What is EMA? How to use exponential moving average with formula

What is an exponential moving average (EMA)?

An exponential moving average (EMA) is a type of moving average (MA) that places 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 simple moving average (SMA), which applies an equal weight to all observations in the period.

Exponential Moving Average (EMA) Formula



EMA Today = ( Value Today ∗ ( Smoothing 1 + Days ) ) where: \begin{aligned} &\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)\end{align}\\ &\textbf{true:}\\ &EMA=\text{Exponential moving average} \end{align}

,EmAToday,=,(ValueToday,∗(1+DaysSmoothing,)),where:,

Although there are many possible choices for the smoothing factor, the most common choice is:

This gives the most recent observation more weight. If the smoothing factor is increased, more recent observations have more influence on the EMO.

Calculation of the EMA

The calculation of the EMA requires one more observation than the SMA. Suppose you want to use 20 days as the number of observations for the EMA. Then you have to wait until the 20th day to obtain the SMA. On the 21st day you can then use the SMA from the previous day as the first EMA for yesterday.

The calculation for the SMA is simple. It is simply the sum of the stock’s closing prices during a period, divided by the number of observations for that period. 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 need to calculate the multiplier to smooth the EMA (weight), which typically follows the formula: [2 ÷ (number of observations + 1)]. For a 20-day moving average, the multiplier would be [2/(20+1)]= 0.0952.

Finally, the following formula is used to calculate the current EMA:

EMA = Closing price x multiplier + EMA (previous day) x (1 multiplier)

The EMA gives a higher weight to recent prices, while the SMA assigns equal weight to all values. The weight given to the most recent price is greater for a shorter period EMA than for a longer period EMA. For example, a multiplier of 18.18% is applied to the most recent price data for a 10-period EMA, while the weight is only 9.52% for a 20-period EMA.

There are also slight variations of the EMA that are achieved by using the open, high, low or median price instead of using the close price.

What does the EMA tell you?

The 12- and 26-day exponential moving averages (EMAs) are often the most quoted and analyzed short-term averages. The 12 and 26 days are used to create indicators such as the moving average convergence divergence (MACD) and the percentage price oscillator (PPO). Generally, the 50- and 200-day EMAs are used as long-term trend indicators. When a stock price crosses its 200-day moving average, it is a technical signal that a reversal has occurred.

Traders using technical analysis find moving averages very useful and informative when applied correctly. However, they also realize that these signals can wreak havoc when misused or misinterpreted. All the moving averages commonly used in technical analysis are lagging indicators.

Hence, the conclusions drawn from applying a moving average to a specific market chart should be to confirm a market move or indicate its strength. The optimal time to enter the market often passes before a moving average shows that the trend has changed.

An EMO does serve to mitigate the negative impact of delays to some extent. Because the EMA calculation puts more weight on the latest data, it “hugs” the price action a bit more and reacts more quickly. This is desirable when using an EMA to derive a trade entry signal.

Like all moving average indicators, EMAs are much better suited for trending markets. When the market is in a strong and sustained uptrend, the EMA indicator line will also show an uptrend and vice versa for a downtrend. An alert trader will pay attention to both the direction of the EMA line and the ratio of the rate of change from one bar to the next. For example, suppose the price action of a strong uptrend begins to flatten and reverse. From an opportunity cost standpoint, it may be time to switch to a more bullish investment.

Examples of how to use the EMA

EMAs are commonly used in conjunction with other indicators to confirm significant market movements and determine their validity. For traders trading intraday and fast moving markets, the EMA is more applicable. Very often, traders use EMAs to determine a trading bias. If an EMA on a daily chart shows a strong uptrend, an intraday trader’s strategy may be to trade only on the long side.

The difference between EMA and SMA

The major difference between an EMA and an SMA is the sensitivity each shows to changes in the data used in its calculation.

More specifically, the EMA gives higher weights to recent prices, while the SMA assigns equal weights to all values. The two averages are similar in that they are interpreted in the same way and are both commonly used by technical traders to iron out price fluctuations.

Since EMAs place a higher weight on recent data than on older data, they are more responsive to the latest price changes than SMAs. This makes the results of EMAs more timely and explains why they are preferred by many traders.

Limitations of the EMA

It is unclear whether more emphasis should be placed on the most recent days in the period or not. Many traders believe that new data better reflects the current trend of the security. At the same time, others feel that overweighting recent dates creates a bias that leads to more false alarms.

Likewise, the EMA relies entirely on historical data. Many economists believe that markets are efficient, meaning that current market prices already reflect all available information. If markets are indeed efficient, using historical data should tell us nothing about the future direction of asset prices.