Technical analysis, ADX, Directional Movement...

Average Directional Index (ADX)

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The Average Directional Index (ADX) was developed by J. Welles Wilder to evaluate the strength of a trend and to define a period of sideway trading. For better results from the signals generated by technical analysis, many traders use ADX to determine whether the market is trending or trading (moving sideways) and adjust their indicators' settings to the current market condition. As a result, dynamic trading systems that use Average Directional Index as one of their indicators are considered to deliver better results.

The ADX is an oscillator that fluctuates between 0 and 100, although readings above 60 are relatively rare. In technical analysis, an ADX is compared to two levels:

• ADX readings below 20 indicate a weak trend;
• ADX readings above 40 indicate a strong trend.

The Average Directional Index does not indicate whether a trend is Bullish or Bearish, it cannot recognize an up- or down-trend. Thus, a reading above 40 can indicate a strong downtrend as well as a strong uptrend. However, an ADX delivers valuable information about changes in the strength of a trend and can be used to identify potential changes in a market from trending to non-trending. When the ADX begins to strengthen by moving above 20 after having been below this level, it is a sign that the trading range is ending and that a trend is developing. When the ADX weakens and drops below 40 after having been above that level, it is a sign that the current trend is losing strength and a trading range may develop.

The ADX is derived from two other indicators, also developed by Wilder, called the Positive Directional Indicator (sometimes written DI+) and the Negative Directional Indicator (DI-). The ADX calculations are somewhat complex and can be handled in several stages:

1. Define Directional Movement Indicator, where +DM is a positive directional Movement indicator and -DM is a negative directional movement indicator.
   1. Define the delta extreme price changes from previous bar:
      
      [Delta High] = [High] - [Previous High]
      [Delta Low] = [Previous Low] - [Low]
   2. If today's range is entirely within yesterday's range, or if the ranges are the same, there has been no directional movement:
      
      if ([Delta High] < 0) and ([Delta Low] < 0) or
                     [Delta High]=[Delta Low] then [+DM]=0 and [-DM]=0
   3. If the range has moved upward, there has been a positive directional move:
      
      if ([Delta High] > [Delta Low]) then [+DM+=[Delta High] and [-DM]=0
   4. If the range has moved downward, there has been a negative directional move:
      
      if ([Delta High] < [Delta Low]) then [+DM]=0 and [-DM]=[Delta Low]
2. Calculate the Average Directional Movement Indicator, where the +ADM is the Average Positive Direction Movement Indicator for N periods and -ADM is the Average Negative Direction Movement Indicator for N periods:
   1. Exponential moving average applied to DM+:
      
      [ADM+] = EMA([+DM])
   2. And exponential moving average applied to DM-:
      
      [ADM-] = EMA([-DM])
3. Calculate the True Range (TR) and the Average True Range (ATR). See Average True Range description.
4. Calculate the Directional index, where +DI is the average positive directional movement indicator normalized by the average true range and -DI is the average negative directional movement indicator normalized by the average true range:
   1.  [+DI] = [+ADM] / ATR * 100
   2. [-DI] = [-ADM] / ATR * 100
5. The next step is to calculate the Directional Movement Index (DX). It is calculated as the ratio of the absolute value of difference of the directional indices to the sum of the directional indices:
   
   [DX] = (|[+DI] - [-DI]|) /  ([+DI] + [-DI]) * 100
   
   Note: If there is no need to calculate the Directional Movement Index (+DI and -DI), then you can simplify the DX and ADX calculations by skipping steps #2 and #3. In that case, you can calculate DX by the following formula:
   
   [DX] = (|[+ADM] - [-ADM]|) /  ([+ADM] + [-ADM]) * 100
6. The last step is to calculate the Average Directional Movement Index (ADX), where ADX is the result of applying the exponential moving average to the Directional Movement Index:
   
   [ADX] = EMA([DX])

The ADX in the Directional Movement system is used to define strong trends. The higher the ADX value, the stronger is the trend. The technical analysis rules state that trend following systems can be used when the ADX is above 25. The use of trend following systems is not recommended when the ADX drops below 20.

Chart 1: S&P 500 -ADX (Average Directional Movement Index)