The Moving Average: A Smoothing Device with a Time Lag
posted under
Philosophy of Technical Analysis
by ceecabolos
The moving average is essentially a trend following device. Its purpose is to identify or signal that a new trend has begun or that an old trend has ended or reversed. Its purpose is to track the progress of the trend. It might be viewed as a curving trendline. It does not, however, predict market action in the same sense that standard chart analysis attempts to do. The moving average is a follower, not a leader. It never anticipates; it only reacts. The moving average follows a market and tells us that a trend has begun, but only after the fact.
The moving average is a smoothing device. By averaging the price data, a smoother line is produced, making it much easier to view the underlying trend. By its very nature, however, the moving average line also lags the market action. A shorter moving average, such as a 20 day average, would hug the price action more closely than a 200 day average. The time lag is reduced with the shorter averages, but can never be completely eliminated. Shorter term averages are more sensitive to the price action, whereas longer range averages are less sensitive. In certain types of markets, it is more advantageous to use a shorter average and, at other times, a longer and less sensitive average proves more useful. (See Figure 9.1b.)
Which Prices to Average
We have been using the closing price in all of our examples so far. However, while the closing price is considered to be the most
important price of the trading day and the price most commonly used in moving average construction, the reader should be aware that some technicians prefer to use other prices. Some prefer to use a midpoint value, which is arrived at by dividing the day's range by two.
Others include the closing price in their calculation by adding the high, low, and closing prices together and dividing the sum by three. Still others prefer to construct price bands by averaging the high and low prices separately. The result is two separate moving average lines that act as a sort of volatility buffer or neutral zone. Despite these variations, the closing price is still the price most commonly used for moving average analysis and is the price that we'll be focusing most of our attention on in this chapter.
The Simple Moving Average
The simple moving average, or the arithmetic mean, is the type used by most technical analysts. But there are some who question its usefulness on two points. The first criticism is that only the period covered by the average (the last 10 days, for example) is taken into account. The second criticism is that the simple moving average gives equal weight to each day's price. In a 10 day average, the last day receives the same weight as the first day in the calculation. Each day's price is assigned a 10% weighting. In a 5 day average, each day would have an equal 20% weighting. Some analysts believe that a heavier weighting should be given to the more recent price action.
The Linearly Weighted Moving Average
In an attempt to correct the weighting problem, some analysts employ a linearly weighted moving average. In this calculation, the closing price of the 10th day (in the case of a 10 day average) would be multiplied by 10, the ninth day by nine, the eighth day by eight, and so on. The greater weight is therefore given to the more recent closings. The total is then divided by the sum of the multipliers (55 in the case of the 10 day average: 10 + 9 + 8 + .. . + 1). However, the linearly weighted average still does not address the problem of including only the price action covered by the length of the average itself.
The Exponentially Smoothed
Moving Average
This type of average addresses both of the problems associated with the simple moving average. First, the exponentially smoothed average assigns a greater weight to the more recent data. Therefore, it is a weighted moving average. But while it assigns lesser importance to past price data, it does include in its calculation all of the data in the life of the instrument. In addition, the user is able to adjust the weighting to give greater or lesser weight to the most recent day's price. This is done by assigning a percentage value to the last day's price, which isadded to a percentage of the previous day's value. The sum of both percentage values adds up to 100. For example, the last day's price could be assigned a value of 10% (.10), which is added to the previous day's value of 90% (.90). That gives the last day 10% of the total weighting. That would be the equivalent of a 20 day average. By giving the last day's price a smaller value of 5% (.05), lesser weight is given to the last day's data and the average is less sensitive. That would be the equivalent of a 40 day moving average.
The computer makes this all very easy for you. You just have to choose the number of days you want in the moving average-10, 20, 40, etc. Then select the type of average you want—simple, weighted, or exponentially smoothed. You can also select as many averages as you want—one, two, or three.
The Use of One Moving Average
The simple moving average is the one most commonly used by technicians, and is the one that we'll be concentrating on. Some traders use just one moving average to generate trend signals. The moving average is plotted on the bar chart in its appropriate trading day along with that day's price action. When the closing price moves above the moving average, a buy signal is generated. A sell signal is given when prices move below the moving average. For added confirmation, some technicians also like to see the moving average line itself turn in the direction of the price crossing. (See Figure 9.3.)
If a very short term average is employed (a 5 or 10 day), the average tracks prices very closely and several crossings occur. This action can be either good or bad. The use of a very sensitive average produces more trades (with higher commission costs) and results in many false signals (whipsaws). If the average is too sensitive, some of the short term random price movement (or "noise") activates bad trend signals.While the shorter average generates more false signals, it has the advantage of giving trend signals earlier in the move. It stands to reason that the more sensitive the average, the earlier the signals will be. So there is a tradeoff at work here. The trick is to find the average that is sensitive enough to generate early signals, but insensitive enough to avoid most of the random "noise." Let's carry the above comparison a step further. While the longer average performs better while the trend remains in motion, it "gives back" a lot more when the trend reverses. The very insensitivity of the longer average (the fact that it trailed the trend from a greater distance), which kept it from getting tangled up in short term corrections during the trend, works against the trader when the trend actually reverses. Therefore, we'll add another corollary here: The longer averages work better as long as the trend remains in force, but a shorter average is better when the trend is in the process of reversing.
It becomes clearer, therefore, that the use of one moving average alone has several disadvantages. It is usually more advantageous to employ two moving averages.
How to Use Two Averages to Generate Signals
This technique is called the double crossover method. This means that a buy signal is produced when the shorter average crosses above the longer. For example, two popular combinations are the 5 and 20 day averages and the 10 and 50 day averages. In the former, a buy signal occurs when the 5 day average crosses above the 20, and a sell signal when the 5 day moves below the 20. In the latter example, the 10 day crossing above the 50 signals an uptrend, and a downtrend takes place with the 10 slipping under the 50. This technique of using two averages together lags the market a bit more than the use of a single average but produces fewer whipsaws. The Use of Three Averages, or the Triple Crossover Method
That brings us to the triple crossover method. The most widely used triple crossover system is the popular 4-9-18-day moving average combination. The 4-9-18 method is used mainly in futures trading. This concept was first mentioned by R.C. Allen in his 1972 book, How to Build a Fortune in Commodities and again later in a 1974 work by the same author, How to Use the 4-Day, 9-Day and 18-Day Moving Averages to Earn Larger Profits from Commodities. The 4-9-18-day system is a variation on the 5, 10, and 20 day moving average numbers, which are widely used in commodity circles. Many commercial chart services publish the 4-9-18-day moving averages. (Many charting software packages use the 4-9-18-day combination as their default values when plotting three averages.).How to Use the 4-9-18-Day Moving Average System
It's already been explained that the shorter the moving average, the closer it follows the price trend. It stands to reason then that the shortest of the three averages—the 4 day—will follow the trend most closely, followed by the 9 day and then the 18. In an uptrend, therefore, the proper alignment would be for the 4 day average to be above the 9 day, which is above the 18 day average. In a downtrend, the order is reversed and the alignment is exactly the opposite. That is, the 4 day would be the lowest, followed by the 9 day and then the 18 day average. (See Figures 9.7a-b.)
A buying alert takes place in a downtrend when the 4 day crosses above both the 9 and the 18. A confirmed buy signal occurs when the 9 day then crosses above the 18. This places the
4 day over the 9 day which is over the 18 day. Some intermingling may occur during corrections or consolidations, but the general uptrend remains intact. Some traders may take profits during the intermingling process and some may use it as a buying opportunity. There is obviously a lot of room for flexibility here in applying the rules, depending on how aggressively one wants to trade.
When the uptrend reverses to the downside, the first thing that should take place is that the shortest (and most sensitive) average—the 4 day—dips below the 9 day and the 18 day. This is only a selling alert. Some traders, however, might use that initial crossing as reason enough to begin liquidating long positions. Then, if the next longer average—the 9 day—drops below the 18 day, a confirmed sell short signal is given.
The moving average is a smoothing device. By averaging the price data, a smoother line is produced, making it much easier to view the underlying trend. By its very nature, however, the moving average line also lags the market action. A shorter moving average, such as a 20 day average, would hug the price action more closely than a 200 day average. The time lag is reduced with the shorter averages, but can never be completely eliminated. Shorter term averages are more sensitive to the price action, whereas longer range averages are less sensitive. In certain types of markets, it is more advantageous to use a shorter average and, at other times, a longer and less sensitive average proves more useful. (See Figure 9.1b.)
Which Prices to Average
We have been using the closing price in all of our examples so far. However, while the closing price is considered to be the most
important price of the trading day and the price most commonly used in moving average construction, the reader should be aware that some technicians prefer to use other prices. Some prefer to use a midpoint value, which is arrived at by dividing the day's range by two.
Others include the closing price in their calculation by adding the high, low, and closing prices together and dividing the sum by three. Still others prefer to construct price bands by averaging the high and low prices separately. The result is two separate moving average lines that act as a sort of volatility buffer or neutral zone. Despite these variations, the closing price is still the price most commonly used for moving average analysis and is the price that we'll be focusing most of our attention on in this chapter.
The Simple Moving Average
The simple moving average, or the arithmetic mean, is the type used by most technical analysts. But there are some who question its usefulness on two points. The first criticism is that only the period covered by the average (the last 10 days, for example) is taken into account. The second criticism is that the simple moving average gives equal weight to each day's price. In a 10 day average, the last day receives the same weight as the first day in the calculation. Each day's price is assigned a 10% weighting. In a 5 day average, each day would have an equal 20% weighting. Some analysts believe that a heavier weighting should be given to the more recent price action.
The Linearly Weighted Moving Average
In an attempt to correct the weighting problem, some analysts employ a linearly weighted moving average. In this calculation, the closing price of the 10th day (in the case of a 10 day average) would be multiplied by 10, the ninth day by nine, the eighth day by eight, and so on. The greater weight is therefore given to the more recent closings. The total is then divided by the sum of the multipliers (55 in the case of the 10 day average: 10 + 9 + 8 + .. . + 1). However, the linearly weighted average still does not address the problem of including only the price action covered by the length of the average itself.
The Exponentially Smoothed
Moving Average
This type of average addresses both of the problems associated with the simple moving average. First, the exponentially smoothed average assigns a greater weight to the more recent data. Therefore, it is a weighted moving average. But while it assigns lesser importance to past price data, it does include in its calculation all of the data in the life of the instrument. In addition, the user is able to adjust the weighting to give greater or lesser weight to the most recent day's price. This is done by assigning a percentage value to the last day's price, which isadded to a percentage of the previous day's value. The sum of both percentage values adds up to 100. For example, the last day's price could be assigned a value of 10% (.10), which is added to the previous day's value of 90% (.90). That gives the last day 10% of the total weighting. That would be the equivalent of a 20 day average. By giving the last day's price a smaller value of 5% (.05), lesser weight is given to the last day's data and the average is less sensitive. That would be the equivalent of a 40 day moving average.
The computer makes this all very easy for you. You just have to choose the number of days you want in the moving average-10, 20, 40, etc. Then select the type of average you want—simple, weighted, or exponentially smoothed. You can also select as many averages as you want—one, two, or three.
The Use of One Moving Average
The simple moving average is the one most commonly used by technicians, and is the one that we'll be concentrating on. Some traders use just one moving average to generate trend signals. The moving average is plotted on the bar chart in its appropriate trading day along with that day's price action. When the closing price moves above the moving average, a buy signal is generated. A sell signal is given when prices move below the moving average. For added confirmation, some technicians also like to see the moving average line itself turn in the direction of the price crossing. (See Figure 9.3.)
If a very short term average is employed (a 5 or 10 day), the average tracks prices very closely and several crossings occur. This action can be either good or bad. The use of a very sensitive average produces more trades (with higher commission costs) and results in many false signals (whipsaws). If the average is too sensitive, some of the short term random price movement (or "noise") activates bad trend signals.While the shorter average generates more false signals, it has the advantage of giving trend signals earlier in the move. It stands to reason that the more sensitive the average, the earlier the signals will be. So there is a tradeoff at work here. The trick is to find the average that is sensitive enough to generate early signals, but insensitive enough to avoid most of the random "noise." Let's carry the above comparison a step further. While the longer average performs better while the trend remains in motion, it "gives back" a lot more when the trend reverses. The very insensitivity of the longer average (the fact that it trailed the trend from a greater distance), which kept it from getting tangled up in short term corrections during the trend, works against the trader when the trend actually reverses. Therefore, we'll add another corollary here: The longer averages work better as long as the trend remains in force, but a shorter average is better when the trend is in the process of reversing.
It becomes clearer, therefore, that the use of one moving average alone has several disadvantages. It is usually more advantageous to employ two moving averages.
How to Use Two Averages to Generate Signals
This technique is called the double crossover method. This means that a buy signal is produced when the shorter average crosses above the longer. For example, two popular combinations are the 5 and 20 day averages and the 10 and 50 day averages. In the former, a buy signal occurs when the 5 day average crosses above the 20, and a sell signal when the 5 day moves below the 20. In the latter example, the 10 day crossing above the 50 signals an uptrend, and a downtrend takes place with the 10 slipping under the 50. This technique of using two averages together lags the market a bit more than the use of a single average but produces fewer whipsaws. The Use of Three Averages, or the Triple Crossover Method
That brings us to the triple crossover method. The most widely used triple crossover system is the popular 4-9-18-day moving average combination. The 4-9-18 method is used mainly in futures trading. This concept was first mentioned by R.C. Allen in his 1972 book, How to Build a Fortune in Commodities and again later in a 1974 work by the same author, How to Use the 4-Day, 9-Day and 18-Day Moving Averages to Earn Larger Profits from Commodities. The 4-9-18-day system is a variation on the 5, 10, and 20 day moving average numbers, which are widely used in commodity circles. Many commercial chart services publish the 4-9-18-day moving averages. (Many charting software packages use the 4-9-18-day combination as their default values when plotting three averages.).How to Use the 4-9-18-Day Moving Average System
It's already been explained that the shorter the moving average, the closer it follows the price trend. It stands to reason then that the shortest of the three averages—the 4 day—will follow the trend most closely, followed by the 9 day and then the 18. In an uptrend, therefore, the proper alignment would be for the 4 day average to be above the 9 day, which is above the 18 day average. In a downtrend, the order is reversed and the alignment is exactly the opposite. That is, the 4 day would be the lowest, followed by the 9 day and then the 18 day average. (See Figures 9.7a-b.)
A buying alert takes place in a downtrend when the 4 day crosses above both the 9 and the 18. A confirmed buy signal occurs when the 9 day then crosses above the 18. This places the
4 day over the 9 day which is over the 18 day. Some intermingling may occur during corrections or consolidations, but the general uptrend remains intact. Some traders may take profits during the intermingling process and some may use it as a buying opportunity. There is obviously a lot of room for flexibility here in applying the rules, depending on how aggressively one wants to trade.
When the uptrend reverses to the downside, the first thing that should take place is that the shortest (and most sensitive) average—the 4 day—dips below the 9 day and the 18 day. This is only a selling alert. Some traders, however, might use that initial crossing as reason enough to begin liquidating long positions. Then, if the next longer average—the 9 day—drops below the 18 day, a confirmed sell short signal is given.
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