Moving Averages: EMA, SMA, LWMA

INTRODUCTION

The moving average is one of the most versatile and widely used of all technical indicators. Because of the way it is constructed and the fact that it can be so easily quantified and tested, it is the basis for many mechanical trend-following systems in use today.

Chart analysis is largely subjective and difficult to test. As a result, chart analysis does not lend itself that well to computer­ization. Moving average rules, by contrast, can easily be pro­grammed into a computer, which then generates specific buy and sell signals. While two technicians may disagree as to whether a given price pattern is a triangle or a wedge, or whether the volume pattern favors the bull or bear side, moving average trend signals are precise and not open to debate.

Let's begin by defining what a moving average is. As the sec­ond word implies, it is an average of a certain body of data. For example, if a 10 day average of closing prices is desired, the prices for the last 10 days are added up and the total is divided by 10. The term moving is used because only the latest 10 days' prices are used in the calculation. Therefore, the body of data to be averaged (the last 10 closing prices) moves forward with each new trading day. The most common way to calculate the moving average is to work from the total of the last 10 days' closing prices. Each day the new close is added to the total and the close 11 days back is subtracted. The new total is then divided by the number of days (10). (See Figure 9.1a.)

The above example deals with a simple 10 day moving average of closing prices. There are, however, other types of mov­ing averages that are not simple. There are also many questions as to the best way to employ the moving average. For example, how many days should be averaged? Should a short term or a long term average be used? Is there a best moving average for all mar­kets or for each individual market? Is the closing price the best price to average? Would it be better to use more than one average?

Figure 9.1a A 10 day moving average applied to a daily bar chart of the S&P 500. Prices crossed the average line several times (see arrows) before finally turning higher. Prices stayed above the average during the subsequent rally.

Which type of average works better—a simple, linearly weighted or exponentially smoothed? Are there times when moving aver­ages work better than others?

There are many questions to be considered when using moving averages. We'll address many of these questions in this chapter and show examples of some of the more common usages of the moving average.

THE MOVING AVERAGE:
A SMOOTHING DEVICE WITH A TIME LAG

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

Figure 9.1b A comparison of a 20 day and a 200 day moving average. During the sideways period from August to January, prices crossed the shorter average several times. However, they remained above the 200 day average throughout the entire period.

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 is added 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. (See Figure 9.2.)

Figure 9.2 The 40 day exponential moving average (dotted line) is more sensitive than the simple arithmetic 40 day moving average (solid line).

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

Figure 9.3 Prices fell below the 50 day average during October (see left circle). The sell signal is stronger when the moving average also turns down (see left arrow). The buy signal during January was confirmed when the average itself turned higher.

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." (See Figure 9.4.)

Figure 9.4 A shorter average gives earlier signals. The longer average is slower, but more reliable. The 10 day turned up first at the bottom. But it also gave a premature buy signal during November and an untimely sell signal during February (see boxes).

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. (See Figures 9.5 and 9.6.)

Figure 9.5 The double crossover method uses two moving averages. The 5 and 20 day combination is popular with futures traders. The 5 day fell below the 20 day during October (see circle) and caught the entire downtrend in crude oil prices.

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.)

Figure 9.6 Stock traders use10 and 50 day moving averages. The 10 day fell below the 50 day in October (left circle), giving a timely sell signal. The bullish crossover in the other direction took place during  January (lower circle).

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

Figure 9.7a Futures traders like the 9 and 18 day moving average combination. A sell signal was given in late October (first circle) when the 9 day fell below the 18. A buy signal was given in early 1998 when the 9 day crossed back above the 18 days