Geometric Mean: What It Is and How to Solve it in Finance

We all know about the arithmetic mean, but have you heard of the geometric mean? In finance, the geometric mean is a preferred method of finding an average investment return over time.

It may seem not very easy, but by the end of this blog post, you'll understand what the geometric mean is and how it can be helpful in finance.

What is the Geometric Mean Formula? 

As mentioned earlier, the geometric mean is another type of average used to calculate the average return of investments over time. It's calculated by multiplying all the values and taking the n th root of the product (n = how many numbers you have). This method is preferable in finance since it gives more weightage to long-term investments.

The formula for calculating averages may seem daunting, but it is relatively simple. It is used to find the median or mean value of a set of given numbers. This method is beneficial when looking at long sets of numbers in a more practical and manageable way.

Averaging whole data set values can make it much easier to conclude various datasets that might otherwise appear disorganized or confusing.

What are Some Geometric Mean Examples?

Let's say you want to calculate the average return on your investments over a period of 5 years. You have invested in different stocks, bonds, and mutual funds over those 5 years and obtained the following returns: 8%, 10%, 12%, 16%, and 20%.

To determine the geometric mean of these numbers, we first multiply all the returns together: 8% x 10% x 12% x 16% x 20%. This gives us a product of 307,200%. We then take the 5th root of this product to get the geometric mean return: 12.52%.

How do I Find the Geometric Mean on a Calculator?

Finding the geometric mean on a calculator is simple. All you need to do is enter in all of your values and then press the “GeoMean” button or key. This will give you the geometric mean with minimal effort! This also works in Excel with the GeoMean function.

If you don't have a calculator with that function, you can also use the formula mentioned earlier and press the y square root of x button and the total number of values you have. So, using the example we made earlier, it would be 8*10*12*16*20 = 307,200, then y square root of x key, then 5. Your total should be 12.5165… rounded to 12.52.

If you don't want to calculate by hand, some online calculators can make the work easy.

How is it Different from Arithmetic Mean? 

The arithmetic mean is calculated by adding all the values and dividing the result by the number of values. The geometric mean, on the other hand, accounts for the compounding effect of interest rates on investments over time. It's better suited for calculating the average value of investment returns over extended periods.

The geometric mean is a powerful tool to gain insight into a set of numbers, as it appears in many places within mathematics and essential calculations. It is the average but calculated differently depending on the numbers being averaged; this result is significant as it gives more accurate results than the arithmetic mean and can be applied beyond simple addition and division.

While it requires some extra background knowledge to understand how it works, understanding the geometric mean allows people to assess their data points more accurately and efficiently.

Knowing the difference between these two forms of averages can prove quite helpful for those looking for accurate results in mathematics or data science.

What is an Example of Calculating Arithmetic Mean?

The arithmetic mean is calculated by adding up data values of all of the given numbers and then dividing the result by the number of values. For example, if you have three numbers (5, 10, and 15), you would add them together to get 30, then divide by 3 (the number of values) to get an answer of 10. This is the arithmetic mean of the three given numbers.

In conclusion, both arithmetic and geometric means are useful tools for calculating averages, but they should not be used interchangeably; each type of average has its own purpose and will provide different results depending on the evaluated data set.

Understanding which type of average best suits your needs and given data values will help you get the most accurate results possible.

Why is Geometric Mean Important in Finance? 

Calculating the return on investments is critical to any investor's financial strategy. Using a metric known as the geometric mean or average return is one way to gauge the effectiveness of that strategy. That calculation considers any return generated over a period and provides an overall picture of the exact return produced.

Knowing exactly how much return you've generated can help you decide where to invest in the future and improve your strategies for maximum yield. Working out your average return is time well spent.

The geometric mean provides a realistic representation of the expected return on investment over time. It's advantageous when comparing investments that may have varying lengths.

Suppose an investment portfolio has an average growth rate of 10% returns on the year. This portfolio would have grown by more than 60% in five years, thanks to the compounding effect.

How Do You Use Geometric Mean in Real Life? 

A geometric mean is an essential tool for investors, business owners, and financial analysts to calculate their returns accurately over time. It's helpful in comparing investment portfolios or calculating bonds and stocks' average returns. For example, if you want to know the average return for a portfolio invested in bonds, calculate the geometric mean of the portfolio.

How Do Business Owners Use Geometric Mean?

Business owners often use the geometric mean to calculate average returns when multiple investments are involved. Using this metric gives them a better understanding of their overall return on investment and what kind of return they can expect in the future.

It's also useful for comparing different portfolios over time, so business owners can make informed decisions about where to invest their money.

Additionally, it can be used to calculate the average return of a product or service over time, giving business owners an idea of how they should price and market their offerings.

Conclusion

In conclusion, the geometric mean is a crucial mathematical tool that can help accurately calculate the returns on investment over extended periods. It's a preferred method in finance since it accounts for the compounding effect of assets over time. With this post, we hope you better understand what the geometric mean is and how it can be helpful in finance.