Moving Average Convergence Divergence

Moving Average Convergence Divergence

Developed by Gerald Appel in the late seventies, Moving Average Convergence-Divergence (MACD) is one of the simplest and most effective momentum indicators available. MACD turns two trend-following indicators, moving averages, into a momentum oscillator by subtracting the longer moving average from the shorter moving average. As a result, MACD offers the best of both worlds: trend following and momentum. MACD fluctuates above and below the zero line as the moving averages converge, cross and diverge. Traders can look for signal line crossovers, centerline crossovers and divergences to generate signals. Because MACD is unbounded, it is not particular useful for identifying overbought and oversold levels.

Standard MACD is the 12-day Exponential Moving Average (EMA) less the 26-day EMA. Closing prices are used to form the moving averages so MACD is based on closing prices. A 9-day EMA of MACD is plotted along side to act as a signal line to identify turns in the indicator. The MACD-Histogram represents the difference between MACD and its 9-day EMA, the signal line. The histogram is positive when MACD is above its 9-day EMA and negative when MACD is below its 9-day EMA.


As its name implies, MACD is all about the convergence and divergence of the two moving averages. Convergence occurs when the moving averages move towards each other. Divergence occurs when the moving averages move away from each other. The shorter moving average (12-day) is faster and responsible for most of the MACD movement. The longer moving average (26-day) is slower and less reactive to price changes in the underlying security. Positive MACD indicates that the 12-day EMA is above the 26-day EMA. Positive values increase as the shorter EMA trades further above the longer EMA. This means upside momentum is increasing. Negative MACD indicates that the 12-day EMA is below the 26-day EMA. Negative values increase as the shorter EMA trades further below the longer EMA. This means downside momentum is increasing. There are times when MACD crosses the zero line, which is also known as the centerline. This signals that the 12-day EMA has crossed the 26-day EMA. The direction of the centerline cross, of course, depends on direction of the moving average cross.

MACD in negative territory as the 12-day EMA trades below the 26-day EMA. The initial cross occurred at the end of September (black arrow) and MACD moved further into negative territory as the 12-day EMA diverged further from the 26-day EMA. The orange area highlights a period of positive MACD, which is when the 12-day EMA was above the 26-day EMA. Notice that the 12-day EMA remained below 1 during this period (red dotted line). This means the distance between the 12-day EMA and 26-day EMA was less than 1 point, which is not a big difference.

Signal Line Crossovers

Signal line crossovers are the most common MACD signals. The signal line is a 9-day EMA of MACD. As a moving average of the indicator, it trails MACD and makes it easier to spot turns in MACD. A bullish crossover occurs when MACD turns up and crosses above the signal line. A bearish crossover occurs when MACD turns down and crosses below the signal line. Crossovers can last a few days or a few weeks, it all depends on the strength of the move that causes the crossover. Signal crossovers are quite common. As such, due diligence is required before relying on these signals. Signal line crossovers at positive or negative extremes should be viewed with caution. Even though MACD is an unbounded oscillator, chartists can estimate historical extremes with a simple visual assessment of the indicator. It takes a strong move in the underlying security to push momentum to an extreme. Even though the move may continue, momentum is likely to slow and this will usually produce a signal line crossover at the extremities. Volatility in the underlying security can also increase the number of crossovers. Chart 2 shows IBM with its 12-day EMA (green), 26-day EMA (red) and MACD (12,26,9) in the indicator window. There were eight signal line crossovers in six months: four up and four down. There were some good signals and some bad signals. The yellow area highlights a period when MACD surged above 2 to reach a positive extreme. There were two bearish signal line crossovers in April and May, but IBM continued trending higher. Even though upward momentum slowed after the surge, upward momentum was still stronger than downside momentum in April and May. The third bearish signal line crossover in May resulted in a good signal.

Centerline Crossovers

Centerline crossovers are the next most common MACD signals. A bullish centerline crossover occurs when MACD moves above the zero line to turn positive. This happens when the 12-day EMA of the underlying security moves above the 26-day EMA. A bearish centerline crossover occurs when MACD moves below the zero line to turn negative. This happens when the 12-day EMA moves below the 26-day EMA. Centerline crossovers can last a few days or a few months. It all depends on the strength of the trend. MACD will remain positive as long as there is a sustained uptrend. MACD will remain negative when there is a sustained downtrend. Chart 3 shows Pulte Homes (PHM) with at least four centerline crosses in a nine month period. The post-crossover moves were quite strong so the resulting signals worked well.


Divergences form when MACD diverges from the price action of the underlying security. A bullish divergence forms when a security records a lower low and MACD forms a higher low. The low lower in the security affirms the current downtrend, but the higher low in MACD shows less downside momentum. The slowing of the downtrend sometimes foreshadows a trend reversal or a sizable rally. Chart 6 shows Google (GOOG) with a bullish divergence in October-November 2008. First, notice that I am using closing prices to identify the divergence.


MACD is special because it brings together momentum and trend in one indicator. This means MACD will never be far removed from price action. MACD’s unique blend of trend and momentum can be applied to daily, weekly or monthly charts. The standard setting for MACD is the difference between the 12 and 26-period EMAs. Chartists looking for more sensitivity may try (5,35,5). Chartists looking for less sensitivity may consider (20,50,10). A less sensitive MACD will still oscillate above/below zero, but the centerline crossovers and signal line crossovers will be less frequent. MACD is not particularly good for identifying overbought and oversold levels. Even though it is possible to identify levels that historically represent overbought and oversold, MACD does not have any upper or lower limits to bind its movement. MACD can continue to overextend beyond historical extremes. MACD calculates the absolute difference between two moving averages and not the percentage difference. A $20 stock may have a MACD range of -1.5 to 1.5, while a $100 stock may have a MACD range from -10 to +10. It is not possible to compare MACD for securities that vary in price. An alternative is to use the Percentage Price Oscillator (PPO), which shows the percentage difference between two moving averages.


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