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# MACD Indicator Explained, with Formula, Examples, and Limitations

## What Is Moving Average Convergence/Divergence (MACD)?

Moving average convergence/divergence (MACD, or MAC-D) is a trend-following momentum indicator that shows the relationship between two exponential moving averages (EMAs) of a security’s price. The MACD line is calculated by subtracting the 26-period EMA from the 12-period EMA.

The result of that calculation is the MACD line. A nine-day EMA of the MACD line is called the signal line, which is then plotted on top of the MACD line, which can function as a trigger for buy or sell signals. Traders may buy the security when the MACD line crosses above the signal line and sell—or short—the security when the MACD line crosses below the signal line. MACD indicators can be interpreted in several ways, but the more common methods are crossovers, divergences, and rapid rises/falls.

### Key Takeaways

• The moving average convergence/divergence (MACD, or MAC-D) line is calculated by subtracting the 26-period exponential moving average (EMA) from the 12-period EMA. The signal line is a nine-period EMA of the MACD line.
• MACD is best used with daily periods, where the traditional settings of 26/12/9 days is the norm.
• MACD triggers technical signals when the MACD line crosses above the signal line (to buy) or falls below it (to sell).
• MACD can help gauge whether a security is overbought or oversold, alerting traders to the strength of a directional move, and warning of a potential price reversal.
• MACD can also alert investors to bullish/bearish divergences (e.g., when a new high in price is not confirmed by a new high in MACD, and vice versa), suggesting a potential failure and reversal.
• After a signal line crossover, it is recommended to wait for three or four days to confirm that it is not a false move.
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## MACD Formula

$\text{MACD}=\text{12-Period EMA }-\text{ 26-Period EMA}$

MACD is calculated by subtracting the long-term EMA (26 periods) from the short-term EMA (12 periods). An EMA is a type of moving average (MA) that places a greater weight and significance on the most recent data points.

The exponential moving average is also referred to as the exponentially weighted moving average. An exponentially weighted moving average reacts more significantly to recent price changes than a simple moving average (SMA), which applies an equal weight to all observations in the period.

## Learning from MACD

MACD has a positive value (shown as the blue line in the lower chart) whenever the 12-period EMA (indicated by the red line on the price chart) is above the 26-period EMA (the blue line in the price chart) and a negative value when the 12-period EMA is below the 26-period EMA. The level of distance that MACD is above or below its baseline indicates that the distance between the two EMAs is growing.

In the following chart, you can see how the two EMAs applied to the price chart correspond to the MACD (blue) crossing above or below its baseline (red dashed) in the indicator below the price chart.

MACD is often displayed with a histogram (see the chart below) that graphs the distance between MACD and its signal line. If MACD is above the signal line, the histogram will be above the MACD’s baseline, or zero line. If MACD is below its signal line, the histogram will be below the MACD’s baseline. Traders use the MACD’s histogram to identify when bullish or bearish momentum is high—and possibly overbought/oversold.

## MACD vs. Relative Strength

The relative strength index (RSI) aims to signal whether a market is considered to be overbought or oversold in relation to recent price levels. The RSI is an oscillator that calculates average price gains and losses over a given period of time. The default time period is 14 periods with values bounded from 0 to 100. A reading above 70 suggests an overbought condition, while a reading below 30 is considered oversold, with both potentially signaling a top is forming, or vice versa (a bottom is forming).

The MACD lines, however, do not have concrete overbought/oversold levels like the RSI and other oscillator studies. Rather, they function on a relative basis. That’s to say an investor or trader should focus on the level and direction of the MACD/signal lines compared with preceding price movements in the security at hand, as shown below.

MACD measures the relationship between two EMAs, while the RSI measures price change in relation to recent price highs and lows. These two indicators are often used together to give analysts a more complete technical picture of a market.

These indicators both measure momentum in a market, but because they measure different factors, they sometimes give contrary indications. For example, the RSI may show a reading above 70 (overbought) for a sustained period of time, indicating a market is overextended to the buy side in relation to recent prices, while MACD indicates the market is still increasing in buying momentum. Either indicator may signal an upcoming trend change by showing divergence from price (price continues higher while the indicator turns lower, or vice versa).

## Limitations of MACD and Confirmation

One of the main problems with a moving average divergence is that it can often signal a possible reversal, but then no actual reversal happens—it produces a false positive. The other problem is that divergence doesn’t forecast all reversals. In other words, it predicts too many reversals that don’t occur and not enough real price reversals.

This suggests confirmation should be sought by trend-following indicators, such as the Directional Movement Index (DMI) system and its key component, the Average Directional Index (ADX). The ADX is designed to indicate whether a trend is in place or not, with a reading above 25 indicating a trend is in place (in either direction) and a reading below 20 suggesting no trend is in place.

Investors following MACD crossovers and divergences should double-check with the ADX before making a trade on an MACD signal. For example, while MACD may be showing a bearish divergence, a check of the ADX may tell you that a trend higher is in place—in which case you would avoid the bearish MACD trade signal and wait to see how the market develops over the next few days.

On the other hand, if MACD is showing a bearish crossover and the ADX is in non-trending territory (<25) and has likely shown a peak and reversal on its own, you could have good cause to take the bearish trade.

Furthermore, false positive divergences often occur when the price of an asset moves sideways in a consolidation, such as in a range or triangle pattern following a trend. A slowdown in the momentum—sideways movement or slow trending movement—of the price will cause MACD to pull away from its prior extremes and gravitate toward the zero lines even in the absence of a true reversal. Again, double-check the ADX and whether a trend is in place before acting.

## Example of MACD Crossovers

As shown on the following chart, when MACD falls below the signal line, it is a bearish signal indicating that it may be time to sell. Conversely, when MACD rises above the signal line, the indicator gives a bullish signal, suggesting that the price of the asset is likely to experience upward momentum. Some traders wait for a confirmed cross above the signal line before entering a position to reduce the chances of being faked out and entering a position too early.

Crossovers are more reliable when they conform to the prevailing trend. If MACD crosses above its signal line after a brief downside correction within a longer-term uptrend, it qualifies as a bullish confirmation and the likely continuation of the uptrend.

If MACD crosses below its signal line following a brief move higher within a longer-term downtrend, traders would consider that a bearish confirmation.

## Example of Divergence

When MACD forms highs or lows that that exceed the corresponding highs and lows on the price, it is called a divergence. A bullish divergence appears when MACD forms two rising lows that correspond with two falling lows on the price. This is a valid bullish signal when the long-term trend is still positive.

Some traders will look for bullish divergences even when the long-term trend is negative because they can signal a change in the trend, although this technique is less reliable.

When MACD forms a series of two falling highs that correspond with two rising highs on the price, a bearish divergence has been formed. A bearish divergence that appears during a long-term bearish trend is considered confirmation that the trend is likely to continue.

Some traders will watch for bearish divergences during long-term bullish trends because they can signal weakness in the trend. However, it is not as reliable as a bearish divergence during a bearish trend.

## Example of Rapid Rises or Falls

When MACD rises or falls rapidly (the shorter-term moving average pulls away from the longer-term moving average), it is a signal that the security is overbought or oversold and will soon return to normal levels. Traders will often combine this analysis with the RSI or other technical indicators to verify overbought or oversold conditions.

It is not uncommon for investors to use the MACD’s histogram the same way that they may use the MACD itself. Positive or negative crossovers, divergences, and rapid rises or falls can be identified on the histogram as well. Some experience is needed before deciding which is best in any given situation, because there are timing differences between signals on the MACD and its histogram.

## How do traders use moving average convergence/divergence (MACD)?

Traders use MACD to identify changes in the direction or strength of a stock’s price trend. MACD can seem complicated at first glance, because it relies on additional statistical concepts such as the exponential moving average (EMA). But fundamentally, MACD helps traders detect when the recent momentum in a stock’s price may signal a change in its underlying trend. This can help traders decide when to enter, add to, or exit a position.

## Is MACD a leading indicator or a lagging indicator?

MACD is a lagging indicator. After all, all the data used in MACD is based on the historical price action of the stock. Because it is based on historical data, it must necessarily lag the price. However, some traders use MACD histograms to predict when a change in trend will occur. For these traders, this aspect of MACD might be viewed as a leading indicator of future trend changes.

## What is an MACD bullish/bearish divergence?

A MACD positive (or bullish) divergence is a situation in which MACD does not reach a new low, despite the fact that the price of the stock reached a new low. This is seen as a bullish trading signal—hence, the term “positive/bullish divergence.” If the opposite scenario occurs—the stock price reaches a new high, but MACD fails to do so—this would be seen as a bearish indicator and termed “negative/bearish divergence.” In both cases, the setups suggest that the move higher/lower will not last, so it is important to look at other technical studies, like the relative strength index (RSI) discussed above.

## The Bottom Line

MACD is a valuable tool of the moving-average type, best used with daily data. Just as a crossover of the nine- and 14-day SMAs may generate a trading signal for some traders, a crossover of the MACD above or below its signal line may also generate a directional signal.

MACD is based on EMAs (more weight is placed on the most recent data), which means that it can react very quickly to changes of direction in the current price move. But that quickness can also be a two-edged sword. Crossovers of MACD lines should be noted, but confirmation should be sought from other technical signals, such as the RSI, or perhaps a few candlestick price charts. Further, because it is a lagging indicator, it argues that confirmation in subsequent price action should develop before taking the signal.

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