- Trends
- Momentum
- Moving Averages and Moving Average Crossovers
- Ratio of Price to a Moving Average
- Cycles
- Cycle Terminology
- Conclusion

## Moving Averages and Moving Average Crossovers

Moving averages are one of the most useful methods of identifying and profiting from trends in prices or in any other economic data. They are one of the oldest tools used by technical analysts, dating back to 1901 with the work of mathematician R. H. Hooker ^{1}. Moving averages dampen out most of the fluctuations shorter than the length of the moving average. A 40-day moving average will reduce the effect of any fluctuations of 40 days or less, for example. One-day fluctuations are almost completely erased. The moving average reflects what occurred over the entire 40 days rather than just 1 day. When a moving average changes direction, we know that the trend represented by that moving average has changed direction.

An average is the sum of a number of specific data, such as prices, divided by the number. A 20-day price average is the sum of 20 days of prices divided by 20, the number of days. (A “moving average” is the average calculation performed over successive periods and usually plotted on a chart for clarity.) A 20-day moving average, as shown in Figure 3.1, is a calculation of the 20-day average over some succession of days. When plotted on a price chart, the moving average is usually a smooth line that dampens the effects of the minor, sometimes erratic oscillations in the data. It thus represents the trend through that data over the period of the moving average and disregards the clutter around it. It is a measure of the trend and is useful for determining when the trend is changing. A rising moving average indicates a rising trend over the period of the moving average. A declining moving average indicates a declining trend. If we calculate a rate of change in a moving average, we can see changes in the trend and thus the trend momentum.

Figure 3.1. Dow Jones Industrial Average with 20-day simple moving average (September 14–December 31, 2010)

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The easiest type of moving average to understand is called a simple moving average, or SMA. Analysts also use other types of moving averages, such as the exponential, the linearly weighted, the Wilder, the geometric, and the triangular. There are even methods that will vary the moving average length based on the historic volatility of the prices known as “adaptive” moving averages. For our purposes, the results of these esoteric calculations provide no extra advantage. The simple moving average is easy to construct and suffices for all your calculations.

The use of moving averages in investing has been widely documented. It is the reason for the success of many commodity traders, and academics have shown that methods using moving averages demonstrate statistical significance. Early studies of moving averages as a timing method for stocks discounted their value. These studies used crossovers of prices and moving averages, not crossovers of moving averages to moving averages, and were statistically primitive. Brock, Lakonishok, and LeBaron (1992) ^{2} conducted the first study to show the validity of using moving average crossover rules, as well as trading range break rules. They found that moving average crossover signals generate statistically significant stock market directional signals. Since then, using market data in other markets and in other countries, additional studies have confirmed much of their original academic work. We use similar methods ourselves when we analyze the data for signals in later chapters.

We know that the markets have many different trends going at one time. There is the long, secular trend, and then the intermediate-term trend, the short-term trend, and other trends above, below, and in between. We can construct a moving average of any length, provided that the price information is available. Generally, shorter-period moving averages represent shorter price trends, and longer moving averages represent longer price trends.

If we calculate more than one moving average over different periods, we see the changes in the shorter trend versus the longer trend. Eventually the shorter moving average will cross over and under the longer moving average. These “crossovers” can be signals of impending change in price trend direction. Any system developed to use these crossovers is called a “moving average crossover system.” The unknown variables in such a system are the lengths of the two moving averages. We can prejudge what those lengths should be, or we can optimize the data to see what lengths give the most reliable signals.

A longer-period length includes more data and more information. Each specific data point becomes less important. A large change in specific data thus has less influence on the longer moving average. However, if this large change in data is the beginning of a significant change in trend, it takes longer for the trend change to be recognized. The longer moving average is slower to pick up trend changes but less likely to indicate a trend change incorrectly from a short-term blip in the data.

Figure 3.2 shows two moving averages in the daily chart of the Dow Jones Industrial Average (DJIA). The shorter-length moving average, 9 days, oscillates around the 18-day average and has a wider range. The 9-day is the “faster” moving average, and the 18-day is the “slower” moving average. The shorter-length moving average is always the faster average because it turns more quickly when a trend change occurs. It is less reliable as an indicator of trend changes, however. In Figure 3.2, notice how the 9-day moving average (dashed line) makes its troughs after the actual price bottoms, and the 18-day moving average (solid line) makes its troughs even farther after the actual price bottoms.

Figure 3.2. Two moving averages: 9-day and 18-day (Dow Jones Industrial: November 4, 2009–December 31, 2010)

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The lag in turning, however, has an advantage. That is the advantage of surety of the signal. A change in direction of a moving average is more accurate the longer the moving average period. A crossover of a fast moving average and a slow moving average will tend to occur near the turning point of the slow moving average, and thus, while occurring long after the actual turn in prices, it is more reliable as a signal. The conflict between accuracy and reliability is a recurring theme in any technical signal. Reliability reduces loss and is thus a preferable characteristic of any signaling system. For this reason, moving average crossover systems are more commonly used for their reliability, even with their late signals.

A flat trend results in moving averages oscillating horizontally and crossovers not followed by directional change in prices. This causes “whipsaws” in signals whereby a buy signal is followed by a sell signal at or below the buy signal price, and vice versa. This major signal fault with moving average crossover systems occurs only when the trends are flat and the trader loses money chasing fluctuating signals.

Figure 3.3 shows a flat period in Core Laboratories’ share price, when the moving average crossovers gave false signals called whipsaws. It is thus important that the moving average period lengths be long enough to bypass any flat trends in the price. Because this is not always possible, moving average crossover systems have a high rate of false signals. Fortunately, the losses are quickly recovered by reverse signals. We can reduce these whipsaws with filters and other methods but never can eliminate them. On the other hand, the advantage of a moving average crossover system is that it will catch every major trend change and “ride” that new trend to its termination. As long as markets trend, the moving average crossover method, when properly applied, will catch the major trends.

Figure 3.3. Simple moving average (SMA) crossovers causing whipsaws in a flat trend (Core Laboratory common stock, daily: October 19–December 23, 2009) from *Technical Analysis*, page 281

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