Moving Average (MA)

A moving average (MA) is a widely used indicator in technical analysis that helps smooth out price action by filtering out the “noise” from random short-term price fluctuations. It is a trend-following, or lagging, indicator because it is based on past prices.

The two basic and commonly used moving averages are the simple moving average (SMA), which is the simple average of a security over a defined number of time periods, and the exponential moving average (EMA), which gives greater weight to more recent prices. The most common applications of moving averages are to identify the trend direction, and to determine support and resistance levels. While moving averages are useful enough on their own, they also form the basis for other technical indicators such as the Moving Average Convergence Divergence (MACD).

Because we have extensive definitions and articles around specific types of moving averages, we will only define the term "moving average" generally here.

Simple Moving Average:

$\begin{aligned} &SMA = \frac{A_1 + A_2 + \dotso + A_n}{n} \\ &\textbf{where:}\\ &A=\text{average in period }n\\ &n=\text{number of time periods}\\ \end{aligned}$​SMA=nA1​+A2​+…+An​​where:A=average in period nn=number of time periods​

The simple moving average calculates the arithmetic mean of a security over a number (n) of time periods, A.

Exponential Moving Average:

$\begin{aligned} &EMA_{\text{today}} = [\text{Value}_{\text{today}}\times (\frac{\text{s}}{1 + d})] + EMA_{\text{yesterday}}\times [1 - (\frac{\text{s}}{1 + d})] \\ &\textbf{where:}\\ &s=\text{smoothing}\\ &d=\text{number of days}\\ \end{aligned}$​EMAtoday​=[Valuetoday​×(1+ds​)]+EMAyesterday​×[1−(1+ds​)]where:s=smoothingd=number of days​

To calculate an EMA, you must first compute the simple moving average (SMA) over a particular time period. Next, you must calculate the multiplier for weighting the EMA (the smoothing), 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. Then you use the smoothing factor combined with the previous EMA to arrive at the current value. The EMA therefore gives a higher weighting to recent prices, while the SMA assigns equal weighting to all values.

A moving average (MA) is calculated in different ways depending on its type.

Let's look at a simple moving average (SMA) of a security with the following closing prices over 15 days:

Week 1 (5 days) – 20, 22, 24, 25, 23

Week 2 (5 days) – 26, 28, 26, 29, 27

Week 3 (5 days) – 28, 30, 27, 29, 28

A 10-day moving average would average out the closing prices for the first 10 days as the first data point. The next data point would drop the earliest price, add the price on day 11 and take the average, and so on as shown below.

Moving averages lag current price action because they are based on past prices; the longer the time period for the moving average, the greater the lag. Thus, a 200-day MA will have a much greater degree of lag than a 20-day MA because it contains prices for the past 200 days. The length of the moving average to use depends on the trading objectives, with shorter moving averages used for short-term trading and longer-term moving averages more suited for long-term investors. The 50-day and 200-day MAs are widely followed by investors and traders, with breaks above and below this moving average considered to be important trading signals.

Moving averages also impart important trading signals on their own, or when two averages cross over. A rising moving average indicates that the security is in an uptrend, while a declining moving average indicates that it is in a downtrend. Similarly, upward momentum is confirmed with a bullish crossover, which occurs when a short-term moving average crosses above a longer-term moving average. Downward momentum is confirmed with a bearish crossover, which occurs when a short-term moving average crosses below a longer-term moving average.

Predicting trends in the stock market is no simple process. While you can not predict what will happen exactly, you can give yourself better odds using technical analysis and research. Putting your research and technical analysis to the test in the market would require a brokerage account. Picking a broker can be frustrating due to the variety among them, but you can pick one of the best online stockbrokers to find the right platform for your needs.