Introduction

Developed by Gerald Appel, Moving Average Convergence/Divergence (MACD) is one of the simplest and most reliable indicators available. MACD uses moving averages, which are lagging indicators, to include some trend-following characteristics. These lagging indicators are turned into a momentum oscillator by subtracting the longer moving average from the shorter moving average. The resulting plot forms a line that oscillates above and below zero, without any upper or lower limits. MACD is a centered oscillator and the guidelines for using centered oscillators apply.

MACD Formula

The most popular formula for the "standard" MACD is the difference between a security's 26-day and 12-day Exponential Moving Averages (EMAs). This is the formula that is used in many popular technical analysis programs, including Sharp Charts, and quoted in most technical analysis books on the subject. Appel and others have since tinkered with these original settings to come up with a MACD that is better suited for faster or slower securities. Using shorter moving averages will produce a quicker, more responsive indicator, while using longer moving averages will produce a slower indicator, less prone to whipsaws. For our purposes in this article, the traditional 12/26 MACD will be used for explanations. Later in the indicator series, we will address the use of different moving averages in calculating MACD.

Of the two moving averages that make up MACD, the 12-day EMA is the faster and the 26-day EMA is the slower. Closing prices are used to form the moving averages. Usually, a 9-day EMA of MACD is plotted along side to act as a trigger line. A bullish crossover occurs when MACD moves above its 9-day EMA, and a bearish crossover occurs when MACD moves below its 9-day EMA. The Merrill Lynch (MER) chart below shows the 12-day EMA (thin blue line) with the 26-day EMA (thin red line) overlaid the price plot. MACD appears in the box below as the thick black line and its 9-day EMA is the thin blue line. The histogram represents the difference between MACD and its 9-day EMA. The histogram is positive when MACD is above its 9-day EMA and negative when MACD is below its 9-day EMA.

What Does MACD Do?

MACD measures the difference between two Exponential Moving Averages (EMAs). A positive MACD indicates that the 12-day EMA is trading above the 26-day EMA. A negative MACD indicates that the 12-day EMA is trading below the 26-day EMA. If MACD is positive and rising, then the gap between the 12-day EMA and the 26-day EMA is widening. This indicates that the rate-of-change of the faster moving average is higher than the rate-of-change for the slower moving average. Positive momentum is increasing, indicating a bullish period for the price plot. If MACD is negative and declining further, then the negative gap between the faster moving average (blue) and the slower moving average (red) is expanding. Downward momentum is accelerating, indicating a bearish period of trading. MACD centerline crossovers occur when the faster moving average crosses the slower moving average.

This Merrill Lynch (MER) chart shows MACD as a solid black line, and its 9-day EMA as the thin blue line. Even though moving averages are lagging indicators, notice that MACD moves faster than the moving averages. In this example, MACD provided a few good trading signals as well:

1. In March and April, MACD turned down ahead of both moving averages, and formed a negative divergence ahead of the price peak.
2. In May and June, MACD began to strengthen and make higher Lows while both moving averages continued to make lower Lows.
3. Finally, MACD formed a positive divergence in October while both moving averages recorded new Lows.

MACD Bullish Signals

MACD generates bullish signals from three main sources:

1. Positive Divergence
2. Bullish Moving Average Crossover
3. Bullish Centerline Crossover

Positive Divergence

A Positive Divergence occurs when MACD begins to advance and the security is still in a downtrend and makes a lower reaction low. MACD can either form as a series of higher Lows or a second Low that is higher than the previous Low. Positive Divergences are probably the least common of the three signals, but are usually the most reliable, and lead to the biggest moves.

Bullish Moving Average Crossover

A Bullish Moving Average Crossover occurs when MACD moves above its 9-day EMA, or trigger line. Bullish Moving Average Crossovers are probably the most common signals and as such are the least reliable. If not used in conjunction with other technical analysis tools, these crossovers can lead to whipsaws and many false signals. Bullish Moving Average Crossovers are used occasionally to confirm a positive divergence. A positive divergence can be considered valid when a Bullish Moving Average Crossover occurs after the MACD Line makes its second "higher Low".

Sometimes it is prudent to apply a price filter to the Bullish Moving Average Crossover to ensure that it will hold. An example of a price filter would be to buy if MACD breaks above the 9-day EMA and remains above for three days. The buy signal would then commence at the end of the third day.

Bullish Centerline Crossover

A Bullish Centerline Crossover occurs when MACD moves above the zero line and into positive territory. This is a clear indication that momentum has changed from negative to positive, or from bearish to bullish. After a Positive Divergence and Bullish Centerline Crossover, the Bullish Centerline Crossover can act as a confirmation signal. Of the three signals, moving average crossover are probably the second most common signals.(stockcharts.com)