The Moving Average (MA) is a widely used indicator in technical analysis that helps smooth out price action by filtering out the “Noise” from random price fluctuations.

While moving average information is typically included in trading summary tables (see table: 50-day MA, 200-day MA), the most common way to get a thorough understanding of the trading opportunities is to analyze the charts.

Let’s review the line chart below. Do you see how the blue line has a lot of volatility?

The objective of using the moving average is to smooth out this volatility so we can better see the broader trends. The red line, which is the 100-day moving average, smooths out the trend and depicts a gradual upward slope of the stock price through time.

A moving average (MA) is a trend-following or lagging indicator, because it is based on past prices. For example, each point on the red line represents a simple average of the past 100 data points.

The longer the moving average time frame, the smoother the curve. A 100-day moving average, as shown above, is considered a long-term moving average and that is why much of the volatility is eliminated from the red line.

There are two types of moving average calculations which we will discuss, the Simple Moving Average and the Exponential Moving Average:

1) Simple Moving Average, also called SMA or MA, is just the simple average of the closing price of a security over a defined number of time periods (days, weeks, months, or years).

One common analysis is to fit a moving average curve to the price trend such that we can see the price barriers which prevent a stock from moving too high or too low.

These barriers are called support and resistance.

Support is the price level through which a stock rarely falls.

Resistance is the price level that a stock rarely goes above.

For example, a 10-day MA for Apple smooths out the daily prices, fits nicely to the trend line, and allows us to see the support and resistance levels:

The 10-day MA props up the prices in an uptrend and acts as a resistance in a downtrend. Why is this important? What does it signify?

The price of a security is based on supply from sellers and demand from buyers.

In the market, there is always a tension between supply and demand, such that the prices of a stock rarely move above (resistance) or below (support).

If the security breaks trend, we know that there has been a shift in the psychology of the market. Understanding this gives us an advantage of strategic entry and exit points.

Another usage of SMA is to compare two or more moving average lines which are set to different time periods.

Let’s compare a 20-day Moving Average to a 50-day Moving Average for Apple:

Notice how the 20-day MA (green line) responds quicker to price changes than does the 50-day MA (red line). Because the 20-day MA moves quicker, there are times when it “crosses over” the 50 day line (moves from below the 50-day curve to above it, or vice-versa). These crossover points are of interest to the Technical Trader. When the 20 MA crosses above the 50 MA, it signifies that the stock is gaining price momentum. However, when the 20 MA crosses below the 50 MA, the price is losing ground.

The simple moving average is just that — simple. It is simple in the sense that it equally weights all prices, even though some are near-term and some happened long ago. A more accurate depiction can be achieved through placing more weight on the near-term prices. This is what Exponential Moving Average (EMA) does.

2) Exponential Moving Average – (EMA)

The Exponential Moving Average is a type of moving average which gives greater importance or weight to more recent price changes than a Simple Moving Average. As such, it is even more sensitive to near-term price changes.

Look at the difference in the response times between the SMA and the EMA using a 26-day moving average time frame for Apple’s stock:

Notice that the EMA line tracks closer to the price trend. This is due to the greater weight on the more recent prices.

All of the analysis we discussed using SMA can also be applied to EMA, including the directional trends, support, and resistance. In addition, EMAs are the basis for other very common analytical indicators. One of them, which we will discuss next, is the Moving Average Convergence Divergence (MACD). For MACD analysis, we usually compare a short-term EMA of 12-days to a slightly longer-term 26 days.

As its name implies, the Moving Average Convergence Divergence, called “MACD” for short, is all about the convergence and divergence of two moving averages. Convergence occurs when the moving averages move towards each other. Divergence occurs when the moving averages move away from each other.

The theory of MACD is that when two moving averages cross, a significant change of trend in the stock’s price is more likely to occur. Identifying this change in momentum helps us to determine the optimal strategic entry and exit points.

As with all indicators, the moving average crossover is not a “sure thing” and should not be considered an absolute truth as you trade stocks.

The MACD Line

The typical MACD Line is based on a shorter-term 12-day EMA which is compared to a longer-term 26-day EMA. The 12-day EMA reacts fast and is responsible for most MACD movements. The longer-term 26-day EMA is slower and less reactive to price changes in the underlying security.

Here are Apple’s 12-day EMA and 26-day EMA lines plotted on a traditional Bar Chart. The MACD Line is just the difference between the 12-day EMA and the 26-day EMA:

What does this MACD Line tell us? Notice how it oscillates above and below the zero line, which is also known as the centerline. These are called “centerline crossovers” which occur when the 12-day EMA crosses the 26-day EMA. This signals a change in momentum.

Positive MACD (above the centerline) indicates that the 12-day EMA is above the 26-day EMA. As the shorter EMA diverges in a positive direction further away from the longer EMA, it means upside momentum is increasing.

The opposite happens when MACD values are negative (below the centerline). This means that the 12-day EMA is below the 26-day EMA and, as the shorter EMA diverges in a negative direction from the longer EMA, then downside momentum is increasing.

In Apple’s chart above, we first see that Apple had ten crossover points in 2014 – five were negative and five were positive. The red area shows the MACD Line in negative territory as the 12-day EMA trades below the 26-day EMA. The initial cross occurred at the end of January and the MACD moved further into negative territory as the 12-day EMA diverged further from the 26-day EMA.

The green area highlights a period of positive MACD values. This occurs when the 12-day EMA is above the 26-day EMA. The positive divergence is a very good indicator of momentum, but could also alert the investor that stock is overpriced.

In summary, the MACD Line is measuring the rate of growth or decline of a stock compared to its history. When the MACD Line is moving toward zero it is said to be converging, alerting us that the stock is trending downwards and losing momentum. When it moves away from zero, it is diverging. This is a sign of an upward trend in the stock and an increase in momentum.

MACD and its Signal Line

Some Technical Analysts attempt to improve on this MACD concept by adding a second line to the plot, called the Signal Line. The Signal Line is a 9-day EMA of the MACD Line (it trails, or dampens the volatility of the MACD Line). This Signal Line is plotted on top of the MACD Line and functions as a trigger for buy and sell signals.

Let’s look at the plot for Apple below. Note that the MACD Line is still in black, we have added a Signal Line in red, and the blue histogram is simply the delta between those two lines. This chart is usually labeled MACD (12,26,9) as it was derived from three EMAs: a 12-day and a 26-day EMA combined to make the MACD Line, and the 9-day EMA on that MACD Line.

When the Signal Line is added to the MACD plot, we look for “signal crossovers” which occur when the MACD Line crosses over the Signal Line.

We use the same methodology to analyze the MACD with Signal Line as we do for the MACD Line. In this example, we have 11 crossovers. The Upward Cross, also called bullish crossover, occurs when the MACD Line turns up and crosses above the Signal Line. It signifies positive momentum. The Downward Cross, referred to as a bearish crossover, occurs when the MACD Line turns down and crosses below the Signal Line.

Crossovers can last a few days or a few weeks, it all depends on the strength of the move.

When analyzing charts, some programs plot MACD as a histogram.

Please pay attention and make sure you understand how to read the graph given the particular program you are utilizing. Do not assume that all graphs look and feel the same.

For example, the Apple Inc. MACD Chart below is from Yahoo Finance. In this chart, MACD is plotted as a histogram (bars) and the Signal is the Line.

The Relative Strength Index, RSI, is a technical momentum indicator that compares the average gains to the average losses in an attempt to determine “overbought” and “oversold” conditions of an asset.

An overbought situation occurs when the demand for the stock is so high that the price spikes to unjustifiable levels which are not supported by the fundamentals.

Using charts, we can see when the price has risen to the level of the upper-bound, and RSI is an indicator that signals when this occurs.

When it hits the upper bound, generally it means that the price of the asset is becoming overvalued and may experience a sell-off soon.

An oversold situation is exactly the opposite of an overbought condition. It happens when price has fallen sharply and is below the true value indicated by the fundamentals. In this case, the RSI indicator reaches a lower bound, generally indicating that the price of the asset is undervalued and that it could be a great time to buy.

RSI is calculated using the following formula, which is normalized to a scale between 0 and 100:

RSI = 100 – (100 ÷(1+RS)), where

RS = (average gains over x # of days’ up closes) ÷ (average loss over x # of days’ down closes)

Technical Analysts typically use 14 days as the standard time-frame. To calculate RSI, we first separate the stock price gains from the stock price losses for the 14 day period. Then we do the following: A) we add the gains and divide by 14; B) we add the losses and divide by 14; C) we calculate RS by dividing the average of the losses into the average of the gains (A ÷ B); and finally, D) we put the RS number into the RSI formula to normalize it to an index between 0 and 100.

Now it’s time to look at Apple’s RSI chart:

Notice on the RSI chart, there are two lines — one at 70 and one at 30. If the RSI moves up past the 70 line, it is considered an overbought condition (colored in green). If RSI dips under 30, it is considered an oversold situation.

In the chart above, there are two oversold situations in 2013, which would have signaled a buying opportunity. In 2014, Apple had numerous overbought occurrences, which would have signaled a selling opportunity.

To better understand how RSI is an early warning indicator, we need a pictorial view with more granularity.

Let’s look at the June oversold and August overbought situations, zooming in on RSI so we can see the early warning.

First, in June you will notice Apple had an oversold condition as the RSI indicator moved below 30, represented by pink on the chart.

The RSI indicator gave an early warning indicator on June 24^th, approximately four days in advance of the price moving up on June 28^th.

Likewise, in August there was an overbought condition. See how RSI moved above 70, colored in green. The warning was given on August 13^th, approximately two weeks in advance of the price dropping on August 26^th.

Care should be taken to ensure we use a variety of different indicators in an integrated fashion to assess market conditions. Too narrow a view may cause us to draw less than accurate conclusions on the market movements.

The Money Flow Index, which is similar to RSI, is a useful tool to add insights from a different perspective.

The Money Flow Index (MFI) is a momentum indicator that uses a stock’s price and volume to predict the reliability of the current trend. Because the Money Flow Index adds trading volume to the Relative Strength Index (RSI), it is sometimes referred to as a volume-weighted RSI.

MFI is similar to the Relative Strength Index (RSI) in both interpretation and calculation of overbought and oversold conditions. However, MFI is a more rigid indicator in that it is volume-weighted, and is therefore a good measure of the strength of money flowing in and out of a security.

For example, it compares “positive money flow” to “negative money flow” to create an indicator that can identify the strength or weakness of a trend.

The value of using MFI lies in the fact that it allows us to detect the reversal of a trend.

For example, given the situation where the stock price is on the decline, a trader wants to know if this decline is going to continue.

We figure this out by looking at the flow of money. Is it positive (market demand is increasing), or is it negative (market is pulling back)? If the flow of money is predominantly negative, we know the decline will continue. If however, the flow is positive, we know the trend will reverse quickly. This is the value of analyzing MFI compared to RSI.

We typically use 14 days for the MFI time frame, and mark the overbought boundary at 80 and the oversold boundary at 20. Like the RSI, the MFI is measured on a scale of 0 – 100.

Let’s analyze Apples’s run-up in prices in June of 2014. Is this price escalation sustainable? Could we have predicted a drop-off? Check it out:

Notice the climb in prices between June 6th and June 10th. The MFI indicates an overbought condition (as did RSI). In addition, analyze the direction of the MFI line. It is horizontal, meaning it shows a diversion from the upward price trend. Obviously, volume (demand) is dropping, signaling an end to this trend.

The Price Rate Of Change (ROC), which is also referred to as simply Momentum, measures the percentage of change between the most recent price and the price “x” periods in the past. This measures the velocity, or momentum of price trends.

Here is the formula:

ROC= (Today’s Closing Price – Closing Price “x” Periods Ago) ÷
Closing Price “x” Periods Ago

where: x = 12 time periods (typical in industry)

The chart fluctuates above and below the zero line as the Rate-of-Change moves from positive to negative.

As long as the ROC remains positive, prices are rising and there is an increase in upward momentum. If it’s expanding past zero, the greater the momentum.

Conversely, there is momentum to sell (falling prices) when ROC is negative. The more negative the larger the acceleration of decline.

Let’s look at Apple’s ROC from March through May of 2013:

Notice that for most of April there was pressure to sell (ROC less than zero), but by May the trend had shifted to an increase in upward momentum (ROC > 0). Understanding when the momentum will shift is very valuable to traders.

ROC is a useful tool to indicate shift in momentum. This shift is signaled on the charts when the price trend and the ROC trend diverge from each other.

Put simply, when the price of the asset and the trend of ROC are headed in opposite directions, that indicates a reversal in the market, or a shift in momentum.

In the chart above we see that ROC is trending relatively flat while the price is plummeting. This is an early indication that the sharp decline may reverse soon.

The Stochastic Indicator (STO) is another method used to identify overbought and oversold conditions.

The concept behind this indicator is that as a stock’s price moves in an upward trend, its closing price for any given day tends to be near the high of the price range, where the range is defined as a set period of time. In a downtrend the opposite will be true and the stock will tend to close near to the low end of its trading range.

A typical trading range is 14 time periods for STO, with a moving average of 3 time periods (called STO 14,3). Changing the time period will change STO’s sensitivity to market movements. Let’s look at the formula:

%K = 100[(C – L14) ÷ (H14 – L14)]
D%=(K%₁+ K%₂+ K%₃) ÷ 3

where:
C = the most recent closing price
L14 = the low of the 14 previous trading sessions
H14 = the highest price traded during the same 14-day period
%K = 14 “period” (could be days, weeks, months, years)
%D = 3 “period” moving average of %K

The Stochastic Oscillator is generally put on a scale of 0 to 100. If the indicator is above 80 the stock may be becoming overbought and may be about to lose momentum. When it dips below 20, it is considered to be in the oversold range and may indicate that the stock will move higher.

Here is Apple’s STO from January through April of 2014:

Notice three time periods where the closing price traded at a high, middle, and low of the 14 day trading range. The high above 80 is considered overbought and the low below 20 is considered oversold.

Using this indicator for trading, we would consider buying stocks when the STO moved upward after being in the oversold region (0 to 20). We would also consider selling a stock, when it moved lower after being in the overbought region (80 to 100).

The Bollinger Bands® plot is one of the most popular technical analysis techniques. It measures two standard deviations away from a simple moving average (SMA) and provides an outlook for support and resistance. The industry standard time-frame for the SMA is 20 days. (Note: Bollinger Bands® is a registered trademark of John Bollinger.)

Bollinger Bands® consist of three simple calculations:

Middle Band = Simple Moving Average of Closing Price

Top Band = Middle Band + Standard Deviation

Lower Band = Middle Band – Standard Deviation

where:
Standard Deviation is a statistical calculation that calculates the Sum of the Square of the differences between the closing price and the moving average for each of the 20 days, or periods.

The Bollinger Bands® are a measure of volatility. As market conditions change so do the bands.

For example, when the market is volatile, the bands widen, moving further away from the SMA. Likewise, during less volatile periods, the bands contract, moving toward the SMA. The tightening of the bands is often used by technical traders as an early indication that the volatility is about to increase sharply.

In addition, as prices move toward the upper band, the market is considered overbought (trigger to sell). As they move to the lower band, it is an oversold condition (trigger to buy).

Here is the Bollinger Bands® Chart for Apple in 2014:

Notice how the upper and lower bands act as strong barriers of support and resistance. At the end of January the prices were hovering on the lower band, signaling the potential for an upturn. Price quickly rebounded. In May, the bands widened dramatically, signaling volatility as the prices climbed. In June, the prices traded near the upper band, triggering an overbought situation and a potential downturn. Prices declined shortly thereafter.

Parabolic Indicator, also called Stop and Reversal (SAR), is a technical analysis used to determine good exit and entry points in an upward or downward trending market. It is not a valuable tool to be used in a sideways trending market, or in a market which is choppy.

The Parabolic Indicator trails above or below the price of an asset through a downward or upward trend respectively. It is designed to catch the trend so that we can strategically enter and exit at the right times to maximize profit.

The Parabolic Indicator is plotted in a rather unorthodox fashion: a stop-loss is calculated for each day using the previous day’s data. A stop-loss relates to an order to sell a security or commodity at a specified price in order to limit a loss. Conversely, you can place an order to buy at a specified price if you feel there is an uptrend. This calculation has the distinct advantage that it can be made prior to the opening of the market each day.

For example, the SAR indicator latches on to an upward trend and is plotted below the prices. It will hold onto this trend until the closing price reverses. At that time, the calculation changes and the SAR indicator is now above the line for the downward trend.

This is called “stop and reversal” or “SAR”. It is also known as Parabolic Stop and Reverse (PSAR).

While the calculation for this indicator is beyond the scope of this article, what we need to understand is that there is an Acceleration Factor (AF) which directly impacts the sensitivity of the SAR indicator.

A low AF moves SAR further from the price, which makes a reversal less likely. A higher AF moves SAR closer to the prices and increases sensitivity, which makes a reversal more likely. Calibrating the AF to a security is important. Too high an AF will create whipsaws and fail to capture the trend.

For example, compare the two charts. The top chart has AF set to 0.02 and it shows two trend lines (one reversal). For the same price trend, the bottom chart has AF set to 0.05. SAR tracks close to the price trend and identified four distinct trends (three reversals).

The SAR plotted on a price chart will occasionally intersect with price due to a reversal or loss of momentum in the security in question.

When this intersection occurs, the trade is considered to be “stopped out” and the opportunity exists to take the other side of the market. SAR helps us identify the time to buy and to sell.

Here is the SAR Chart for Apple:

In trading, a stop level below the current price indicates that your position is long (you are holding the security and you will benefit from price escalation). The stop will move up every day until activated, when the price falls to the stop level.

A stop level above the current price indicates that your position is short (you do not hold the asset and would benefit in purchasing when the price drops). The stop will move down every day until triggered, when the price rises to the stop level.

The parabolic stop and reverse (SAR) technique provides stop-loss levels to protect profits for both sides of the market, moving incrementally each day with changes in price.

It helps us determine strategic entry points at a price which is not too high, and strategic exits at a price that is not too low.