Average Directional Movement Index (ADX)

Introduction

The Average Directional Movement Index (ADX) is a technical analysis indicator used to quantify the strength of a trend in a stock, commodity, or currency pair. Developed by J. Welles Wilder Jr. in his book New Concepts in Technical Trading Systems, the ADX is a component of the Directional Movement System, which includes two other indicators: the Plus Directional Indicator (+DI) and the Minus Directional Indicator (−DI).

While the ADX measures the strength of a trend, it does not indicate the direction of the trend.

Calculation of ADX

The ADX is derived from the moving average of the directional movement index, calculated as follows:

Calculate the Directional Movement (+DM and -DM):
- +DM = Current High - Previous High (if positive and greater than 0; otherwise, 0)
- -DM = Previous Low - Current Low (if positive and greater than 0; otherwise, 0)
Calculate the True Range (TR):
Calculate the Average True Range (ATR):
- Typically calculated as a moving average of the True Range over a specified period (often 14 days).
Calculate the Directional Indicators:
- +DI:
- −DI:
Calculate the ADX:
- The ADX is then calculated as the average of the absolute differences between +DI and -DI over a specified period (usually 14 days):

Example Calculation

Assume we have the following data for a stock over five days:

Day	High	Low	Close
1	20	18	19
2	22	19	21
3	23	20	22
4	20	19	19
5	21	18	20

Step 1: Calculate +DM and -DM

Day 2:
- +DM = 22 - 20 = 2
- -DM = 0 (Previous Low = 18, Current Low = 19)
Day 3:
- +DM = 1 (Current High = 23, Previous High = 22)
- -DM = 0
Day 4:
- +DM = 0 (Current High = 20 ≤ Previous High = 23)
- -DM = 1 (Previous Low = 19, Current Low = 19)
Day 5:
- +DM = 0
- -DM = 1 (Previous Low = 19, Current Low = 18)

Day	+DM	-DM
2	2	0
3	1	0
4	0	1
5	0	1

Step 2: Calculate True Range (TR)

Day 2:
Day 3:
Day 4:
Day 5:

Step 3: Calculate Average True Range (ATR)

For simplicity, assume the ATR over 4 days is calculated as follows:

Step 4: Calculate +DI and -DI

Day 2:
Day 3:
Day 4:
Day 5:

Step 5: Calculate ADX

After calculating the values of +DI and -DI over the chosen period, the ADX can be calculated as:

Python Code

import pandas as pd

def calculate_true_range(data):
    """Calculate the True Range (TR)."""
    data['previous_close'] = data['Close'].shift(1)
    data['high_low'] = data['High'] - data['Low']
    data['high_prev_close'] = (data['High'] - data['previous_close']).abs()
    data['low_prev_close'] = (data['Low'] - data['previous_close']).abs()
    
    # Calculate True Range
    data['True Range'] = data[['high_low', 'high_prev_close', 'low_prev_close']].max(axis=1)
    return data

def calculate_adx(data, n=14):
    """Calculate the ADX."""
    data = calculate_true_range(data)
    
    # Calculate +DM and -DM
    data['+DM'] = (data['High'].diff() > data['Low'].diff()).where(data['High'].diff() > 0, 0)
    data['-DM'] = (data['Low'].diff() < data['High'].diff()).where(data['Low'].diff() > 0, 0)
    
    # Calculate the smoothed TR, +DM, and -DM using a rolling window
    data['ATR'] = data['True Range'].rolling(window=n).mean()
    data['+DI'] = 100 * (data['+DM'].rolling(window=n).mean() / data['ATR'])
    data['-DI'] = 100 * (data['-DM'].rolling(window=n).mean() / data['ATR'])
    
    # Calculate ADX
    data['DX'] = 100 * (abs(data['+DI'] - data['-DI']) / (data['+DI'] + data['-DI']))
    data['ADX'] = data['DX'].rolling(window=n).mean()
    
    return data[['Date', 'Close', '+DI', '-DI', 'ADX']]

Interpretation of ADX

Trend Strength:
- Values above 20 or 25 indicate a strong trend.
- Values below 20 suggest a weak trend or a range-bound market.
Trend Direction:
- +DI above -DI: Indicates a bullish trend.
- -DI above +DI: Indicates a bearish trend.
Crossovers:
- Traders may use crossovers between +DI and -DI as buy/sell signals.

Analogy

Think of the ADX as a weather forecast for trends. Just as meteorologists predict stormy or clear weather by analyzing patterns in temperature, wind, and pressure, traders can use the ADX to gauge whether a security is in a strong trend or a period of low volatility. A high ADX indicates a stormy market (strong trend), whereas a low ADX indicates clear skies and calm conditions (low volatility).

Conclusion

The Average Directional Movement Index (ADX) is a valuable tool for traders seeking to assess the strength of a trend. By understanding how to calculate and interpret the ADX, traders can enhance their trading strategies and make more informed decisions.

References

Wilder, J. W. (1978). New Concepts in Technical Trading Systems. Trend Research.
Investopedia: Average Directional Index (ADX)](https://www.investopedia.com/terms/a/adx.asp)
TradingView: Average Directional Index](https://www.tradingview.com/wiki/Average_Directional_Index_%28ADX%29)

Average True Range

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