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You have likely encountered average or averaging when learning about trading and investing. The moving average, one of the simplest and most common trading indicators, uses the idea of averaging.
If you have paid attention to your math classes, you should know how to calculate the average. However, the traditional average has its weaknesses. To offset these weaknesses, the concept of the weighted average was developed.
So, what is a weighted average? What makes it different? And, is it useful? You will learn the answers to these questions and more in this article.
What Does the Weighted Average Mean?
The weighted average is the average value of a particular set of numbers, with different levels of relevance assigned to each number.
Simple Weighted Average Formula
where is the relative weight (as a percentage), and is the number.
It’s best to start with the traditional average to understand the weighted average better. With a traditional average, you add multiple data points and divide them equally. The weighted average is different because it places more importance on one or more data points. As a result, your final calculation will differ from a traditional average, as the weighted average will put more “weight” on pre-determined data points.
Calculating the weighted average is also different from calculating the traditional average. With a traditional average, the first step is to add all the data points. With a weighted average, the first step is multiplying each data point by its assigned weight. After obtaining the product for all the data points, you divide these products by the sum of the weights.
The assigned weight is arbitrary and largely depends on who is doing the calculation. However, the result is the same: one or more data points will impact the overall average more.
Why Use Weighted Average?
There are plenty of instances where the weighted average is better than the traditional average. One of the most common reasons for its use is to get a more accurate picture of the data set.
For example, if you want to know the average price of a stock over one year to predict its future price, you might start by noting the price at the end of each month. So, in total, you have twelve data points.
However, you might think the December price should be more critical than the January price because it’s more recent. By placing more importance on the more recent data points, you might predict the price movement more accurately. In this specific case, you’ll need to use a weighted average. You assign a more significant weight to the recent prices and a smaller weight to the earlier prices. As a result, your average is weighted towards the recent prices.
Remember that the scenario above is just an example and not a guaranteed method. There is already an indicator for such a scenario called the weighted moving average. The weighted average has other applications, such as in a stock portfolio.
Weighted Average in Stock Portfolio
It is typical for investors to buy the same stock multiple times over many years. It can be challenging to keep track of the cost of shares and how much their value has changed.
One way to solve this problem is by calculating the weighted average to get a clearer picture of the average purchase costs for a specific stock. To do this, note the number of shares and the stock price at the purchase time. Then, multiply the two together. Repeat the process for each time you buy the stock. Then, add all the products and divide by the total shares. You will arrive at a number that represents the weighted average stock cost.
Weighted Average Example 1:
An investor buys 100 shares at $10. After a year, the investor buys another 50 shares at $40 of the same stock. To get the weighted average stock price, multiply 100 shares by $10 and 50 by $40. Add the two results to get $3,000. The last step is to divide $3,000 by the total number of shares, which is 150. The weighted average stock price is $20.
Weighted Average Example 2:
Weighted Average Growth Calculation and Weighted Average Rate of Return:
- Total initial investment: $30,000
- 5% growth on $20,000: $21,000
- 15% growth on $10,000: $11,500
- Combined value after one year: $32,500
The weighted average rate of return is 8.33%.
Applications of Weighted Average
The weighted average has various applications across different fields:
1. Finance and Investing:
In finance and investing, the weighted average calculates the average cost of shares purchased at different times and prices. It helps investors understand the actual cost basis of their investments.
2. Academic Grading:
In education, weighted averages are used to calculate final grades when different assignments, tests, and projects are of different importance. For example, a final exam might be heavier than homework assignments.
3. Project Management:
In project management, the weighted average can calculate the expected time or cost to complete a project. Different tasks may have different levels of importance or risk, and the weighted average helps to account for these differences.
4. Economic Indicators:
Economic indicators, such as inflation rates and GDP growth, often use weighted averages to account for the varying importance of different economic sectors or components.
5. Business Decision Making:
In business, weighted averages can be used in decision-making processes, such as evaluating the performance of different products or services. By assigning weights to different factors, businesses can make more informed decisions.
Advantages and Disadvantages of Weighted Average
Advantages:
- More Accurate Representation: The weighted average provides a more accurate representation of a data set by giving more importance to specific data points.
- Flexibility: The weights can be adjusted based on the relevance or importance of each data point, providing flexibility in calculations.
- Better Decision Making: By using weighted averages, investors and businesses can make better-informed decisions based on a more accurate data analysis.
- Mitigates Outliers: Weighted averages can mitigate the impact of outliers or extreme values in a data set, leading to a more balanced result.
Disadvantages:
- Complexity: Calculating weighted averages can be more complex and time-consuming than traditional averages.
- Subjectivity: The assignment of weights can be subjective and may vary depending on who is performing the calculation, leading to inconsistencies.
- Requires More Data: Weighted averages require more detailed data, including the weights for each data point, which may not always be readily available.
Conclusion
The weighted average is a variation of the traditional average, allowing one or more data points to impact the final average result significantly. It has numerous applications, from trading indicators to stock portfolio management, academic grading, project management, and business decision-making. By understanding the concept and application of weighted averages, individuals and businesses can make more accurate and informed decisions. While it has advantages and disadvantages, the weighted average remains a valuable tool in various fields, providing a more accurate representation of data sets with varying levels of importance.
He is an expert in financial niche, long-term trading, and weekly technical levels.
The primary field of Igor's research is the application of machine learning in algorithmic trading.
Education: Computer Engineering and Ph.D. in machine learning.
Igor regularly publishes trading-related videos on the Fxigor Youtube channel.
To contact Igor write on:
igor@forex.in.rs
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