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## Thursday, September 22, 2011

### Exponential Moving Average (EMA)

n order to reduce the lag in simple moving averages, technicians often use exponential moving averages (also called exponentially weighted moving averages). EMA’s reduce the lag by applying more weight to recent prices relative to older prices. The weighting applied to the most recent price depends on the specified period of the moving average. The shorter the EMA’s period, the more weight that will be applied to the most recent price. For example: a 10-period exponential moving average weighs the most recent price 18.18% while a 20-period EMA weighs the most recent price 9.52%. As we’ll see, the calculating and EMA is much harder than calculating an SMA. The important thing to remember is that the exponential moving average puts more weight on recent prices. As such, it will react quicker to recent price changes than a simple moving average.

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 it’s 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:

(2 / (Time periods + 1) ) = (2 / (10 + 1) ) = 0.1818 (18.18%)
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:

(C – P) = (57.15 – 59.439) = -2.289
(C – P) x K = -2.289 x .181818 = -0.4162
( (C – P) x K) + P = -0.4162 + 59.439 = 59.023

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

Note that, in theory, every previous closing price in the data set is used in the calculation of each EMA that makes up the EMA line. While the impact of older data points diminishes over time, it never fully disappears. This is true regardless of the EMA’s specified period. The effects of older data diminish rapidly for shorter EMA’s. than for longer ones but, again, they never completely disappear.