Moving Average Convergence Divergence (MACD)

Name Type Prerequisite Use Cases
Moving Average Convergence Divergence (MACD) Momentum EMA Identifying momentum shifts and signal line crossovers.

Definition

The Moving Average Convergence Divergence (MACD) is a trend-following momentum indicator that shows the relationship between two moving averages of a security's price. It is one of the most popular tools in technical analysis because it provides signals for both trend direction and momentum strength.

Mathematical Equation

The MACD is calculated by subtracting the long-term EMA (26 periods) from the short-term EMA (12 periods).

\[ \text{MACD Line} = EMA_{12} - EMA_{26} \]

A "Signal Line", which is a 9-day EMA of the MACD Line, is then plotted on top of the MACD Line:

\[ \text{Signal Line} = EMA_9(\text{MACD Line}) \]

Finally, the MACD Histogram represents the difference between the MACD Line and the Signal Line:

\[ \text{MACD Histogram} = \text{MACD Line} - \text{Signal Line} \]

Special cases

  • Maximum possible value: Unbounded
  • Minimum possible value: Unbounded
  • Behavior: Oscillates around a zero line, showing the convergence and divergence of two moving averages.

Visualization

MACD

Trading Significance

  1. Signal Line Crossovers:

    • Bullish: The MACD Line crosses above the Signal Line.

    • Bearish: The MACD Line crosses below the Signal Line.

  2. Zero Line Crossovers:

    • Bullish: The MACD Line crosses above the zero line (short-term EMA above long-term EMA).

    • Bearish: The MACD Line crosses below the zero line.

  3. Divergence: When the security price diverges from the MACD, it signals the end of the current trend.

    • Bullish Divergence: Price records a lower low, but MACD forms a higher low.

    • Bearish Divergence: Price records a higher high, but MACD forms a lower high.