Exponential Moving Average

Calculation and Theory of EMA

The Exponential Moving Average

The Exponential Moving Average differs from a Simple Moving Average both by calculation method and in the way that prices are weighted. The Exponential Moving Average (shortened to the initials EMA) is effectively a weighted moving average. With the EMA, the weighting is such that the recent days' prices are given more weight than older prices. The theory behind this is that more recent prices are considered to be more important than older prices, particularly as a long-term simple average (for example a 200 day) places equal weight on price data that is over 6 months old and could be thought of as slightly out-of-date.

Calculation of the EMA is a little more complex than the Simple Moving Average but has the advantage that a large record of data covering each and every closing price for the last 200 days (or however many days are being considered) does not have to be kept. All you need are the EMA for the previous day and today's closing price to calculate the new Exponential Moving Average.

Calculating the Exponent

Initially, for the EMA, an exponent needs to be calculated. To start, take the number of days' EMA that you want to calculate and add one to the number of days that you're considering (for example for a 200 day moving average, add one to get 201 as part of the calculation). We'll call this Days+1.

Then, to get the Exponent, simply take the number 2 and divide it by Days+1. For example the Exponent for a 200 day moving average would be:

Which equals 0.01

Full Calculation if the Exponential Moving Average

Once we've got the exponent, all we need now are two more bits of information to enable us to perform the full calculation. The first is yesterday's Exponential Moving Average. We'll assume we already know this as we would have calculated it "yesterday". However, if you aren't already aware of yesterday's EMA, you can start by calculating the Simple Moving Average for yesterday, and using this in place of the EMA for the first calculation (ie "today's" calculation) of the EMA. Then tomorrow you can use the EMA you calculated today, and so on...

The second piece of information we need is today's closing price. Let's assume that we want to calculate today's 200 day Exponential Moving Average for a share or stock which has a previous day's EMA of 120 pence (or cents) and a current day's closing price of 136 pence.

The full calculation is always as follows:
Today's Exponential Moving Average=(current day's closing price x Exponent) + (previous day's EMA x (1-Exponent))

So, using our example figures above, today's 200 day EMA would be:
(136 x 0.01) + (120 x (1-0.01))
Which equals an EMA for today of 120.16.

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