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Exponential Moving Average - EMA Definition

What is Exponential Moving Average - EMA: An exponential moving average (EMA) is a type of moving average (MA) that places a greater weight and significance on the most recent data points. The exponential moving average is also referred to as the exponentially weighted moving average. An exponentially weighted moving average reacts more significantly to recent price changes than a simple moving average (SMA), which applies an equal weight to all observations in the period.


The Formula For EMA Is

\begin{aligned} EMA_{\text{Today}}=&\left(\text{Value}_{\text{Today}}\ast\left(\frac{\text{Smoothing}}{1+\text{Days}}\right)\right)\\ &+EMA_{\text{Yesterday}}\ast\left(1-\left(\frac{\text{Smoothing}}{1+\text{Days}}\right)\right)\\ &\textbf{where:}\\ &EMA=\text{exponential moving average} \end{aligned}
The three basic steps to calculating the EMA are:
  • Calculate the SMA.
  • Calculate the multiplier for smoothing/weighting factor for the previous EMA.
  • Calculate the current EMA.


To calculate an EMA, you must first compute the simple moving average (SMA) over a particular time period. The calculation for the SMA is straightforward: it is simply the sum of the stock's closing prices for the number of time periods in question, divided by that same number of periods. So, for example, a 20-day SMA is just the sum of the closing prices for the past 20 trading days, divided by 20.
Next, you must calculate the multiplier for smoothing (weighting) the EMA, which typically follows the formula: [2 ÷ (selected time period + 1)]. So, for a 20-day moving average, the multiplier would be [2/(20+1)]= 0.0952.
Finally, to calculate the current EMA, the following formula is used: [Closing price-EMA (previous day)] x multiplier + EMA (previous day)
The EMA gives a higher weighting to recent prices, while the SMA assigns equal weighting to all values. The weighting given to the most recent price is greater for a shorter-period EMA than for a longer-period EMA. For example, an 18.18% multiplier is applied to the most recent price data for a 10-period EMA, whereas for a 20-period EMA, only a 9.52% multiplier weighting is used. There are also slight variations of the EMA arrived at by using the open, high, low or median price instead of using the closing price.
What Does The Exponential Moving Average Tell You: The 12- and 26-day exponential moving averages (EMAs) are often the most popularly quoted or analyzed short-term averages. The 12- and 26-day are used to create indicators like the moving average convergence divergence (MACD) and the percentage price oscillator (PPO). In general, the 50- and 200-day EMAs are used as signals of long-term trends. When a stock prices crosses its 200-day moving average, it is a technical indicator that a reversal has occurred.

Traders who employ technical analysis find moving averages very useful and insightful when applied correctly but create havoc when used improperly or are misinterpreted. All the moving averages commonly used in technical analysis are, by their very nature, lagging indicators. Consequently, the conclusions drawn from applying a moving average to a particular market chart should be to confirm a market move or to indicate its strength. Very often, by the time a moving average indicator line has made a change to reflect a significant move in the market, the optimal point of market entry has already passed. An EMA does serve to alleviate this dilemma to some extent. Because the EMA calculation places more weight on the latest data, it “hugs” the price action a bit more tightly and therefore reacts more quickly. This is desirable when an EMA is used to derive a trading entry signal.
Updated Apr 17, 2019

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