Calculation and Theory of EMA

EXPONENTIAL MOVING AVERAGE

As we had elucidated earlier, Exponential Moving Averages basically reduces the lag in simple moving averages and gives more weightage to the most recent data. The shorter the exponential moving average the more weight that will be applied to the more recent prices of a data or security. For example : a 7?period exponential moving average weighs the most recent price 25 % and a 20-period exponential moving average weighs the most recent price 9.52 % and a 100-period exponential moving average weighs the most recent price 1.98 %. One thing is very clear that exponential moving average puts more weightage on the more centr prices and shall react quicker to recent price fluctuations as compared to a simple moving average.

Calculation of Exponential Moving Average

The formula for an exponential moving average is:

X = (K x (P – S)) + S

X = Current EMA
P = Current Price
S = Previous period’s EMA #
K = Exponent or the Smoothing constant
( # For the first period’s calculation a Simple Moving Average is considered)

The Exponent or smoothing constant applies the appropriate weightage to the most recent price relative to the previous exponential moving average. The formula for the same is :

K = 2/(1+n)
n = Number of periods for EMA

For a 7-period EMA, the smoothing constant would be .25.

K = 2 / (1+7) = 2 / 8 = 0.25

The EMA formula works by weighting the difference between the current period’s price and the previous period’s EMA and adding the result to the previous period’s EMA.

Hence if the current price (P) is higher than the previous period’s EMA (S) then the constant K is applied to the difference giving a positive figure and added to the previous period’s EMA (S) thus resulting into increasing EMA for the day.

Similarly, if the current price (P) is lower than the previous period’s EMA (S) then the constant K