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## Thursday, January 13, 2011

### MOVING AVERAGES

Moving averages are one of the most popular and easy to use tools available to the technical analyst. They smooth a data series and make it easier to spot trends, something that is especially helpful in volatile markets. They also form the building blocks for many other technical indicators and overlays.
The two most popular types of moving averages are the Simple Moving Average (SMA) and the Exponential Moving Average (EMA). They are described in more detail below.
Simple Moving Average (SMA)
A simple moving average is formed by computing the average (mean) price of a security over a specified number of periods. While it is possible to create moving averages from the Open, the High, and the Low data points, most moving averages are created using the closing price. For example: a 5-day simple moving average is calculated by adding the closing prices for the last 5 days and dividing the total by 5.
(10+ 11 + 12 + 13 + 14 = 60) ( (60 / 5) = 12)
The calculation is repeated for each price bar on the chart. The averages are then joined to form a smooth curving line – the moving average line. Continuing our example, if the next closing price in the average is 15, then this new period would be added and the oldest day, which is 10, would be dropped. The new 5-day simple moving average would be calculated as follows:
(11 + 12 + 13 + 14 +15 = 65) ( (65 / 5) = 13)
Over the last 2 days, the SMA moved from 12 to 13. As new days are added, the old days will be subtracted and the moving average will continue to move over time. In this example , using closing prices , day 10 is the first day possible to calculate a 10-day simple moving average. As the calculation continues, the newest day is added and the oldest day is subtracted. The 10-day SMA for day 11 is calculated by adding the prices of day 2 through day 11 and dividing by 10. The averaging process then moves on to the next day where the 10-day SMA for day 12 is calculated by adding the prices of day 3 through day 12 and dividing by 10.The chart above is a plot that contains the data sequence in the table. The simple moving average begins on day 10 and continues.
This simple illustration highlights the fact that all moving averages are lagging indicators and will always be “behind” the price. The price is trending down, but the simple moving average, which is based on the previous 10 days of data, remains above the price. If the price were rising, the SMA would most likely be below. Because moving averages are lagging indicators, they fit in the category of trend following indicators. When prices are trending, moving averages work well. However, when prices are not trending, moving averages can give misleading signals.
Exponential Moving Average Calculation:
Exponential Moving Averages can be specified in two ways – as a percent-based EMA or as a period-based EMA. A percent-based EMA has a percentage as its single parameter while a period-based EMA has a parameter that represents the duration of the EMA.
The formula for an exponential moving average is:
EMA(current) = ( (Price(current) – EMA(prev) ) x Multiplier) + EMA(prev)
For a percentage-based EMA, “Multiplier” is equal to the EMA’s specified percentage.
For a period-based EMA, “Multiplier” is equal to 2 / (1 + N) where N is the specified number of periods.
For example, a 10-period EMA’s Multiplier is calculated like this:
This means that a 10-period EMA is equivalent to an 18.18% EMA.
Below is a table with the results of an exponential moving average calculation for Eastman Kodak. For the first period’s exponential moving average, the simple moving average was used as the previous period’s exponential moving average (yellow highlight for the 10th period). From period 11 onward, the previous period’s EMA was used. The calculation in period 11 breaks down as follows:
1. (C – P) = (61.33 – 63.682) = -2.352
2. (C – P) x K = -2.352 x .181818 = -0.4276
3. ((C – P) x K) + P = -0.4276 + 63.682 = 63.254

The 10-period simple moving average is used for the first calculation only. After that the previous period’s EMA is used.