Moving Average Convergence-Divergence (MACD)

Introduction

Developed by Gerald Appel in the late seventies, the Moving Average Convergence-Divergence (MACD) indicator is one of the simplest and most effective momentum indicators available. The 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, the MACD offers the best of both worlds: trend following and momentum. The 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 the MACD is unbounded, it is not particularly useful for identifying overbought and oversold levels.
Note: MACD can be pronounced as either "MAC-DEE" or "M-A-C-D".

Calculation

MACD Line: (12-day EMA - 26-day EMA) 

Signal Line: 9-day EMA of MACD Line

MACD Histogram: MACD Line - Signal Line

The MACD Line is the 12-day Exponential Moving Average (EMA) less the 26-day EMA. Closing 
prices are used for these moving averages. A 9-day EMA of the MACD Line is 
plotted with the indicator to act as a signal line and identify turns. The MACD 
Histogram represents the difference between MACD and its 9-day EMA, the Signal 
line. The histogram is positive when the MACD Line is above its Signal line and 
negative when the MACD Line is below its Signal line. 

The values of 12, 26 and 9 are the typical setting used with the MACD, 
however other values can be substituted depending on your trading style and 
goals. 




Interpretation

As its name implies, the 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 MACD movements. The longer moving average (26-day) is slower and less 
reactive to price changes in the underlying security. 

The MACD Line oscillates above and below the zero line, which is also known 
as the centerline. These crossovers signal that the 12-day EMA has crossed the 
26-day EMA. The direction, of course, depends on direction of the moving average 
cross. Positive MACD indicates that the 12-day EMA is above the 26-day EMA. 
Positive values increase as the shorter EMA diverges further from the longer 
EMA. This means upside momentum is increasing. Negative MACD values indicates 
that the 12-day EMA is below the 26-day EMA. Negative values increase as the 
shorter EMA diverges further below the longer EMA. This means downside momentum is increasing. 









Signal Line Crossovers

Signal line crossovers are the most common MACD signals. The signal line is a 
9-day EMA of the MACD Line. As a moving average of the indicator, it trails the 
MACD and makes it easier to spot MACD turns. A bullish crossover occurs when the 
MACD turns up and crosses above the signal line. A bearish crossover occurs when 
the 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. 

Due diligence is required before relying on these common signals. Signal line 
crossovers at positive or negative extremes should be viewed with caution. Even 
though the MACD does not have upper and lower limits, chartists can estimate 
historical extremes with a simple visual assessment. 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. 





Conclusions

The MACD indicator is special because it brings together momentum and trend 
in one indicator. This 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 a shorter short-term moving average and a longer long-term moving average. 
MACD(5,35,5) is more sensitive than MACD(12,26,9) and might be better suited for 
weekly charts. Chartists looking for less sensitivity may consider lengthening 
the moving averages. A less sensitive MACD will still oscillate above/below 
zero, but the centerline crossovers and signal line crossovers will be less 
frequent. 

The MACD is not particularly good for identifying overbought and oversold 
levels. Even though it is possible to identify levels that are historically 
overbought or oversold, the MACD does not have any upper or lower limits to bind 
its movement. During sharp moves, the MACD can continue to over-extend beyond 
its historical extremes. 

Finally, remember that the MACD Line is calculated using the actual 
difference between two moving averages. This means MACD values are dependent on 
the price of the underlying security. The MACD values for a $20 stocks may range 
from -1.5 to 1.5, while the MACD values for a $100 may range from -10 to +10. It 
is not possible to compare MACD values for a group of securities with varying 
prices.