Exponential Moving Average

Weighted Moving Averages are helpful for the purpose of identifying trend reversals. However, the time consuming calculations required to construct and maintain such averages prior to the widespread use of computers greatly detracted from their usefulness.

An exponential moving average (EMA) is a shortcut to obtaining a form of weighted Moving Average. In order to construct a 20­week Exponential Moving Average, it is necessary to calculate a simple 20-week Moving Average first, that is, the total of 20 weeks of observations divided by 20.

In the 20-week average becomes the starting point for the Exponential Moving Average. It is transferred to column 2 for the following week. Next, the entry for the 21st week is compared with the Exponential Moving Average, and the difference is added or subtracted; 100 - 99 = 1.00. This difference is then multiplied by the exponent, which for a 20-week Exponential Moving Average is 0.1. This exponentially treated difference, 1.00 X 0.1, is then added to the previous week's Exponential Moving Average, and the calculation is repeated each succeeding week.

If the difference between the new weekly observation and the previous week's Exponential Moving Average is negative, the exponentially treated difference is subtracted from the previous week's Exponential Moving Average.

The exponent used varies with the time span of the Moving Average. In effect, however, the exponent 0.1 can be used for any measure of 20-hours, days, weeks, months, years, or an even longer period.

Exponents for time periods can easily be calculated by dividing 2 by the time span. For example, a 5-week average will need to be twice as sensitive as a 10-week average; thus, 2 divided by 5 gives an exponent of 0.4. On the other hand, since a 20-week average should be half as sensitive as for a 10-week period (0.2), its exponent is halved to 0.1.

If an Exponential Moving Average proves to be too sensitive for the trend being monitored, one solution is to extend its time period. Another is to smooth the Exponential Moving Average by another Exponential Moving Average. This method uses an Exponential Moving Average, as calculated previously, and repeats the process using a further exponent. There is no reason why a third or fourth smoothing could not be tried, but the resulting Exponential Moving Average, while smoother, would be far less sensitive. Remember, all forms of MAs represent a compromise between timeliness and sensitivity.

By definition, Exponential Moving Average crossovers and reversals occur simultaneously. Buy and sell signals are therefore triggered in the same way as simple Moving Average crossovers.

Researcher tested all the time spans between 1- and 75-week Exponential Moving Averages for the U.S. stock market between 1968 and 1987. They discovered that the 42-week Exponential Moving Average gave the best performance, offering an equity gain of 97 + points, but lagged behind the 45-week simple Moving Average, which experienced a gain of 111 + points.