_{n}[DM^{-}]_{t}}{ATR_{t}}}.}$

The directional index is

${\displaystyle DX_{t}=100\,{\frac {\left|DI_{t}^{+}-DI_{t}^{-}\right|}{DI_{t}^{+}+DI_{t}^{-}}}.}$

Finally, the ADX is obtained by smoothing the directional index:

${\displaystyle ADX_{t}=S_{n}[DX]_{t}.}$

Thus, after initialization with the arithmetic mean of the first ${\displaystyle n}$ available values of ${\displaystyle DX_{t}}$, subsequent values satisfy

${\displaystyle ADX_{t}={\frac {(n-1)ADX_{t-1}+DX_{t}}{n}}.}$

The ratio formulas above apply when their denominators are nonzero.

Variations of the calculation use other moving averages, including an exponential moving average, a weighted moving average, or an adaptive moving average.

Interpretation

The ADX does not indicate trend direction or momentum, only trend strength. It is a lagging indicator; that is, a trend must have established itself before the ADX will generate a signal that a trend is under way. ADX will range between 0 and 100. Generally, ADX readings below 20 indicate a weak trend, while readings above 40 indicate a strong trend. An exceptionally strong trend is typically indicated by readings above 50. Alternative interpretations have also been proposed and adopted by technical analysts. For example, ADX has been described as a reliable coincident indicator of classical chart pattern development, with readings below 20 often occurring shortly before pattern breakouts. The value of the ADX is proportional to the slope of the trend. The slope of the ADX line is proportional to the acceleration of the price movement (changing trend slope). If the trend is a constant slope then the ADX value tends to flatten out.

Timing

Various market timing methods have been devised using ADX. One of these methods is discussed by Alexander Elder in his book Trading for a Living. One of the best buy signals is when ADX turns up when below both Directional Lines and +DI is above -DI. You would sell when ADX turns back down.

References