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.

MACD Formula

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

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.

What Is the Ichimoku Cloud?

The Ichimoku Cloud is a collection of technical indicators that show support and resistance levels, as well as momentum and trend direction. It does this by taking multiple averages and plotting them on a chart. It also uses these figures to compute a “cloud” that attempts to forecast where the price may find support or resistance in the future.

The Ichimoku Cloud was developed by Goichi Hosoda, a Japanese journalist, and published in the late 1960s. It provides more data points than the standard candlestick chart. While it seems complicated at first glance, those familiar with how to read the charts often find it easy to understand with well-defined trading signals.

The Formulas for the Ichimoku Cloud

The following are the five formulas for the lines that comprise the Ichimoku Cloud indicator.

$\begin{aligned}&\text{Conversion Line (tenkan sen)} = \frac {\text{9-PH} + \text{9-PL}}{2} \\&\text{Base Line (kijun sen)} = \frac{\text{26-PH + 26-PL}}{2} \\&\text{Leading Span A (senkou span A)} = \frac{\text{CL + Base Line}}{2} \\&\text{Leading Span B (senkou span B)}= \frac{\text{52-PH + 52-PL}}{2} \\&\text{Lagging Span (chikou span)} = \text{Close plotted 26 periods} \\&\phantom{\text{Lagging Span (chikou span)} =} \text{in the past} \\&\textbf{where:} \\&\text{PH} = \text{Period high} \\&\text{PL} = \text{Period low} \\&\text{CL} = \text{Conversion line}\end{aligned}$​Conversion Line (tenkan sen)=29-PH+9-PL​Base Line (kijun sen)=226-PH + 26-PL​Leading Span A (senkou span A)=2CL + Base Line​Leading Span B (senkou span B)=252-PH + 52-PL​Lagging Span (chikou span)=Close plotted 26 periodsLagging Span (chikou span)=in the pastwhere:PH=Period highPL=Period lowCL=Conversion line​

How to Calculate the Ichimoku Cloud

The highs and lows are the highest and lowest prices seen during the period—for example, the highest and lowest prices seen over the last nine days in the case of the conversion line. Adding the Ichimoku Cloud indicator to your chart will do the calculations for you, but if you want to calculate it by hand, here are the steps:

1. Calculate the Conversion Line and the Base Line.
2. Calculate Leading Span A based on the prior calculations. Once calculated, this data point is plotted 26 periods into the future.
3. Calculate Leading Span B. Plot this data point 26 periods into the future.
4. For the Lagging Span, plot the closing price 26 periods into the past on the chart.
5. The difference between Leading Span A and Leading Span B is colored in to create the cloud.
6. When Leading Span A is above Leading Span B, color the cloud green. When Leading Span A is below Leading Span B, color the cloud red.
7. The above steps will create one data point. To create the lines, as each period comes to an end, go through the steps again to create new data points for that period. Connect the data points to each other to create the lines and cloud appearance.

What Does the Ichimoku Cloud Tell You?

The technical indicator shows relevant information at a glance by using averages.

The overall trend is up when the price is above the cloud, down when the price is below the cloud, and trendless or transitioning when the price is in the cloud.

When Leading Span A is rising and above Leading Span B, this helps to confirm the uptrend and the space between the lines is typically colored green. When Leading Span A is falling and below Leading Span B, this helps confirm the downtrend. The space between the lines is typically colored red in this case.

Traders will often use the Ichimoku Cloud as an area of support and resistance depending on the relative location of the price. The cloud provides support/resistance levels that can be projected into the future. This sets the Ichimoku Cloud apart from many other technical indicators that only provide support and resistance levels for the current date and time.

Traders should use the Ichimoku Cloud in conjunction with other technical indicators to maximize their risk-adjusted returns. For example, the indicator is often paired with the relative strength index (RSI), which can be used to confirm momentum in a certain direction. It’s also important to look at the bigger trends to see how the smaller trends fit within them. For example, during a very strong downtrend, the price may push into the cloud or slightly above it, temporarily, before falling again. Only focusing on the indicator would mean missing the bigger picture that the price was under strong longer-term selling pressure.

Crossovers are another way that the indicator can be used. Watch for the conversion line to move above the base line, especially when the price is above the cloud. This can be a powerful buy signal. One option is to hold the trade until the conversion line drops back below the base line. Any of the other lines could be used as exit points as well.

The Difference Between the Ichimoku Cloud and Moving Averages

While the Ichimoku Cloud uses averages, they are different than a typical moving average. Simple moving averages take closing prices, add them up, and divide that total by how many closing prices there are. In a 10-period moving average, the closing prices for the last 10 periods are added, then divided by 10 to get the average.

Notice how the calculations for the Ichimoku Cloud are different. They are based on highs and lows over a period and then divided by two. Therefore, Ichimoku averages will be different than traditional moving averages, even if the same number of periods are used.

One indicator is not better than another; they just provide information in different ways.

Limitations of Using the Ichimoku Cloud

The indicator can make a chart look busy with all the lines. To remedy this, most charting software allows certain lines to be hidden. For example, all of the lines can be hidden except for Leading Span A and Leading Span B, which create the cloud. Each trader needs to focus on which lines provide the most information, then consider hiding the rest if all of the lines are distracting.

Another limitation of the Ichimoku Cloud is that it is based on historical data. While two of these data points are plotted in the future, there is nothing in the formula that is inherently predictive. Averages are simply being plotted in the future.

The cloud can also become irrelevant for long periods of time, as the price remains way above or way below it. At times like these, the conversion line, the base line, and their crossovers become more important, as they generally stick closer to the price.

The Bottom Line

In order to create a “cloud” to show where prices may find future resistance or support, the Ichimoku Cloud plots multiple averages on a chart. This shows not only support and resistance but also trend direction and momentum, all of which appear as a group of technical indicators. While there are some limitations to the Ichimoku Cloud, it is neither better nor worse than existing technical indicators such as moving averages. It simply represents information in a different way.

What Is the Head and Shoulders Pattern?

A head and shoulders pattern is used in technical analysis. It is a specific chart formation that predicts a bullish-to-bearish trend reversal. The pattern appears as a baseline with three peaks, where the outside two are close in height, and the middle is highest.

The head and shoulders pattern forms when a stock’s price rises to a peak and then declines back to the base of the prior up-move. Then, the price rises above the previous peak to form the “head” and then declines back to the original base. Finally, the stock price peaks again at about the level of the first peak of the formation before falling back down.

The head and shoulders pattern is considered one of the most reliable trend reversal patterns. It is one of several top patterns that signal, with varying degrees of accuracy, that an upward trend is nearing its end.

Understanding the Head and Shoulders Pattern

A head and shoulders pattern has four components:

1. After long bullish trends, the price rises to a peak and subsequently declines to form a trough.
2. The price rises again to form a second high substantially above the initial peak and declines again.
3. The price rises a third time, but only to the first peak level, before declining again.
4. The neckline, drawn at the two troughs or peaks (inverse).

The first and third peaks are the shoulders, and the second peak forms the head. The line connecting the first and second troughs is called the neckline.

Inverse Head and Shoulders

The opposite of a head and shoulders chart is the inverse head and shoulders, also called a head and shoulders bottom. It is inverted with the head and shoulders bottoms used to predict reversals in downtrends. This pattern is identified when the price action of a security meets the following characteristics:

• The price falls to a trough, then rises
• The price falls below the former trough, then rises again
• The price falls again but not as far as the second trough
• Once the final trough is made, the price heads upward toward the resistance (the neckline) found near the top of the previous troughs.

Of these, the second trough is the lowest (the head), and the first and third are slightly shallower (the shoulders). The final rally after the third dip signals that the bearish trend has reversed, and prices are likely to keep rallying upward.

What Does the Head and Shoulders Pattern Tell You?

The head and shoulders pattern indicates that a reversal is possible. Traders believe that three sets of peaks and troughs, with a larger peak in the middle, means a stock’s price will begin falling. The neckline represents the point at which bearish traders start selling.

The pattern also indicates that the new downward trend will likely continue until the right shoulder is broken—where prices move higher than the prices at the right peak.

Advantages and Disadvantages of the Head and Shoulders Pattern

Advantages Explained

• Experienced traders identify it easily: The pattern is very recognizable to an experienced trader.
• Defined profit and risk: Short and long entry levels and stop distance can be clearly defined with confirmation openings and closings.
• Big market movements can be profited from: The timeframe for a head and shoulders pattern is fairly long, so a market can move significantly from entry to close price.
• Can be used in all markets: The pattern can be used in forex and stock trading.

Disadvantages Explained

• Novice traders might miss it: The head and shoulders pattern may not present with a flat neckline; it may be skewed, which can throw off new traders.
• Large stop loss distances possible: Large downward movement over long timeframes can result in a large stop distance.
• Neckline can appear to move: If the price pulls back, the neckline might be retested, confusing some traders.

The Bottom Line

The head and shoulders is a pattern used by traders to identify price reversals. A bearish head and shouders has three peaks, with the middle one reaching higher than the other two. It indicates a reversal of an upward trend.

A bullish head and shoulders has three troughs, with the middle one reaching lower than the other two. It indicates a reversal of a downward trend.

What Are Fibonacci Retracement Levels?

Fibonacci retracement levels—stemming from the Fibonacci sequence—are horizontal lines that indicate where support and resistance are likely to occur.

Each level is associated with a percentage. The percentage is how much of a prior move the price has retraced. The Fibonacci retracement levels are 23.6%, 38.2%, 61.8%, and 78.6%. While not officially a Fibonacci ratio, 50% is also used.

The indicator is useful because it can be drawn between any two significant price points, such as a high and a low. The indicator will then create the levels between those two points.

Suppose the price of a stock rises $10 and then drops $2.36. In that case, it has retraced 23.6%, which is a Fibonacci number. Fibonacci numbers are found throughout nature. Therefore, many traders believe that these numbers also have relevance in financial markets.

Fibonacci retracement levels were named after Italian mathematician Leonardo Pisano Bigollo, who was famously known as Leonardo Fibonacci.  However, Fibonacci did not create the Fibonacci sequence. Instead, Fibonacci introduced these numbers to western Europe after learning about them from Indian merchants. Fibonacci retracement levels were formulated in ancient India between 450 and 200 BCE.

Numbers First Formulated in Ancient India

Despite its name, the Fibonacci sequence was not developed by its namesake. Instead, centuries before Leonardo Fibonacci shared it with western Europe, it was developed and used by Indian mathematicians.

Most notably, Indian mathematician Acarya Virahanka is known to have developed Fibonacci numbers and the method of their sequencing around 600 A.D. Following Virahanka’s discovery, other subsequent generations of Indian mathematicians—Gopala, Hemacandra, and Narayana Pandita—referenced the numbers and method. Pandita expanded its use by drawing a correlation between the Fibonacci numbers and multinomial co-efficients.

It is estimated that Fibonacci numbers existed in Indian society as early as 200 B.C.

The Formula for Fibonacci Retracement Levels

Fibonacci retracement levels do not have formulas. When these indicators are applied to a chart, the user chooses two points. Once those two points are chosen, the lines are drawn at percentages of that move.

Suppose the price rises from $10 to $15, and these two price levels are the points used to draw the retracement indicator. Then, the 23.6% level will be at $13.82 ($15 – ($5 × 0.236) = $13.82). The 50% level will be at $12.50 ($15 – ($5 × 0.5) = $12.50).

How to Calculate Fibonacci Retracement Levels

As discussed above, there is nothing to calculate when it comes to Fibonacci retracement levels. They are simply percentages of whatever price range is chosen.

However, the origin of the Fibonacci numbers is fascinating. They are based on something called the Golden Ratio. Start a sequence of numbers with zero and one. Then, keep adding the prior two numbers to get a number string like this:

• 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987…with the string continuing indefinitely.

The Fibonacci retracement levels are all derived from this number string. After the sequence gets going, dividing one number by the next number yields 0.618, or 61.8%. Divide a number by the second number to its right, and the result is 0.382 or 38.2%. All the ratios, except for 50% (since it is not an official Fibonacci number), are based on some mathematical calculation involving this number string.

Interestingly, the Golden Ratio of 0.618 or 1.618 is found in sunflowers, galaxy formations, shells, historical artifacts, and architecture.

What Do Fibonacci Retracement Levels Tell You?

Fibonacci retracements can be used to place entry orders, determine stop-loss levels, or set price targets. For example, a trader may see a stock moving higher. After a move up, it retraces to the 61.8% level. Then, it starts to go up again. Since the bounce occurred at a Fibonacci level during an uptrend, the trader decides to buy. The trader might set a stop loss at the 61.8% level, as a return below that level could indicate that the rally has failed.

Fibonacci levels also arise in other ways within technical analysis. For example, they are prevalent in Gartley patterns and Elliott Wave theory. After a significant price movement up or down, these forms of technical analysis find that reversals tend to occur close to certain Fibonacci levels.

Fibonacci retracement levels are static, unlike moving averages. The static nature of the price levels allows for quick and easy identification. That helps traders and investors to anticipate and react prudently when the price levels are tested. These levels are inflection points where some type of price action is expected, either a reversal or a break.

Fibonacci Retracements vs. Fibonacci Extensions

While Fibonacci retracements apply percentages to a pullback, Fibonacci extensions apply percentages to a move in the trending direction. For example, a stock goes from $5 to $10, then back to $7.50. The move from $10 to $7.50 is a retracement. If the price starts rallying again and goes to $16, that is an extension.

Limitations of Using Fibonacci Retracement Levels

While the retracement levels indicate where the price might find support or resistance, there are no assurances that the price will actually stop there. This is why other confirmation signals are often used, such as the price starting to bounce off the level.

The other argument against Fibonacci retracement levels is that there are so many of them that the price is likely to reverse near one of them quite often. The problem is that traders struggle to know which one will be useful at any particular time. When it doesn’t work out, it can always be claimed that the trader should have been looking at another Fibonacci retracement level instead.

The Bottom Line

Fibonacci retracements are useful tools that help traders identify support and resistance levels. With the information gathered, traders can place orders, identify stop-loss levels, and set price targets. Although Fibonacci retracements are useful, traders often use other indicators to make more accurate assessments of trends and make better trading decisions.