MACD

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MACD 12,26,9

MACD, which stands for Moving Average Convergence / Divergence, is a technical analysis indicator created by Gerald Appel in the 1960s. It shows the difference between a fast and slow exponential moving average (EMA) of closing prices. Fast means a short-period average, and slow means a long period one. The standard periods are 12 and 26 days:

$MACD = EMA[12]\,of\,price - EMA[26]\,of\,price$

A signal line (or trigger line) is then formed by smoothing this with a further EMA. The standard period for this is 9 days,

$signal = EMA[9]\,of\,MACD$

The difference between the MACD and the signal line is often calculated and shown not as a line, but a solid block histogram style. This construction was made by Thomas Aspray in 1986. The calculation is simply

h i s t o g r a m = M A C D - s i g n a l

The example graph above right shows all three of these together. The upper graph is the prices. The lower graph has the MACD line in green and the signal line in red. The solid white histogram style is the difference between them.

The set of periods for the averages, often written as say 12,26,9, can be varied. Appel and others have experimented with various combinations.

[edit] Interpretation

MACD is a trend following indicator, and is designed to identify trend changes. It's generally not recommended for use in ranging market conditions. Three types of trading signals are generated,

MACD line crossing the signal line.
MACD line crossing zero
Divergence between price and MACD levels

The signal line crossing is the usual trading rule. This is to buy when the MACD crosses up through the signal line, or sell when it crosses down through the signal line. These crossings may occur too frequently, and other tests may be needed to be applied.

The purpose of the histogram is to help show when a crossing occurs, since when it crosses through zero the MACD crosses the signal line. The histogram can also help visualizing when the two lines are coming together. Both may still be rising, but coming together, so a falling histogram suggests a crossover may be approaching.

A crossing of the MACD line up through zero is interpreted as bullish, or down through zero as bearish. These crossings are of course simply the original EMA(12) line crossing up or down through the slower EMA(26) line.

Positive divergence between MACD and price arises when price makes a new selloff low, but the MACD doesn't make a new low, ie. it remains above where it fell to on that previous price low. This is interpreted as bullish, suggesting the downtrend may be nearly over. Negative divergence is the same thing when rising, ie. price makes a new rally high, but MACD doesn't rise as high as it did before; this is interpreted as bearish.

Divergence may be similarly interpreted on the price versus the histogram, ie. new price levels not confirmed by new histogram levels. Longer and sharper divergences (distinct peaks or troughs) are regarded as more significant than small shallow patterns in this case.

John Murphy (in Technical Analysis of the Financial Markets) also recommended looking at a MACD on a weekly scale before looking at a daily scale, so as to avoid making short term trades against the direction of the intermediate trend.