### Moving Average: Holy Grail or Fairy Tale - Part 1

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Buying and holding a diversified portfolio works well during good times, but falls short when supposedly uncorrelated asset classes drop in unison in bear markets. Are there alternative investment strategies that work for all seasons? The 10-month *Moving Average Crossover *(MAC) system is a solid candidate, as it sidestepped two recent bear markets in 2000 and 2008. But did it work in previous bear markets? Is 10 months the optimum length?

Let’s examine historical evidence to find out if MAC is the Holy Grail or just a fairy tale.

### Background

Electrical engineers routinely use moving average as a *low-pass filter* in analog and digital signal processing. It blocks transient perturbations from the input and only allows the core signals to pass, hence the term *low-pass filter*. Transient perturbation is a fancy name for short-lived popcorn noise that obscures the underlying signal.

Random spikes in an otherwise smooth signal are undesirable. We can reduce the amplitude of these noisy spikes by averaging the values of the data points neighboring on either side of the spike. *Figure 1 *shows how the filtered output closely tracks the original signal but the unwanted spikes are attenuated. The degree of noise suppression depends on the number of points used in the averaging. The longer the averaging period, the smoother the output. Because we can’t predict when random spikes will appear, we slide the filter block across the entire data stream from start to finish. The term *moving average *literally describes this function.

As an engineer, I have always been skeptical of the way stock market technicians plot MA curves. Traditionally, engineers align the midpoint of the MA curve with the center of the original data curve. This way, the MA curve is centered with respect to the original time series as shown by the red curve in *Figure 2*. Technicians, on the other hand, shift the end of the MA curve to match the most recent price point as shown by the blue curve in *Figure 2*. The lag between the original data curve and the shifted MA curve created by this peculiar plotting convention is the core of the MAC system. Without shifting the MA, there is no lag. Without the lag, there is no crossover.

### The Moving Average Crossover system

MAC is the simplest and probably the oldest trading system. You buy when the price rises above its moving average, and you sell when it drops below. Although there are several forms of moving averages, I prefer the* Exponential Moving Average (EMA)* to the *Simple Moving Average (SMA) *because EMA gives slightly smaller lag.