Overview

A Moving Average is an indicator that shows the average value of a security’s price over a period of time. When calculating a

moving average, a mathematical analysis of the security’s average value over a predetermined time period is made. As

the security’s price changes, its average price moves up or down.There are five popular types of moving averages: simple (also

referred to as arithmetic), exponential, triangular, variable, and weighted. Moving averages can be calculated on any data

series including a security’s open, high, low, close, volume, or another indicator. A moving average of another moving

average is also common.The only significant difference between the various types of moving averages is the weight assigned to the most recent data. Simple moving averages apply equal weight to the prices. Exponential and weighted averages apply more weight

to recent prices. Triangular averages apply more weight to prices in the middle of the time period. And variable moving

averages change the weighting based on the volatility of prices.

Interpretation

The most popular method of interpreting a moving average is to compare the relationship between a moving average of the

security’s price with the security’s price itself. A buy signal is generated when the security’s price rises above its moving average and a sell signal is generated when the security’s price falls below its moving average.The following chart shows the Dow Jones Industrial Average (“DJIA”) from 1970 through 1993.

This type of moving average trading system is not intended to get you in at the exact bottom nor out at the exact top. Rather,

it is designed to keep you in line with the security’s price trend by buying shortly after the security’s price bottoms and selling

shortly after it tops.

The critical element in a moving average is the number of time periods used in calculating the average. When using hindsight,

you can always find a moving average that would have been profitable (using a computer, I found that the optimum number

of months in the preceding chart would have been 43). The key is to find a moving average that will be consistently profitable.

The most popular moving average is the 39-week (or 200-day) moving average. This moving average has an excellent track

record in timing the major (long-term) market cycles.

The length of a moving average should fit the market cycle you wish to follow. For example if you determine that a security has

a 40-day peak to peak cycle, the ideal moving average length would be 21 days calculated using the following formula:

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Trend Moving Average

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Very Short Term 5-13 days

Short Term 14-25 days

Minor Intermediate 26-49 days

Intermediate 50-100 days

Long Term 100-200 days

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You can convert a daily moving average quantity into a weekly moving average quantity by dividing the number of days by 5

(e.g., a 200-day moving average is almost identical to a 40-week moving average). To convert a daily moving average

quantity into a monthly quantity, divide the number of days by 21 (e.g., a 200-day moving average is very similar to a 9-

month moving average, because there are approximately 21 trading days in a month).Moving averages can also be calculated and plotted on indicators. The interpretation of an indicator’s moving average is similar to the interpretation of a security’s moving average:

when the indicator rises above its moving average, it signifies a continued upward movement by the indicator; when the

indicator falls below its moving average, it signifies a continued downward movement by the indicator.

Indicators which are especially well-suited for use with moving average penetration systems include the MACD, Price ROC,

Momentum, and Stochastics.Some indicators, such as short-term Stochastics, fluctuate so erratically that it is difficult to tell what their trend really is. By erasing the indicator and then plotting a moving average of the indica-tor, you can see the general trend of the indicator rather than its day-to-day fluctuations.

Whipsaws can be reduced, at the expense of slightly later signals, by plotting a short-term moving average (e.g., 2-10

day) of oscillating indicators such as the 12-day ROC, Stochas-tics, or the RSI. For example, rather than selling when the

Stochastic Oscillator falls below 80, you might sell only when a 5-period moving average of the Stochastic Oscillator falls

below 80.

Example

The following chart shows Lincoln National and its 39-week exponential moving average.

Although the moving average does not pinpoint the tops and bottoms perfectly, it does provide a good indication of the

direction prices are trending.

Calculation

The following sections explain how to calculate moving averages of a security’s price using the various calculation

techniques.

Simple

A simple, or arithmetic, moving average is calculated by adding the closing price of the security for a number of time periods

(e.g., 12 days) and then dividing this total by the number of time periods. The result is the average price of the security

over the time period. Simple moving averages give equal weight to each daily price.

For example, to calculate a 21-day moving average of IBM: First, you would add IBM’s closing prices for the most recent

21 days. Next, you would divide that sum by 21; this would give you the average price of IBM over the preceding 21 days.

You would plot this average price on the chart. You would perform the same calculation tomorrow: add up the previous

21 days’ closing prices, divide by 21, and plot the resulting figure on the chart.

Where:

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