*This “Throwback Thursday” article comes from AAII’s extensive archives spanning four decades. While these articles may have been written long ago, the investment topics they cover are just as relevant today as they were when they were written. We are pleased to reintroduce them to a new audience.*

Timing would be easy if we only knew the future price direction of our investments. Technology is not quite up to providing a clear glimpse of the future. The only time machine available to investors runs on historical data. The premise: A clear view of the past may help divine the future.

There are two opposing camps on the issue. Efficient market adherents believe that all information is reflected in the current price of a stock and that looking at past trends or stock price patterns has no value in determining future prices. On the other hand, market timers, many times grouped under the title of technical analysts, believe equally fervently that trends do persist and can be determined before they are history.

Although most of the empirical evidence to date on stock price patterns supports the efficient marketers, technicians argue that some techniques have been successful over certain time periods. Efficient marketers respond that the techniques were only successful in retrospect and that, if you look at historical data long enough, a successful technique can be back-fitted to the data. The debate will no doubt continue.

Investors must judge for themselves the results of any investment approach, and to do so they must have a working knowledge of how to apply the technique.

This workshop focuses on one of the techniques used in technical analysis, explaining the construction and interpretation of one of its more commonly watched measures—the moving average.

The purpose of the moving average is to provide summary price behavior information by reducing shorter-term variations to reveal basic price trends.

There are three basic types of moving averages commonly used by investors: simple, weighted and exponential. All can be used for any length or interval of time: for instance, five days, 50 days or 200 days; or five weeks, 10 weeks or 26 weeks. Any number of periods—even or odd—is workable; the choice is up to the investor. The important relationship to remember is that moving averages dampen or smooth variations within the time interval of the average, and they emphasize the variations for time intervals greater than the average. For example, a four-quarter moving average would smooth seasonal variations and would concentrate attention on year-long and longer-term trends.

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The simple moving average does not require intricate calculation, but it may require substantial data storage, depending on the time interval and unit of measurement. **Table 1** creates a five-week simple moving average for a hypothetical stock. The first five weeks are required as an initialization period, and the moving average should be interpreted from the sixth week on. The calculation of the average for each week requires adding up the five most recent weekly prices and dividing the sum by five. All the prices are given equal weight and determine the level of the average. The prices that are added and deleted each week greatly affect the moving average, causing the week-to-week variations. Importantly, the simple moving average does not recognize that the most recent price may have more meaning than distant prices for purposes of spotting a trend.

The weighted moving average allows flexibility in determining what relative contribution each price will make to the value of the average. **Table 2** provides an example, using the same stock price movements as in **Table 1**. This example assigns heavier weights to the most recent prices. However, any weighting system is possible. When there are sharp movements in recent prices, the weighted moving average may differ significantly from the simple moving average.

The exponential moving average is the most sophisticated, yet it requires less historical data than the other two forms, making it the easiest to calculate. The mathematical form of the moving average is given in the following relationship:

This model automatically corrects for differences between past moving averages and the actual price. If the actual price is greater than the prior moving average, the difference between the two multiplied by the smoothing constant is added to the prior moving average to arrive at the new moving average; if the actual price is less than the previous moving average, the difference between the two is negative, and thus that figure multiplied by the smoothing constant is subtracted from the previous moving average to arrive at the new moving average.

The smoothing constant is a weight, from zero to one, given to adjust the difference between the prior average and the actual price. The greater the value of the smoothing constant, the more adjustment is made and thus the greater the weight given to the recent price. While there are many statistical tests to determine what smoothing constant would have fit the past data the best, a smoothing constant that approximates a simple moving average is:

where T = time interval of the moving average

For instance, for a five-week exponential moving average, the smoothing constant would be:

**Table 3** presents an example of a five-week exponential moving average; for purposes of showing the calculation, the second form of the equation was used. To start the exponential average, the moving average in week one was assumed to be equal to the actual price in week one.

Moving averages are designed to smooth out variations over the time interval of the average and to highlight trends. A basic interpretation would be to sell when the actual price falls below the moving average and to buy when the actual price rises above the moving average. The longer the time interval of the moving average, the longer the term of the trend highlighted and the fewer the signals given by the average.

The three examples indicate buy and sell signals; the three different types of moving averages in the examples gave similar signals, despite the slight differences in moving average figures. This will generally hold true, unless there are dramatic price changes.

There are, of course, infinite combinations of time periods and weights for moving averages, but choosing the “best" is probably impossible. If you look at historical price data for a particular period, some moving averages will have worked better than others. But whether that average will work in the future is unknown.

All of these moving average techniques are readily computerized and, in fact, there are numerous software packages available that will calculate and graphically display moving averages for stocks and mutual funds, noting any buy or sell signals. Services are also available that will send graphs of moving averages. Investors should keep one important caution in mind: Signals from moving averages trigger transactions costs and potential tax consequences. They are, however, popular, and many newsletters and brokers rely upon them.

Whether you use moving averages or not, it is important that you have a basic grasp of how they work to better judge the recommendations of others.

*This article was written by John Markese for the October 1986 issue of the *AAII Journal. *At the time, Markese was the director of research at AAII. He is also a former president of AAII and currently serves as vice chairman.*

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