Exponential Moving Average

What is Exponential Moving Average?

An Exponential Moving Average (EMA) assigns a weighting factor to each value in the data series according to its age. Here, too, the most recent data gets the greatest weight and each price value gets a smaller weight as we go back in the series chronologically. The weight of each data point decreases exponentially, hence the name.

First, calculate the simple moving average. An exponential moving average (EMA) has to start somewhere so a simple moving average is used as the previous period's EMA in the first calculation. Second, calculate the weighting multiplier. Third, calculate the exponential moving average. The formula below is for a 10-day EMA.

SMA: 10 period sum / 10 

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

EMA: {Close - EMA(previous day)} x multiplier + EMA(previous day). 

Significance of EMA

Critics of the simple moving average argue that it is too simple in the sense that it gives the same weight to each point in moving average calculation. The problem with this it is argued is that the more recent data points deserve a greater weighting in the formula as they are more relevant to the future price action of the instrument. 

To solve this problem traders came up with the exponential moving average, which gives more weight to the more recent price points in calculating the moving average line.

Calculation

To Calculate an EMA


Current EMA= ((Price(current) - previous EMA)) X multiplier) + previous EMA. 

 The most important factor is the smoothing constant that = 2/(1+N) where N = the number of days. 


 A 10-day EMA = 2/( 10+1) = 18.8


 This means a 10-period EMA weights the most recent price 18.8%, a 20-day EMA 9.52 % and 50-day EMA 3.92% weight on the most recent day. The EMA works by weighting the difference between the current period's price and the previous EMA, and adding the result to the previous EMA. The shorter the period, the more weight applied to the most recent price.

With the EMA the calculation is a bit more complex in that it weighs the different closing prices within the moving average range. The EMA gives more weight to prices near the end of the range and less to those prices in the beginning of the range. This gives more influence to the current market activities of the stock. 

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