What is the difference between simple and exponential moving average?

[Benjamin Schmitz]

[Sheila Olson]

Moving averages are technical indicators that show price movement over a period of time. They’re especially useful to spot trends and reversals, and to highlight trade signals. They also smooth out price movements to show more dynamic support and resistance lines. In the chart below, the 15-day simple moving average (SMA) is plotted in blue. You’ll notice that when the price is trending above the SMA, the SMA acts as support, and when price is below the SMA, it acts as resistance. The simple moving average is exactly what it sounds like—the simple unweighted average of prices over a period of time. The formula for calculating SMA is equally simple, where n represents the number of time periods being measured:

SMA = (P1+P2+P3+P4...Pn)/n

So if you want to calculate the 5-day SMA for a stock that closed at $12, $12.25, $12.10, $11.80, and $11.65, it would be $59.80/5, or $11.96. Of course, you don’t need to bother with the math because charting tools will calculate and overlay it for you. You just need to choose the SMA from the indicators menu and specify the number of days. The most common periods are 20, 50, 100, and 200, and the value plotted on the chart indicates the average price over the last x days. An exponential moving average (EMA) is a weighted moving average, where the most weight is given to the most recent price and weight decreases exponentially the further you get from the current value. The formula looks like this:

EMA = [Pclosing − previous EMA] x (2/n+1) + previous EMA

Again, you don’t need to know the math because your charting tool will calculate and plot it for you. The EMA’s value is that it is more responsive to price changes because it weights recent data. Look at the chart below; the SMA is again plotted in blue and the EMA is plotted in red. Notice that it hugs the price curves more tightly. Moving averages form the basis for several trading strategies, the most basic of which is the crossover. The crossover happens when a stock price starts on one side of the moving average and closes on the other side. This usually indicates a momentum shift, a fairly reliable trade signal. In the chart below, the price crosses over the EMA on October 8, suggesting a shift in momentum, which was borne out. Again on the 27th, the price crossed on the other side, suggesting an upward shift in momentum. Another type of crossover occurs when the short-term EMA crosses over the long-term EMA. This is generally interpreted by traders as a signal that a strong shift in momentum is coming. In the Tesla chart below, the 15-day EMA crossed the 100-day EMA on the 29th of September, signaling the start of a major reversal. It crossed over in the other direction on the 2nd of November, which again signaled the beginning of a steep and sustained uptrend. For beginning technical traders, crossovers are ideal trade signals. They are easy to spot and interpret. There is an element of emotion, psychology, and science in interpreting technical indicators; it can take a bit of practice. But the crossover patterns are straightforward and remove all emotion from the equation.