Weighted Moving Average (WMA)

What is the Weighted Moving Average (WMA)?

The weighted moving average (WMA) is a technical indicator that traders use to generate trade direction and make a buy or sell decision. It assigns greater weighting to recent data points and less weighting on past data points. The weighted moving average is calculated by multiplying each observation in the data set by a predetermined weighting factor.

Traders use the weighted average tool to generate trade signals. For example, when the price action moves towards or above the weighted moving average, the signal can be an indication to exit a trade. However, if the price action dips near or just below the weighted moving average, it can be an indication of a favorable time to enter a trade.

Using the weighted moving average to determine trend direction is more accurate than the simple moving average, which assigns identical weights to all numbers in the data set.

How to Calculate the Weighted Moving Average

When calculating the weighted moving average, the recent data points are assigned a greater weighting, whereas past data points are assigned less weighting. It is used when the figures in the data set come with different weights, relative to each other. The sum of the weight should be equal to 1 or 100%.

It is different from the simple moving average, where all numbers are assigned an equal weighting. The final weighted moving average value reflects the importance of each data point, and it is, therefore, more descriptive of the frequency of concurrency than the simple moving average.

Example 1

Follow the following steps when calculating weighted moving average:

1. Identify the numbers you want to average

The first step is to create a list of the numbers for which the user needs to find the weighted average. Here, we can use the closing prices of ABC stock for the period starting January 1 to January 5. The closing prices are $90, $88, $89, $90, and $91, with the first number being the most recent.

2. Determine the weights of each number

After identifying the numbers for which to calculate the weighted average, the next step is to determine the weight of each number. The equation we use for weighting each number is the day number divided by the sum of all the day numbers.  Since we are looking at five days, the sum of all the day numbers in this example is 15 (i.e., 5 + 4 + 3 + 2 + 1). We give the greatest weighting to the most recent data point, as shown in the table below:

3. Multiply each number by the weighting factor

After determining the weighting for each number, the next step is to multiply each of the numbers from January 1 to 5 by the corresponding weighting factor and then sum up the resulting values. It is shown below:

The formula for the weighted moving average is expressed as follows:

Where:

• N is the time period

4. Add up resulting values to get the weighted average

The final step is to add up the resulting values to get the weighted average for the closing prices of ABC Stock.

WMA = $30.00 + $23.47 + $17.80 + $12.00 + $6.07

WMA = $89.34

Therefore, the weighted moving average for the period from January 1 to January 5 is $89.34.

Example 2

Assume that the number of periods is 4, and we want a weighted moving average of four stock prices of $70, $66, $68, and $69, with the first price being the most recent.

Using the information given, the most recent weighting will be 4/10, the previous period before that will be 3/10, and the next period before that will be 2/10, and the initial period weighting will be 1/10. Recall that we get the denominator of 10 by adding the periods together.  In this instance, 4 + 3 + 2 + 1 = 10.

The weighting average for the four different prices will be calculated as follows:

WMA = [70 x (4/10)] + [66 x (3/10)] + [68 x (2/10)] + [69 x (1/10)]

WMA = $28.00 + $19.80 + $13.60 + $6.90 = $68.30

Simple Moving Average vs. Weighted Moving Average

Simple moving average and weighted moving average are the two widely used statistics in the world, and they are used to find the average of observations in a data set.

The main difference between the two statistical measures is that simple moving average calculates the average by summing up all the observations in a data set and dividing the total by the total number of observations. In simple terms, it applies equal weighting to all the observations in the sample.

On the other hand, weighted moving average assigns a specific weight or frequency to each observation, with the most recent observation being assigned a greater weight than those in the distant past to obtain the average.

Related Readings

Thank you for reading CFI’s guide to Weighted Moving Average. To keep learning and developing your knowledge base, please explore the additional relevant resources below:

• How To Read Stock Charts
• Kaufman’s Adaptive Moving Average (KAMA)
• Momentum Investing
• Noise Trader
• See all equities resources