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 trendfollowing 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. The most popular formula for the “standard” MACD is the difference between a security’s 26day and 12day Exponential Moving Averages (EMAs). This is the formula that is used in many popular technical analysis programs, including SharpCharts, 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 12day EMA is the faster and the 26day EMA is the slower. Closing prices are used to form the moving averages. Usually, a 9day EMA of MACD is plotted along side to act as a trigger line. A bullish crossover occurs when MACD moves above its 9day EMA, and a bearish crossover occurs when MACD moves below its 9day EMA. The Merrill Lynch (MER) chart below shows the 12day EMA (thin blue line) with the 26day EMA (thin red line) overlaid the price plot. MACD appears in the box below as the thick black line and its 9day EMA is the thin blue line. The histogram represents the difference between MACD and its 9day EMA. The histogram is positive when MACD is above its 9day EMA and negative when MACD is below its 9day EMA. MACD measures the difference between two Exponential Moving Averages (EMAs). A positive MACD indicates that the 12day EMA is trading above the 26day EMA. A negative MACD indicates that the 12day EMA is trading below the 26day EMA. If MACD is positive and rising, then the gap between the 12day EMA and the 26day EMA is widening. This indicates that the rateofchange of the faster moving average is higher than the rateofchange 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 9day 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:
MACD generates bullish signals from three main sources:
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. A Bullish Moving Average Crossover occurs when MACD moves above its 9day 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 9day EMA and remains above for three days. The buy signal would then commence at the end of the third day. 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. Even though some traders may use only one of the above signals to form a buy or a sell signal, using a combination can generate more robust signals. In the Halliburton (HAL)example, all three bullish signals were present and the stock still advanced another 20%. The stock formed a lower Low at the end of February, but MACD formed a higher Low, thus creating a potential Positive Divergence. MACD then formed a Bullish Moving Average Crossover by moving above its 9day EMA. And finally, MACD traded above zero to form a Bullish Centerline Crossover. At the time of the Bullish Centerline Crossover, the stock was trading at 32 1/4 and went above 40 immediately after that. In August, the stock traded above 50.
MACD generates bearish signals from three main sources. These signals are mirror reflections of the bullish signals:
A Negative Divergence forms when the security advances or moves sideways, and the MACD declines. The Negative Divergence in MACD can take the form of either a lower High or a straight decline. Negative Divergences are probably the least common of the three signals, but are usually the most reliable, and can warn of an impending peak. The FedEx (FDX) chart shows a Negative Divergence when MACD formed a lower High in May, and the stock formed a higher High at the same time. This was a rather blatant Negative Divergence, and signaled that momentum was slowing. A few days later, the stock broke the uptrend line, and the MACD formed a lower Low. There are two possible means of confirming a Negative Divergence. First, the indicator can form a lower Low. This is traditional peakandtrough analysis applied to an indicator. With the lower High and subsequent lower Low, the uptrend for MACD has changed from bullish to bearish. Second, a Bearish Moving Average Crossover (which is explained below) can act to confirm a negative divergence. As long as MACD is trading above its 9day EMA, or trigger line, it has not turned down and the lower High is difficult to confirm. When MACD breaks below its 9day EMA, it signals that the shortterm trend for the indicator is weakening, and a possible interim peak has formed. The most common signal for MACD is the moving average crossover. A Bearish Moving Average Crossover occurs when MACD declines below its 9day EMA. Not only are these signals the most common, but they also produce the most false signals. As such, moving average crossovers should be confirmed with other signals to avoid whipsaws and false readings. Sometimes a stock can be in a strong uptrend, and MACD will remain above its trigger line for a sustained period of time. In this case, it is unlikely that a Negative Divergence will develop. A different signal is needed to identify a potential change in momentum. This was the case with Merck (MRK) in February and March. The stock advanced in a strong uptrend, and MACD remained above its 9day EMA for 7 weeks. When a Bearish Moving Average Crossover occurred, it signaled that upside momentum was slowing. This slowing momentum should have served as an alert to monitor the technical situation for further clues of weakness. Weakness was soon confirmed when the stock broke its uptrend line and MACD continued its decline and moved below zero. A Bearish Centerline Crossover occurs when MACD moves below zero and into negative territory. This is a clear indication that momentum has changed from positive to negative, or from bullish to bearish. The centerline crossover can act as an independent signal, or confirm a prior signal such as a moving average crossover or negative divergence. Once MACD crosses into negative territory, momentum, at least for the short term, has turned bearish. The significance of the centerline crossover will depend on the previous movements of MACD as well. If MACD is positive for many weeks, begins to trend down, and then crosses into negative territory, it would be bearish. However, if MACD has been negative for a few months, breaks above zero, and then back below, it might be a correction. In order to judge the significance of a centerline crossover, traditional technical analysis can be applied to see if there has been a change in trend, higher High or lower Low. The Unisys (UIS) chart depicts a Bearish Centerline Crossover that preceded a 25% drop in the stock that occurs just off the right edge of the chart. Although there was little time to act once this signal appeared, there were other warnings signs prior to the dramatic drop:
In addition to the signals mentioned above, a Bearish Centerline Crossover occurred after MACD had been above zero for almost two months. From 20 Sept on, MACD had been weakening and momentum was slowing. The break below zero acted as the final straw of a long weakening process. As with bullish MACD signals, bearish signals can be combined to create more robust signals. In most cases, stocks fall faster than they rise. This was definitely the case with Unisys (UIS), and only two bearish MACD signals were present. Using momentum indicators like MACD, technical analysis can sometimes provide clues to impending weakness. While it may be impossible to predict the length and duration of the decline, being able to spot weakness can enable traders to take a more defensive position. In 2002, Intel (INTC) dropped from above 36 to below 28 in a few months. Yet it would seem that smart money began distributing the stock before the actual decline. Looking at the technical picture, we can spot evidence of this distribution and a serious loss of momentum:
For those waiting for a recovery in the stock, the continued decline of momentum suggested that selling pressure was increasing, and not about to decrease. Hindsight is 20/20, but with careful study of past situations, we can learn how to better read the present and prepare for the future.
One of the primary benefits of MACD is that it incorporates aspects of both momentum and trend in one indicator. As a trendfollowing indicator, it will not be wrong for very long. The use of moving averages ensures that the indicator will eventually follow the movements of the underlying security. By using Exponential Moving Averages (EMAs), as opposed to Simple Moving Averages(SMAs), some of the lag has been taken out. As a momentum indicator, MACD has the ability to foreshadow moves in the underlying security. MACD divergences can be key factors in predicting a trend change. A Negative Divergence signals that bullish momentum is waning, and there could be a potential change in trend from bullish to bearish. This can serve as an alert for traders to take some profits in long positions, or for aggressive traders to consider initiating a short position. MACD can be applied to daily, weekly or monthly charts. MACD represents the convergence and divergence of two moving averages. The standard setting for MACD is the difference between the 12 and 26period EMA. However, any combination of moving averages can be used. The set of moving averages used in MACD can be tailored for each individual security. For weekly charts, a faster set of moving averages may be appropriate. For volatile stocks, slower moving averages may be needed to help smooth the data. Given that level of flexibility, each individual should adjust the MACD to suit his or her own trading style, objectives and risk tolerance. One of the beneficial aspects of the MACD is also one of its drawbacks. Moving averages, be they simple, exponential or weighted, are lagging indicators. Even though MACD represents the difference between two moving averages, there can still be some lag in the indicator itself. This is more likely to be the case with weekly charts than daily charts. One solution to this problem is the use of the MACDHistogram. MACD is not particularly good for identifying overbought and oversold levels. Even though it is possible to identify levels that historically represent overbought and oversold levels, MACD does not have any upper or lower limits to bind its movement. MACD can continue to overextend beyond historical extremes. MACD calculates the absolute difference between two moving averages and not the percentage difference. MACD is calculated by subtracting one moving average from the other. As a security increases in price, the difference (both positive and negative) between the two moving averages is destined to grow. This makes its difficult to compare MACD levels over a long period of time, especially for stocks that have grown exponentially. The Amazon (AMZN) chart demonstrates the difficult in comparing MACD levels over a long period of time. Before 1999, Amazon’s MACD is barely recognizable, and appears to trade close to the zero line. MACD was indeed quite volatile at the time, but this volatility has been dwarfed since the stock rose from below 20 to almost 100. An alternative is to use the Price Oscillator, which shows the percentage difference between two moving averages:
(12 day EMA – 26 day EMA) / (26 day EMA)
(20 – 18) / 18 = .11 or +11%
The resulting percentage difference can be compared over a longer period of time. On the Amazon chart, we can see that the Price Oscillator provides a better means for a longterm comparison. For the short term, MACD and the Price Oscillator are basically the same. The shape of the lines, the divergences, moving average crossovers and centerline crossovers for MACD and the Price Oscillator are virtually identical. Since Gerald Appel developed the MACD, there have been hundreds of new indicators introduced to technical analysis. While many indicators have come and gone, the MACD has stood the test of time. The concept behind its use is straightforward, and its construction is simple, yet it remains one of the most reliable indicators around. The effectiveness of the MACD will vary for different securities and markets. The lengths of the moving averages can be adapted for a better fit to a particular security or market. As with all indicators , MACD is not infallible and should be used in conjunction with other technical analysis tools. In 1986, Thomas Aspray developed the MACDHistogram. Some of his findings were presented in a series of articles for Technical Analysis of Stocks and Commodities. Aspray noted that MACD’s lag would sometimes miss important moves in a security, especially when applied to weekly charts. He first experimented by changing the moving averages and found that shorter moving averages did indeed speed up the signals. However, he was looking for a means to anticipate MACD crossovers. One of the answers he came up with was the MACDHistogram. The MACDHistogram represents the difference between the MACD and its trigger line, the 9day EMA of MACD. The plot of this difference is presented as a histogram, making centerline crossovers and divergences easily identifiable. A centerline crossover for the MACDHistogram is the same as a moving average crossover for MACD. If you will recall, a moving average crossover occurs when MACD moves above or below the trigger line. If the value of MACD is larger than the value of its 9day EMA, then the value on the MACDHistogram will be positive. Conversely, if the value of MACD is less than its 9day EMA, then the value on the MACDHistogram will be negative. Further increases or decreases in the gap between MACD and its trigger line will be reflected in the MACDHistogram. Sharp increases in the MACDHistogram indicate that MACD is rising faster than its 9day EMA and bullish momentum is strengthening. Sharp declines in the MACDHistogram indicate that MACD is falling faster than its 9day EMA and bearish momentum is increasing. On the chart above, we can see that the MACDHistogram movements are relatively independent of the actual MACD. Sometimes the MACD is rising while the MACDHistogram is falling. At other times, the MACD is falling while the MACDHistogram is rising. The MACDHistogram does not reflect the absolute value of the MACD, but rather the value of the MACD relative to its 9day EMA. Usually, but not always, a move in the MACD is preceded by a corresponding divergence in the MACDHistogram.
Thomas Aspray designed the MACDHistogram as a tool to anticipate a moving average crossover in the MACD. Divergences between MACD and the MACDHistogram are the main tool used to anticipate moving average crossovers. A Positive Divergence in the MACDHistogram indicates that the MACD is strengthening and could be on the verge of a Bullish Moving Average Crossover. A Negative Divergence in the MACDHistogram indicates that the MACD is weakening, and it foreshadows a Bearish Moving Average Crossover in the MACD. In his book, Technical Analysis of the Financial Markets, John Murphy asserts that the best use for the MACDHistogram is in identifying periods when the gap between the MACD and its 9day EMA is either widening or shrinking. Broadly speaking, a widening gap indicates strengthening momentum and a shrinking gap indicates weakening momentum. Usually a change in the MACDHistogram will precede any changes in the MACD. The main signal generated by the MACDHistogram is a divergence followed by a moving average crossover. A bullish signal is generated when a Positive Divergence forms and there is a Bullish Centerline Crossover. A bearish signal is generated when there is a Negative Divergence and a Bearish Centerline Crossover. Keep in mind that a centerline crossoverfor the MACDHistogram represents a moving average crossover for the MACD. Divergences can take many forms and varying degrees. Generally speaking, two types of divergences have been identified: the slant divergence and the peaktrough divergence. A Slant Divergence forms when there is a continuous and relatively smooth move in one direction (up or down) to form the divergence. Slant Divergences generally cover a shorter time frame than divergences formed with two peaks or two troughs. A Slant Divergence can contain some small bumps (peaks or troughs) along the way. The world of technical analysis is not perfect and there are exceptions to most rules and hybrids for many signals. A peaktrough divergence occurs when at least two peaks or two troughs develop in one direction to form the divergence. A series of two or more rising troughs (higher lows) can form a Positive Divergence and a series of two or more declining peaks (lower highs) can form a Negative Divergence. Peaktrough Divergences usually cover a longer time frame than slant divergences. On a daily chart, a peaktrough divergence can cover a time frame as short as two weeks or as long as several months. Usually, the longer and sharper the divergence is, the better any ensuing signal will be. Short and shallow divergences can lead to false signals and whipsaws. In addition, it would appear that Peaktrough Divergences are a bit more reliable than Slant Divergences. Peaktrough Divergences tend to be sharper and cover a longer time frame than Slant Divergences. The main benefit of the MACDHistogram is its ability to anticipate MACD signals. Divergences usually appear in the MACDHistogram before MACD moving average crossovers do. Armed with this knowledge, traders and investors can better prepare for potential trend changes. The MACDHistogram can be applied to daily, weekly or monthly charts. (Note: This may require some tinkering with the number of periods used to form the original MACD; shorter or faster moving averages might be necessary for weekly and monthly charts.) Using weekly charts, the broad underlying trend of a stock can be determined. Once the broad trend has been determined, daily charts can be used to time entry and exit strategies. In Technical Analysis of the Financial Markets, John Murphy advocates this type of twotiered approach to investing in order to avoid making trades against the major trend. The weekly MACDHistogram can be used to generate a longterm signal in order to establish the tradable trend. Then only shortterm signals that agree with the major trend would be considered. After the trend has been established, MACDHistogram divergences can be used to signal impending reversals. If the longterm trend was bullish, a negative divergences with bearish centerline crossovers would signal a possible reversal. If the longterm trend was bearish, traders would watch for a positive divergences with bullish centerline crossovers. On the IBM weekly chart, the MACDHistogram generated four signals. Before each moving average crossover in the MACD, a corresponding divergence formed in the MACDHistogram. To make adjustments for the weekly chart, the moving averages have been shortened to 6 and 12. This MACD is formed by subtracting the 6week EMA from the 12week EMA. A 6week EMA has been used as the trigger. The MACDHistogram is calculated by taking the difference between MACD (6/12) and the 6day EMA of MACD (6/12).
The third signal was based on a Peaktrough Divergence Two readily identifiable and consecutive lower peaks formed to create the divergence. The peaks and troughs on the previous divergences, although identifiable, do not stand out as much. The MACDHistogram is an indicator of an indicator or a derivative of a derivative. The MACD is the first derivative of the price action of a security, and the MACDHistogram is the second derivative of the price action of a security. As the second derivative, the MACDHistogram is further removed from the actual price action of the underlying security. The further removed an indicator is from the underlying price action, the greater the chances of false signals. Keep in mind that this is an indicator of an indicator. The MACDHistogram should not be compared directly with the price action of the underlying security. Because MACDHistogram was designed to anticipate MACD signals, there is a temptation to jump the gun. The MACDHistogram should be used in conjunction with other aspects of technical analysis. This will help to alleviate the temptation for early entry. Another means to guard against early entry is to combine weekly signals with daily signals. Of course, there will be more daily signals than weekly signals. However, by using only the daily signals that agree with the weekly signals, there will be fewer daily signals to act on. By acting only on those daily signals that are in agreement with the weekly signals, you are also assured of trading with the longer trend and not against it. Be careful of small and shallow divergences. While these may sometimes lead to good signals, they are also more apt to create false signals. One method to avoid small divergences is to look for larger divergences with two or more readily identifiable peaks or troughs. Compare the peaks and troughs from past action to determine significance. Only peaks and troughs that appear to be significant should warrant attention. Using SharpCharts, the MACD can be set as an indicator above or below or behind a security’s price plot. Once the indicator is chosen from the drop down list, the Parameters text box to the right is used to adjust the settings. The default setting is “12,26,9,” which automatically appears. The MACD created would be calculated using a 12day EMA and 26day EMA to calculate MACD and a 9day EMA of MACD as the signal/trigger line. The Position dropdown menu determines where the indicator appears in relation to the price plot chart. The MACDHistogram, which measures the difference between the MACD and its signal/trigger line, shows the MACD’s settings in the Parameter text box to its right. It, too, can be displayed above, below, or behind the price plot window.

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