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Description: most popular indicators in technical analysis, basics of technical analysis, formula, calculations, chart example, how to use and how to generate signals.


In technical analysis the MACD (Moving Average Convergence/Divergence) is a indicator that shows the relationship between two moving averages. It was first implemented by Gerald Appel in 1970s and later in 1986 MACD Histogram was added to MACD by Thomas Aspray.

The MACD is simple and reliable. It is calculated as a difference between the fast and slow moving averages. The historically popular is the difference between a security's 26-day and 12-day Exponential Moving Averages (EMAs). However, the MACD setting may greatly differ from a stock to stock and from a timeframe to a timeframe. Different moving averages (simple, exponential, weighted and etc.) could be used as well.

MACD is an oscillator and is plotted as a line that moves above and below zero line (center line). On index and stock charts, MACD consists of three lines - MACD itself, exponential moving average applied to MACD and used as a signal line and MACD Histogram. The MACD-Histogram represents the difference between the MACD and its signals line (EMA). If the value of MACD is larger than the value of its EMA signal, then the value on the MACD-Histogram will be positive. Conversely, if the value of MACD is less than its EMA signal, then the value on the MACD-Histogram will be negative. The MACD histogram makes centerline crossovers and divergences more easily identifiable. On the Nasdaq 100 chart below you may see an example of MACD.

Chart 1: MACD (Moving Average Convergence/Divergence)

MACD Chart

You have to understand that MACD is lagging indicator and the lag depends on the bar period setting. The lag could be reduced by selecting smaller MACD's bar period setting, yet MACD line will become choppier. Controversially, MACD's bar period setting could be increase to make MACD line smoother which will increase the lag. The art of technical analysis is to find setting that would satisfy you need.

Technical Analysis, Signals, Trading Systems

By measuring the difference between two Exponential Moving Averages (EMAs), MACD can be positive or negative. A positive MACD indicates that the Fast EMA is trending above the Slow EMA, indicating a bullish period. A negative MACD indicates that the fast EMA is trending below the slow EMA, indicating a bearish period. When the faster moving average crosses the slower moving average - MACD crosses over centerline.

The basic mechanics behind MACD is comparison of two moving averages. Fast MA (MA with smaller bar period setting) reacts faster on the changes in price by reflecting smaller shorter-term trends while Slow MA (MA with bigger bar period settings) has bigger lag and reveals longer-term trend. Since Fast MA reacts on the price move faster, during an up-trend it rises faster than the Slow MA and during a down-trend it slides down faster than the Slow MA. Basically, MACD compares shorter-term trend to the longer-term trend. Shorter-term trend (Fast MA) may move up and down, yet, while it fluctuates above Slow MA (MACD > 0) it is a sign of a longer-term bullish trend (trend defined by Slow MA). Respectfully, as long as Fast MA fluctuates below Slow MA (MACD < 0) the trend defined by Slow MA is considered bearish.

At the moment when Fast MA drops below Slow MA (MACD crosses zero line after being above it) a technical analyst would say that the short-term trend defined by fast moving average moved down strongly and deeply enough to consider changes in the trend defined by Slow MA. Here, based on the historical observations technical analysis assumes that the odds of further slide down are higher. Controversially, when MACD becomes positive after being negative (Fast MA raises above Slow MA) technical analysis assumes that the odds are high the recent up-move could be a beginning of an up-trend.

A simple trading system based on MACD would tell to:

  • Sell when MACD drops below 0 (zero) - becomes negative after being positive,
  • Buy when MACD raises above 0 (zero) - becomes positive after being negative.

On the S&P 500 chart below (chart #2) you may see an example of this simple trading system.

Chart #2: S&P 500 index and signals based on crossovers of MACD and zero line

S&P 500 charts and MACD signals

In similar to the described above way, MACD Signal line (EMA applied to MACD) reacts with bigger than MACD lag on changes in a trend. In the same way, crossovers of MACD and its signal line could be used to generate signals. Since MACD Histogram represent the difference between MACD and its signal line, MACD and its signal line crossovers are equivalent to the crossovers of MACD Histogram and 0 (zero) line. In this case technical analysis would tell to

  • Sell when MACD Histogram becomes negative  - drops below zero line,
  • Buy when MACD Histogram becomes positive - raises above zero line.

On the DJI (Dow Jones Industrials) index chart below (chart #3) you may see an example of generating trading signals on crossovers of MACD Histogram and zero center line.

Chart #3: DJI index and signals based on crossovers of MACD Histogram and zero line

DJI charts and MACD Histogram signals

Important: MACD is based on the moving averages and it is a lagging indicator. It follows the trend rather than predicting it. It is still a good indicator, yet, if it is does not react on the price trend's reversal as you would expect, then you may consider changing this indicator's bar period setting. During the periods of high volatility price makes trend changes faster and stronger. In periods of low volatility price tends to change its trend slower. Respectfully it should be logical to use different MACD settings for different periods of volatility. That is why it is highly recommended monitoring volatility when MACD is used to generated trading signals. ATR (Average True Rage) is one of the most used technical indicators to track volatility level.

There are two ways of adjusting MACD to volatility. As a rule during longer-term down-trends (on higher time-frames) when analyzed stock (index or ETF) becomes highly volatile, a trader may prefer to increase MACD's bar period in order to avoid strong fluctuations and choppy trading. On the other hand, during the same longer-term down-trends when volatility is high, on smaller intraday timeframes, another trader could be willing to cache these small fluctuations in order to benefit from strong swings. In this case this trader could be considering reducing MACD's bar period setting.

As was already mentioned above, MACD is a lagging indicator, however, there is a way to use it as a leading indicator to predict future trend reversals. In many cases technical analysis is looking for a divergence between an indicator and a stock (index, ETF) price movements. This method of analysis has become quite popular and my traders and analysts use MACD for this. Technical analysis would say to:

  • Expect a trend reversal down in the near future when negative divergence is noted - price makes new highs, yet, MACD fails to make a new high,
  • Expect a trend reversal up in the near future when positive divergence is noted - price drops to a new low, yet, MACD fails to make a new low.

On the DJI chart below (chart #4) you may see an illustration of the negative divergence with further trend reversal down and on the other DJI chart (chart #5) you may see an example of positive divergence with following trend reversal up.

Chart #4: DJI index and negative divergence of price and MACD Histogram

DJI charts - negative divergence of price and MACD Histogram

Chart #5: DJI index and positive divergence of price and MACD Histogram

DJI charts - positive divergence of price and MACD Histogram

In technical analysis also is looking for divergence between MACD and other technical indicators. It becomes more and more popular to compare MACD and Stochastics trends, to compare MACD and RSI (Relative Strength Index) trends and etc.

MACD Formula and Calculations

MACD consist of three components: MACD line, MACD Signal Line and MACD Histogram:

MACD = Fast Moving Average - Slow Moving Average

MACD Signal = EMA (MACD)

MACD Histogram= MACD - MACD Signal

Victor Kalitowski

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