# Introduction to the Exponential Moving Average (EMA)

The exponential moving average of a security is a measure of its value over time with more weight given to recent changes. Exponential moving average is a slight variation from simple moving average. The simple moving average of a security compares one data point over a certain period. For example, closing price could be compared over 10 days. The simple average is the sum of the closing price over 10 days divided by 10. The exponential moving average is similar, except it weights the values of each day so more consideration is given to the most recent data.

Exponential Moving Average over Simple Moving Average

Any average index on a security is designed to show you the general region where its data lie. You may be viewing average volatility, average trading price or another factor. Finding an average is useful for many reasons. First, it can help you compare two securities; it can also help you determine if the security is approaching the limit of its previous average, which can present opportunities. However, using average alone is not as insightful as using an exponential moving average. By weighting the average, an investor or analyst can see which direction it is currently headed in.

Exponential Moving Average Example

Consider exponential moving average in common terms. You have a bank account with an average balance of \$5,000 over the past month. You need your average to be \$7,000 in order to qualify for a loan you would like to attain. The \$5,000 average may seem too low, but what if your bank account started at just \$2,000 this month? This means you recently have raised your account holdings well-beyond \$7,000, and you will likely qualify for your loan next month. Taking the exponential moving average of your account would show you the degree to which the account is trending upward, providing key insight into your position. This same principle is applied to securities analysis. The most recent data impacts your decision more than the distant data.

Applying Exponential Moving Average

Consider a real-world scenario where EMA would be useful. You would like to purchase a bond, and you would like to achieve the highest possible interest rate on that bond. The bond's current rate is 1.3 percent on a five-year note. In deciding whether you should purchase today, you consider the bond's average rate for the past six months. You find this rate is 1.1 percent, which would lead you to believe buying today is a good idea. However, when you use the exponential moving average, you realize the average rate in the past two months has been 1.5 percent, and the EMA is more like 1.4 percent. With this in mind, you may feel it is unwise to purchase the bond today. Thankfully, EMA is relatively easy to calculate. Simply apply a greater weight to the figures in recent months with this formula:

Data from month 1 + Data from month 2 (time 1.1) + Data from month 3 (1.2) and so on / Number of months

While some EMA formulae are more complicated than this simple model, they all use this principle.