Harmonic cycles are composed of three measures: period, amplitude, and phase. Because market cycles are not true cycles in the harmonic sense—otherwise they would have been identified more precisely long ago and would be easily recognized through standard harmonic mathematics such as Fourier analysis—we find that the only consistent measure is that of “period.” This refers to the time it takes to progress through one complete cycle from bottom to top to bottom again. Amplitude in markets, the amount by which prices rise from bottom to top, is not easily analyzed because it varies with the volatility of the market, which in turn is based on the emotions of the market players. It is quantifiable but is not predictable. Phase is the position of the cycle in relation to other cycles and is not considered in markets. The only measure we are interested in then is the period—how long the cycle is and thus when is it due to bottom in the future.
It is best to measure stock market cycles from bottom to bottom because tops are generally rounded and bottoms are usually sharp Vs. This difference in configuration seems to be due to their different psychological backgrounds. Panic often accompanies bottoms, and panic can come very quickly to the mass psyche. Thus, market bottoms tend to be sharp and completed quickly. On the other hand, greed is the most prevalent emotion at tops, but greed takes more time to develop. Thus, tops are rarely sharp spikes but more often are rounded and at times difficult to identify even in retrospect. In economic data series, the differences in shape between tops and bottoms are less obvious. Although we might use different length moving averages to catch the tops and bottoms, in economic data it does not seem to make much difference. We therefore use the same length moving averages to hunt for tops and bottoms in economic data.
There are various ways to measure cycle periods. The easiest is to look at a ratio chart like that shown in Figure 3.4. This chart shows the ratio of the current price to its 20-day moving average. As the price oscillates around the moving average, we see definite peaks and valleys in the ratio. If these peaks and valleys appear to occur at relatively equal intervals, we likely have a cycle period in the data. In Figure 3.5, the price chart is of the DJIA on a monthly basis with a 24-month moving average, and the lower graph shows the ratio of the current price with its moving average. The four-year market cycle is readily apparent and marked with vertical dashed lines. This is the major market cycle in the stock market and the one that we should concentrate on for market timing of investments.
Figure 3.5. Ratio of monthly close to a 24-month moving average showing 4-year cycle lows (April 1986–December 2010)
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Notice in Figure 3.5 that the cycle is not perfect. Nothing is. The major declines in 1987 and 2008 did not occur at the normal four-year interval. It turns out they are part of a longer speculative cycle, but for our purposes, the four-year cycle assumption is not perfectly accurate. For this reason, as you will see in the next chapter, we use filters and stops to prevent our being hurt by unexpected events. These methods will signal us to leave the stock market despite what the fundamental and technical analysis suggests.