Simple Moving Average (SMA): What It Is and the Formula

What Is a Simple Moving Average (SMA)?

A simple moving average (SMA) calculates the average price of an asset, usually using closing prices, during a specified period of days.

Understanding Simple Moving Average (SMA)

A simple moving average (SMA) is an arithmetic moving average calculated by adding recent prices and then dividing that figure by the number of time periods in the calculation average. For example, one could add the closing price of a security for a number of time periods and then divide this total by that same number of periods. Short-term averages respond quickly to changes in the price of the underlying security, while long-term averages are slower to react. There are other types of moving averages, including the exponential moving average (EMA) and the weighted moving average (WMA).

The formula for SMA is:

$\begin{aligned} &\text{SMA}=\dfrac{A_1 + A_2 + ... + A_n}{n} \\ &\textbf{where:}\\ &A_n=\text{the price of an asset at period } n\\ &n=\text{the number of total periods}\\ \end{aligned}$​SMA=nA1​+A2​+...+An​​where:An​=the price of an asset at period nn=the number of total periods​

For example, this is how you would calculate the simple moving average of a security with the following closing prices over a 15-day period.

Week One (5 days): 20, 22, 24, 25, 23

Week Two (5 days): 26, 28, 26, 29, 27

Week Three (5 days): 28, 30, 27, 29, 28

20 + 22 + 24 + 25 + 23 + 26 + 28 + 26 + 29 + 27 + 28 + 30 + 27 + 29 + 28 = 392

392 / 15 = 26.13

The 15-day simple moving average for this security would be $26.13.

A 10-day moving average would average out the closing prices only the most recent 10 days rather than using all 15. Each day when the stock market closes, there is a new most recent closing price. This replaces the oldest one being used, and a new, up-to-date moving average is calculated. A 50-day moving average would use 50 days worth of data to compute the average price on a rolling basis.

A simple moving average is customizable because it can be calculated for different numbers of time periods. This is done by adding the closing price of the security for a number of time periods and then dividing this total by the number of time periods, which gives the average price of the security over the time period.

A simple moving average smooths out volatility and makes it easier to view the price trend of a security. If the simple moving average points up, this means that the security's price is increasing. If it is pointing down, it means that the security's price is decreasing. The longer the time frame for the moving average, the smoother the simple moving average. A shorter-term moving average is more volatile, but its reading is closer to the source data.

Special Considerations

Analytical Significance

Moving averages are an important analytical tool used to identify current price trends and the potential for a change in an established trend. The simplest use of an SMA in technical analysis is using it to quickly determine if an asset is in an uptrend or downtrend.

Another popular, albeit slightly more complex, analytical use is to compare a pair of simple moving averages with each covering different time frames. If a shorter-term simple moving average is above a longer-term average, an uptrend is expected. On the other hand, if the long-term average is above a shorter-term average then a downtrend might be the expected outcome.

Popular Trading Patterns

Two popular trading patterns that use simple moving averages include the death cross and a golden cross. A death cross occurs when the 50-day SMA crosses below the 200-day SMA. This is considered a bearish signal, indicating that further losses are in store. The golden cross occurs when a short-term SMA breaks above a long-term SMA. Reinforced by high trading volumes, this can signal further gains are in store.

Simple Moving Average vs. Exponential Moving Average

In contrasting an exponential moving average (EMA) and a simple moving average the major difference 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 an 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 Simple Moving Average

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. At the same time, other traders feel that privileging certain dates over others will bias the trend. Therefore, the SMA may rely too heavily on outdated data since it treats the 10th or 200th day's impact the same as the first or second day's.

Similarly, the SMA relies wholly on historical data. Many people (including some economists) believe that markets are efficient. This is known as the efficient market hypothesis. It holds 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. There are some economic and financial thinkers who support this hypothesis, and plenty of others who oppose it.