Moving averages

Moving averages are popular and versatile for identifing price trends. They smooth out fluctua- tions in market prices, thereby making it easier to determine underlying trends.

Their other function is to signal significant changes in direction as early as possible.

The simple moving average is the most widely used. Its calculation is shown above in mathemati- cal form and displayed in the chart on the right. For a 5-day moving average, you simply add the closing prices of the last five closings and divide this sum by 5. You add each new closing and skip the oldest. Thus, the sum of closings always re- mains constant at 5 days.

Whether you choose a 10-day average o r a 40- week average, the calculation is the same; instead

of adding five days, you add 10 days or 40 weeks and divide the sum by 10 or 40, respectively.

In most of our research, we use the moving average length out of the Fibonacci series (see page 29). To analyse the short-term trend, we use the 13-day and 21-day averages. For the medium-term  trend, we use the 34-day and 55-day averages. For the long-term trend, we use the 89-day and 144- day averages. Moreover, we also analyze very long-term trends, the so-called secular trends with the 233-day, 377-day, 610-day and 987-day moving averages.

The simple moving average (SMA)

The simple moving average yields the mean of a data set for a given period. For example: a  21- day simple moving average (SMA) would include the last 21 days of data divided by 21, resulting in an average (see chart above for the Dow Industrial Index). This can be calculated at any given time using the last 21 days; hence, the average moves forward with each trading day. The moving average is usually plotted on the same chart as price movements, so a change in direction of trend can be indicated by the penetration/crossover of the SMA. Generally a buy signal is generated when a price breaks above the moving average and a sell signal is generated by a price break below the moving average. It is added confirmation when the moving average line turns in the direction of the price trend.

The moving average naturally lags behind price movement, and the extent by which it lags (or its sensitivity) is a function of the time span. Generally, the shorter the moving average, the more sensitive it is. A 5-day moving average will react more quickly to a change in price than the 21-day moving average, for example. However,  the 5-day moving average is more likely   to give false signals and “whipsaw” than the 21-day one, which gives signals later and suffers from opportunity loss.

Generally, if the market is trending (in an uptrend or downtrend), a longer time period would be used. If it is ranging (consolidating), the shorter time frame will catch the minor moves more easily. Moving averages can act as support and resistance (as shown by the arrows on the chart above for the Dow Jones Industrial Index), similar to the support and resistance dis- cussed on pages 8 and 9.

Long-term, medium-term and short-term averages

We incorporate two basic moving averages to track the three investment horizons as discussed on page 10. They are shown on the three charts on this page.

On the monthly chart above, the 13-month and 21-month moving averages track the long-term trend.

On the weekly chart above, the 13-week and 21- week moving averages track the medium-term trend.

On the daily chart to the right, the 13-day and 21- day moving averages track the short-term trend. The direction of the moving averages indicates the direction of the three basic trends in force.

Instead of showing the moving averages on three separate charts to illustrate the three basic trends, we more often display all moving averages on a single daily chart. This is shown on the next page. The long-term moving average is not shown on the monthly chart, but on the daily chart. The medium-term moving average is also shown on the daily chart instead of the weekly chart.

Moving average crossover

The short-term, medium-term and long-term moving averages are all shown here on the daily chart. The 21-day moving average is shown here for the short-term trend, the 55-day moving average for the medium-term trend and the 144-day moving average for the long-term trend. Displaying the three moving averages on one single chart provides important signals based on the moving average trends and crossovers.

BUY and SELL signals are given

• when the price crosses the moving average
• when the moving average itself changes direction

and

• when the moving averages cross each other

A short-term (trading) buy signal (B1) is given when the price rises above the 21-day moving average. The buy signal is confirmed when the 21-day average itself starts rising. A short-term (trading) sell signal (S1) is given in the opposite direction.

A medium-term (tactical) buy signal (B2) is given when the price breaks above the 55-day moving average. It is confirmed when the 21-day average crosses above the 55-day average and the 55-day average itself starts rising. A medium-term (tactical) sell signal (S2) is given in the opposite direction. A long-term (strategic) buy signal (B3) is given when the price rises above the 144-day moving aver- age. It is confirmed when the 55-day average crosses above the 144-day moving average and the 144-day average itself starts rising. A long-term (strategic) sell signal (S3) is given in the opposite direction.