Using a Combination of 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 9-day 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.

Bearish Signals

MACD generates bearish signals from three main sources. These signals are mirror reflections of the bullish signals:

1. Negative Divergence
2. Bearish Moving Average Crossover
3. Bearish Centerline Crossover

Negative Divergence

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 peak-and-trough 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 9-day EMA, or trigger line, it has not turned down and the lower High is difficult to confirm. When MACD breaks below its 9-day EMA, it signals that the short-term trend for the indicator is weakening, and a possible interim peak has formed.

Bearish Moving Average Crossover

The most common signal for MACD is the moving average crossover. A Bearish Moving Average Crossover occurs when MACD declines below its 9-day 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 9-day 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.

Bearish Centerline Crossover

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:

1. After the drop to trend line support, a Bearish Moving Average Crossover formed.
2. When the stock rebounded from the drop, MACD did not even break above the trigger line, indicating weak upside momentum.
3. The peak of the reaction rally was marked by a shooting star candlestick (blue arrow) and a gap down on increased volume (red arrows).
4. After the gap down, the blue trend line extending up from Apr, 1999, was broken.

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.

Combining Signals

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:

1. In December, a negative divergence formed in MACD.
2. Chaikin Money Flow turned negative on December 21.
3. Also in December, a Bearish Moving Average Crossover occurred in MACD (black arrow).
4. The trend line extending up from October was broken on 20 December.
5. A Bearish Centerline Crossover occurred in MACD on 10 Feb (green arrow).
6. On 15 February, support at 31 1/2 was violated (red arrow).

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.

MACD Benefits

One of the primary benefits of MACD is that it incorporates aspects of both momentum and trend in one indicator. As a trend-following 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 26-period 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.

MACD Drawbacks

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 MACD-Histogram.

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 long-term 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.

Pros and Cons of the MACD

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. (stockcharts.com)

MACD-Histogram

In 1986, Thomas Aspray developed the MACD-Histogram. 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 MACD-Histogram.

Definition and Construction

The MACD-Histogram represents the difference between the MACD and its trigger line, the 9-day 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 MACD-Histogram 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 9-day EMA, then the value on the MACD-Histogram will be positive. Conversely, if the value of MACD is less than its 9-day EMA, then the value on the MACD-Histogram will be negative.

Further increases or decreases in the gap between MACD and its trigger line will be reflected in the MACD-Histogram. Sharp increases in the MACD-Histogram indicate that MACD is rising faster than its 9-day EMA and bullish momentum is strengthening. Sharp declines in the MACD-Histogram indicate that MACD is falling faster than its 9-day EMA and bearish momentum is increasing.

On the chart above, we can see that the MACD-Histogram movements are relatively independent of the actual MACD. Sometimes the MACD is rising while the MACD-Histogram is falling. At other times, the MACD is falling while the MACD-Histogram is rising. The MACD-Histogram does not reflect the absolute value of the MACD, but rather the value of the MACD relative to its 9-day EMA. Usually, but not always, a move in the MACD is preceded by a corresponding divergence in the MACD-Histogram.

1. The first point shows a sharp positive divergence in the MACD-Histogram that preceded a Bullish Moving Average Crossover.
2. On the second point, the MACD continued to new Highs but the MACD-Histogram formed two equal Highs. Although not a textbook case of Positive Divergence, the equal High failed to confirm the strength seen in the MACD.
3. A Positive Divergence formed when the MACD-Histogram formed a higher Low and the MACD continued lower.
4. A Negative Divergence formed when the MACD-Histogram formed a lower High and the MACD continued higher.

Usage

Thomas Aspray designed the MACD-Histogram as a tool to anticipate a moving average crossover in the MACD. Divergences between MACD and the MACD-Histogram are the main tool used to anticipate moving average crossovers. A Positive Divergence in the MACD-Histogram indicates that the MACD is strengthening and could be on the verge of a Bullish Moving Average Crossover. A Negative Divergence in the MACD-Histogram 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 MACD-Histogram is in identifying periods when the gap between the MACD and its 9-day 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 MACD-Histogram will precede any changes in the MACD.

Signals

The main signal generated by the MACD-Histogram 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 crossover for the MACD-Histogram 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 peak-trough divergence.

Slant 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.

Peak-Trough Divergence

A peak-trough 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. Peak-trough Divergences usually cover a longer time frame than slant divergences. On a daily chart, a peak-trough 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 Peak-trough Divergences are a bit more reliable than Slant Divergences. Peak-trough Divergences tend to be sharper and cover a longer time frame than Slant Divergences.

MACD-Histogram Benefits

The main benefit of the MACD-Histogram is its ability to anticipate MACD signals. Divergences usually appear in the MACD-Histogram before MACD moving average crossovers do. Armed with this knowledge, traders and investors can better prepare for potential trend changes.

The MACD-Histogram 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 two-tiered approach to investing in order to avoid making trades against the major trend. The weekly MACD-Histogram can be used to generate a long-term signal in order to establish the tradable trend. Then only short-term signals that agree with the major trend would be considered.

After the trend has been established, MACD-Histogram divergences can be used to signal impending reversals. If the long-term trend was bullish, a negative divergences with bearish centerline crossovers would signal a possible reversal. If the long-term trend was bearish, traders would watch for a positive divergences with bullish centerline crossovers.

On the IBM weekly chart, the MACD-Histogram generated four signals. Before each moving average crossover in the MACD, a corresponding divergence formed in the MACD-Histogram. To make adjustments for the weekly chart, the moving averages have been shortened to 6 and 12. This MACD is formed by subtracting the 6-week EMA from the 12-week EMA. A 6-week EMA has been used as the trigger. The MACD-Histogram is calculated by taking the difference between MACD (6/12) and the 6-day EMA of MACD (6/12).

1. The first signal was a Bearish Moving Average Crossover in January, 1999. From its peak in late November, 1998, the MACD-Histogram formed a Negative Divergence that preceded the Bearish Moving Average Crossover in the MACD.
2. The second signal was a Bullish Moving Average Crossover in April. From its low in mid-February, the MACD-Histogram formed a Positive Divergence that preceded the Bullish Moving Average Crossover in the MACD.
3. The third signal was a Bearish Moving Average Crossover in late July. From its May peak, the MACD-Histogram formed a Negative Divergence that preceded a Bearish Moving Average Crossover in the MACD.
4. The final signal was a Bullish Moving Average Crossover, which was preceded by a slight Positive Divergence in the MACD-Histogram.

The third signal was based on a Peak-trough 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.

MACD-Histogram Drawbacks

The MACD-Histogram 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 MACD-Histogram is the second derivative of the price action of a security. As the second derivative, the MACD-Histogram 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 MACD-Histogram should not be compared directly with the price action of the underlying security.

Because MACD-Histogram was designed to anticipate MACD signals, there is a temptation to jump the gun. The MACD-Histogram 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.

MACD and SharpCharts

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 12-day EMA and 26-day EMA to calculate MACD and a 9-day EMA of MACD as the signal/trigger line. The Position drop-down menu determines where the indicator appears in relation to the price plot chart.

The MACD-Histogram, 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.

Introduction

Developed by George C. Lane in the late 1950s, the Stochastic Oscillator is a momentum indicator that shows the location of the current close relative to the high/low range over a set number of periods. Closing levels that are consistently near the top of the range indicate accumulation (buying pressure) and those near the bottom of the range indicate distribution (selling pressure).

Calculation

A 14-day %K (14-period Stochastic Oscillator) would use the most recent close, the highest high over the last 14 days and the lowest low over the last 14 days. The number of periods will vary according to the sensitivity and the type of signals desired. As with RSI, 14 is a popular number of periods for calculation.

%K tells us that the close (115.38) was in the 57th percentile of the high/low range, or just above the mid-point. Because %K is a percentage or ratio, it will fluctuate between 0 and 100. A 3-day simple moving average of %K is usually plotted alongside to act as a signal or trigger line, called %D.

Slow versus Fast versus Full

There are three types of Stochastic Oscillators: Fast, Slow, and Full. The Full Stochastic is discussed later. For now, let's look at Fast versus Slow. As shown above, the Fast Stochastic Oscillator is made up of %K and %D. In order to avoid confusion between the two, I'll use %K (fast) and %D (fast) to refer to those used in the Fast Stochastic Oscillator, and %K (slow) and %D (slow) to refer to those used in the Slow Stochastic Oscillator. The driving force behind both Stochastic Oscillators is %K (fast), which is found using the formula provided above.

In the CSCO example, the Fast Stochastic Oscillator is plotted in the box just below the price plot. The thick black line represents %K (fast) and the thin red line represents %D (fast). Also called the trigger line, %D (fast) is a smoothed version of %K (fast). One method of smoothing data is to apply a moving average. To smooth %K (fast) and create %D (fast), a 3-period simple moving average was applied to %K (fast). Notice how the %K (fast) line pierces the %D (fast) line a number of times during May, June and July. To alleviate some of these false breaks and smooth %K (fast), the Slow Stochastic Oscillator was developed.

The Slow Stochastic Oscillator is plotted in the lower box: the thick black line represents %K (slow) and the thin red line represents %D (slow). To find %K (slow) in the Slow Stochastic Oscillator, a 3-day SMA was applied to %K (fast). This 3-day SMA slowed (or smoothed) the data to form a slower version of %K (fast). A close examination would reveal that %D (Fast), the thin red line in the Fast Stochastic Oscillator, is identical to %K (Slow), the thick black line in the Slow Stochastic Oscillator. To form the trigger line, or %D (slow) in the Slow Stochastic Oscillator, a 3-day SMA was applied to %K (Slow).

The Full Stochastic Oscillator takes three parameters. Just as in the Fast and Slow versions, the first parameter is the number of periods used to create the initial %K line and the last parameter is the number of periods used to create the %D (full) signal line. What's new is the additional parameter, the one in the middle. It is a "smoothing factor" for the initial %K line. The %K (full) line that gets plotted is a n-period SMA of the initial %K line (where n is equal to the middle parameter).

The Full Stochastic Oscillator is more advanced and more flexible than it's Fast and Slow cousins. You can even use it to duplicate the other versions. For example, a (14, 3) Fast Stochastic is equivalent to a (14, 1, 3) Full Stochastic and a (12, 2) Slow Stochastic is equal to a (12, 3, 2) Full Stochastic.

%K and %D Recap

• %K (fast) = %K formula presented above using x periods
• %D (fast) = y-day SMA of %K (fast)
• %K (slow) = 3-day SMA of %K (fast)
• %D (slow) = y-day SMA of %K (slow)
• %K (full) = y-day SMA of %K (fast)
• %D (full) = z-day SMA of %K (full)

Where x is the first parameter, y is the second parameter and (in the case of Full stochastics), z is the third parameter. In the case of Fast and Slow Stochastics, x is typically 14 and y is usually set to 3.

Use

Readings below 20 are considered oversold and readings above 80 are considered overbought. However, Lane did not believe that a reading above 80 was necessarily bearish or a reading below 20 bullish. A security can continue to rise after the Stochastic Oscillator has reached 80 and continue to fall after the Stochastic Oscillator has reached 20. Lane believed that some of the best signals occurred when the oscillator moved from overbought territory back below 80 and from oversold territory back above 20.

Buy and sell signals can also be given when %K crosses above or below %D. However, crossover signals are quite frequent and can result in a lot of whipsaws.

One of the most reliable signals is to wait for a divergence to develop from overbought or oversold levels. Once the oscillator reaches overbought levels, wait for a negative divergence to develop and then a cross below 80. This usually requires a double dip below 80 and the second dip results in the sell signal. For a buy signal, wait for a positive divergence to develop after the indicator moves below 20. This will usually require a trader to disregard the first break above 20. After the positive divergence forms, the second break above 20 confirms the divergence and a buy signal is given.

Example

In the IBM example above, it is clear that acting solely on overbought and oversold crossovers can generate false signals. Using crossovers of %D (slow) by %K (slow) can result in some good signals, but there are still whipsaws. By looking for divergences and overbought/oversold crossovers together, the 14-day Slow Stochastic Oscillator can produce fewer yet more reliable signals. The Slow Stochastic Oscillator produced 2 solid signals in IBM between Aug-99 and Mar-00. In Nov-99, a buy signal was given when the indicator formed a positive divergence and moved above 20 for the second time. Note that the double top in Nov-Dec (gray circle) was not a negative divergence – the stock continued higher after this formed. In Jan-00, a sell signal was given when a negative divergence formed and the indicator dipped below 80 for the second time.

Stochastic Oscillators and SharpCharts

In StockCharts.com's SharpCharts tool, the Slow Stochastics oscillator uses %K (slow) and the Fast Stochastics oscillator uses %K (fast). There are two options available for both fast or slow. The first Parameters value represents the number of periods used to calculate %K for each. The second value represents the number of periods used in the moving average to form %D. The defaults are 14 and 3. For the Slow Stochastics oscillator, that would imply a 14-period %K (slow) with a 3-day SMA of %K (slow) to form %D (slow).

The Full Stochastics oscillator uses three parameters: the period for %K (fast), the period for the SMA that smooths %K (fast), and the period of the SMA that forms %D (full). While the tool provides some excellent default values, I encourage you to test different variations to discover what fits with their particular investing style or what works with a particular security....(stockcharts.com)

Introduction

The Price Oscillator is an indicator based on the difference between two moving averages, and is expressed as either a percentage or in absolute terms. The number of time periods can vary depending on user preference. For daily data, longer moving averages might be preferred to filter out some of the randomness associated with daily prices. For weekly data, which will have already filtered out some of the randomness, shorter moving averages may be deemed more appropriate. In addition, a moving average of the ensuing plot can be overlaid to act as a trigger line, much like is done with MACD. In our charts and commentary, we will use the abbreviation PPO to refer to the Percentage Price Oscillator and APO to refer to the Absolute Price Oscillator.

Absolute Price Oscillator (APO)

The Absolute Price Oscillator (APO) is calculated by subtracting the longer moving average from the shorter moving average. For example:

10-period exponential moving average (EMA) minus 30-period EMA

The resulting plot forms an oscillator that fluctuates above and below zero according to the differences in the moving averages. If the shorter moving average is above the longer moving average, then the indicator will be positive. If the shorter moving average is below the longer moving average, then the indicator will be negative.

The Moving Average Convergence Divergence (MACD) indicator calculated as the difference between two exponential moving averages and is essentially equivalent to the APO. StockCharts does not provide an indicator called "APO" in our SharpChart tool - you should use the MACD instead.

Percentage Price Oscillator (PPO)

The Percentage Price Oscillator is found by subtracting the longer moving average from the shorter moving average and then dividing the result by the longer moving average. For example:

(10-period EMA minus 30-period EMA) divided by the 30-period EMA

This formula displays the difference between the two moving averages as a percentage of the longer moving average.

Absolute versus Percentage

The Percentage Price Oscillator (PPO) and the Absolute Price Oscillator (APO) generate many of the same signals and have basically the same shape. All centerline crossovers, which represent the shorter moving average crossing above or below the longer moving average, occur at the same time. However, because the PPO is percentage-based, the shape of its lines can differ in subtle but important ways from the shape of the APO's lines. Below is a chart of the NASDAQ Composite that illustrates some of the differences that may crop up.

1. The green circle shows that the PPO formed a lower high in December while the APO formed a higher high.
2. Later in December, the APO continued higher and the PPO began to flatten out. (red arrows)
3. In early January, the PPO recorded a lower low, which was a day earlier than the APO.

There are two main reasons for using the PPO instead of the APO.

1. With the Percentage Price Oscillator, it is possible to compare Price Oscillator levels from one security to the next. A PPO reading of +5% means that the shorter moving average is 5% higher than the longer moving average. This percentage reading is comparable against another security, regardless of the price of a security. The Percentage Price Oscillator (PPO) for SLB only reached 3% for its highs while that of the NASDAQ Composite rose above 7%.

1. The Percentage Price Oscillator is a better representation of the two moving averages relative to each other. The difference between the two moving averages is shown in relation to the shorter moving average. This allows for comparisons across time periods, regardless of the price of the stock. With the Absolute Price Oscillator, the higher the price of the stock, the greater the extremes of the oscillator. With the Percentage Price Oscillator, a comparison of Amazon over time is possible regardless of whether the stock is at 10 or 100.

PPO-Histogram

Because the Price Oscillator and MACD are so similar, the concept of the MACD-Histogram has been applied to the PPO. The PPO-Histogram shows the difference between the PPO and the 9-day EMA of the PPO. The plot is presented as a histogram so that centerline crossovers and divergences are easily identifiable. The same principles that apply to the MACD-Histogram are also applicable to the PPO-Histogram.

A centerline crossover for the PPO-Histogram is the same as a moving average crossover for the PPO. If the value of the PPO is larger than the value of its 9-day EMA, then the value on the PPO-Histogram will be positive. Conversely, if the value of the PPO is less than its 9-day EMA, then the value of the PPO-Histogram will be negative.

Further increases or decreases in the gap between the PPO and its 9-day EMA will be reflected in the PPO-Histogram. Sharp increases in the PPO-Histogram indicate that the PPO is rising faster than its 9-day EMA – bullish momentum is strengthening. Sharp declines in the PPO-Histogram indicate that the PPO is falling faster than its moving average – bearish momentum is increasing.

PPO and SharpCharts

SharpCharts allows users to chart the Percentage Price Oscillator by selecting "Price Oscillator (PPO)" from any "Indicators" dropdown. The standard settings of "12,26,9" are automatically added to the "Parameters" box and can be changed to any combination of integer numbers. The first parameter is the number of periods to use for the first EMA in the calculation. The second parameter is the number of periods to use for the second (typically longer) EMA. The last parameter is the number of periods to use for the signal line.