### 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.

### Key Takeaways

- The EMA is a moving average that places a greater weight and significance on the most recent data points.
- Like all moving averages, this technical indicator is used to produce buy and sell signals based on crossovers and divergences from the historical average.
- Traders often use several different EMA days, for instance, 20-day, 30-day, 90-day, and 200-day moving averages.

### The Formula For EMA Is

$\begin{aligned} &\begin{aligned} EMA_{\text{Today}}=&\left(\text{Value}_{\text{Today}}\ast\left(\frac{\text{Smoothing}}{1+\text{Days}}\right)\right)\\ &+EMA_{\text{Yesterday}}\ast\left(1-\left(\frac{\text{Smoothing}}{1+\text{Days}}\right)\right)\end{aligned}\\ &\textbf{where:}\\ &EMA=\text{Exponential moving average} \end{aligned}$

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.

### Calculating the 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.

#### Simple Vs. Exponential Moving Averages

### 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.

#### Interpreting the EMA

Like all moving average indicators, they 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 down trend. A vigilant trader will not only pay attention to the direction of the EMA line but also the relation of the rate of change from one bar to the next. For example, as the price action of a strong uptrend begins to flatten and reverse, the EMA’s rate of change from one bar to the next will begin to diminish until such time that the indicator line flattens and the rate of change is zero.

Because of the lagging effect by this point, or even a few bars before, the price action should have already reversed. It follows, therefore, that observing a consistent diminishing in the rate of change of the EMA could itself be used as an indicator that could further counter the dilemma caused by the lagging effect of moving averages.

#### Common Uses of the EMA

EMAs are commonly used in conjunction with other indicators to confirm significant market moves and to gauge their validity. For traders who trade intraday and fast-moving markets, the EMA is more applicable. Quite often, traders use EMAs to determine a trading bias. For example, if an EMA on a daily chart shows a strong upward trend, an intraday trader’s strategy may be to trade only from the long side on an intraday chart.

### The Difference Between EMA and SMA

The major difference between an exponential moving average and a simple moving average is the sensitivity each one shows to changes in the data used in its calculation.

More specifically, the EMA gives a higher weighting to recent prices, while the SMA assigns equal weighting to all values. The two averages are similar because they are interpreted in the same manner and are both commonly used by technical traders to smooth out price fluctuations. Since EMAs place a higher weighting on recent data than on older data, they are more reactive to the latest price changes than SMAs are, which makes the results from EMAs more timely and explains why the EMA is the preferred average among many traders.

### Limitations Of The EMA

It is unclear whether or not more emphasis should be placed on the most recent days in the time period or on more distant data. Many traders believe that new data will better reflect the current trend the security is moving with; meanwhile others feel that privileging certain dates than others will biases the trend. Therefore, the EMA is subject to recency bias.

Similarly, the EMA relies wholly on historical data. Many people (including economists) believe that markets are efficient - that is, 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.