What Is a Moving Average (MA)?

In finance, a moving average (MA) is a stock indicator commonly used in technical analysis. The reason for calculating the moving average of a stock is to help smooth out the price data by creating a constantly updated average price.

By calculating the moving average, the impacts of random, short-term fluctuations on the price of a stock over a specified time frame are mitigated. Simple moving averages (SMAs) use a simple arithmetic average of prices over some timespan, while exponential moving averages (EMAs) place greater weight on more recent prices than older ones over the time period.

Understanding a Moving Average (MA)

Moving averages are calculated to identify the trend direction of a stock or to determine its support and resistance levels. It is a trend-following or lagging, indicator because it is based on past prices.

The longer the period for the moving average, the greater the lag. A 200-day moving average will have a much greater degree of lag than a 20-day MA because it contains prices for the past 200 days. 50-day and 200-day moving average figures are widely followed by investors and traders and are considered to be important trading signals.

Investors may choose different periods of varying lengths to calculate moving averages based on their trading objectives. Shorter moving averages are typically used for short-term trading, while longer-term moving averages are more suited for long-term investors.

While it is impossible to predict the future movement of a specific stock, using technical analysis and research can help make better predictions. A rising moving average indicates that the security is in an uptrend, while a declining moving average indicates that it is in a downtrend.

Similarly, upward momentum is confirmed with a bullish crossover, which occurs when a short-term moving average crosses above a longer-term moving average. Conversely, downward momentum is confirmed with a bearish crossover, which occurs when a short-term moving average crosses below a longer-term moving average.

Types of Moving Averages

Simple Moving Average

A simple moving average (SMA), is calculated by taking the arithmetic mean of a given set of values over a specified period. A set of numbers, or prices of stocks, are added together and then divided by the number of prices in the set. The formula for calculating the simple moving average of a security is as follows:

$\begin{aligned} &SMA = \frac{ A_1 + A_2 + \dotso + A_n }{ n } \\ &\textbf{where:} \\ &A = \text{Average in period } n \\ &n = \text{Number of time periods} \\ \end{aligned}$​SMA=nA1​+A2​+…+An​​where:A=Average in period nn=Number of time periods​

Charting stock prices over 50 days using a simple moving average may look like this:

Exponential Moving Average (EMA)

The exponential moving average gives more weight to recent prices in an attempt to make them more responsive to new information. To calculate an EMA, the simple moving average (SMA) over a particular period is calculated first.

Then calculate the multiplier for weighting the EMA, known as the “smoothing factor,” which typically follows the formula: [2/(selected time period + 1)]. 

For a 20-day moving average, the multiplier would be [2/(20+1)]= 0.0952. The smoothing factor is combined with the previous EMA to arrive at the current value. The EMA thus gives a higher weighting to recent prices, while the SMA assigns an equal weighting to all values.

$\begin{aligned} &EMA_t = \left [ V_t \times \left ( \frac{ s }{ 1 + d } \right ) \right ] + EMA_y \times \left [ 1 – \left ( \frac { s }{ 1 + d} \right ) \right ] \\ &\textbf{where:}\\ &EMA_t = \text{EMA today} \\ &V_t = \text{Value today} \\ &EMA_y = \text{EMA yesterday} \\ &s = \text{Smoothing} \\ &d = \text{Number of days} \\ \end{aligned}$​EMAt​=[Vt​×(1+ds​)]+EMAy​×[1−(1+ds​)]where:EMAt​=EMA todayVt​=Value todayEMAy​=EMA yesterdays=Smoothingd=Number of days​

Simple Moving Average (SMA) vs. Exponential Moving Average (EMA)

The calculation for EMA puts more emphasis on the recent data points. Because of this, EMA is considered a weighted average calculation.

In the figure below, the number of periods used in each average is 15, but the EMA responds more quickly to the changing prices than the SMA. The EMA has a higher value when the price is rising than the SMA and it falls faster than the SMA when the price is declining. This responsiveness to price changes is the main reason why some traders prefer to use the EMA over the SMA.

Example of a Moving Average

The moving average is calculated differently depending on the type: SMA or EMA. Below, we look at a simple moving average (SMA) of a security with the following closing prices over 15 days:

• Week 1 (5 days): 20, 22, 24, 25, 23
• Week 2 (5 days): 26, 28, 26, 29, 27
• Week 3 (5 days): 28, 30, 27, 29, 28

A 10-day moving average would average out the closing prices for the first 10 days as the first data point. The next data point would drop the earliest price, add the price on day 11 and take the average.

Example of a Moving Average Indicator

A Bollinger Band® technical indicator has bands generally placed two standard deviations away from a simple moving average. In general, a move toward the upper band suggests the asset is becoming overbought, while a move close to the lower band suggests the asset is becoming oversold. Since standard deviation is used as a statistical measure of volatility, this indicator adjusts itself to market conditions.

The Bottom Line

A moving average (MA) is a stock indicator commonly used in technical analysis, used to help smooth out price data by creating a constantly updated average price. A rising moving average indicates that the security is in an uptrend, while a declining moving average indicates a downtrend. The exponential moving average is generally preferred to a simple moving average as it gives more weight to recent prices and shows a clearer response to new information and trends.

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.