:max_bytes(150000):strip_icc()/thinkstockphotos_493208894-5bfc2b9746e0fb0051bde2b8.jpg "Applying the Geometric Mean: Key Examples")
One of the goals of investing is to save money and build wealth. But with so many options out there, how do you choose the instruments that are right for you? One way is to calculate how your portfolio may grow by applying the geometric mean. This tool can help you assess the potential returns and growth rates of your investment portfolio. It can also help you predict the movement of financial securities and stock indexes. Below, we highlight why this tool is important and why it’s applied in business and finance.
Key Takeaways
- The geometric mean is commonly applied in business and finance.
- It is calculated by raising the product of a set of numbers to the inverse of the total length of the series.
- The geometric mean is commonly used in business and finance to calculate financial asset and portfolio returns.
What Is the Geometric Mean?
A mean is a statistical measure used in statistics, math, and finance. It is defined as the average of a set of numbers or data points. The mean allows you to evaluate a set of numbers by telling you the average. As such, it can provide some context to each data point.
There are two different types of means. The first is the simplest form of a mean: the arithmetic mean. To use this measure, take the sum of the numbers in a data set and divide the result by the total number of data points.
Another type of mean is the geometric mean, which is what we’ll focus on in this article. The geometric mean is calculated by raising the product of a series of numbers to the inverse of the total length of the series. The geometric mean is most useful when numbers in the series are not independent of each other or if numbers tend to make large fluctuations.
Why Is the Geometric Mean Used?
Applications of the geometric mean are most common in business and finance, where it is frequently used when dealing with percentages to calculate growth rates and returns of individual securities and financial portfolios. It is also used in certain financial and stock market indexes, such as the Financial Times’ Value Line Geometric index.
The geometric mean is also used for number sets, where the values that are multiplied together are exponential. Examples of this phenomenon include the interest rates that may be attached to any financial investments, or the statistical rates of human population growth.
The geometric mean was first conceptualized by Greek philosopher Pythagoras of Samos and is closely associated with two other classical means made famous by him: the arithmetic mean and the harmonic mean.
Where to Use the Geometric Mean
Growth Rates
The geometric mean is used in finance to calculate average growth rates. In this context, it is referred to as the compounded annual growth rate (CAGR). This is the total rate of return needed for an investment to grow from its initial balance to the ending balance. The CAGR assumes that any profits earned by the investment are reinvested.
Consider a stock that grows by 10% in year one, declines by 20% in year two, and then grows by 30% in year three. The geometric mean of the growth rate is calculated as follows:
((1+0.1)*(1-0.2)*(1+0.3))^(1 ÷ 3) = 0.046 or 4.6% annually.
Portfolio Returns
The geometric mean is commonly used to calculate the annual return on a financial portfolio of securities. A financial portfolio consists of different investments for individual investors or by portfolio managers for a fund or other financial instrument.
Consider a portfolio of stocks that goes up from $100 to $110 in year one, then declines to $80 in year two, and goes up to $150 in year three. The return on the portfolio is then calculated as:
($150 ÷ $100)^(1 ÷ 3) = 0.1447 or 14.47%
Stock Indexes
The geometric mean is also occasionally used in constructing stock indexes. Stock indexes are broad-based instruments that try to capture the entire market. Examples include the S&P 500 and the Dow Jones Industrial Average (DJIA). Many of the Value Line indexes maintained by the Financial Times employ the geometric mean.
In this type of index, all stocks have equal weights, regardless of their market capitalizations or prices. The index is calculated by taking the geometric mean of the proportional change in price of each of the stocks within the index.
What Is a Mean?
A mean is a mathematical term. It is the mathematical average of a set of two or more numbers. A mean can be arithmetic or geometric. An arithmetic mean adds up all the numbers in a set and then divides the sum by the total number of data points. A geometrical mean, on the other hand, refers to the average values calculated using the products of the terms. Multiply the values and take the root of the sum that is equal to the number of values within that data set to get the geometric mean.
What Is a Mean Return?
A mean return is commonly referred to as the expected return. It is the return that an investor or portfolio manager expects to achieve from an investment portfolio. This is done using probably rates of return and historical data. Determining the mean return can help investors and professionals identify some of the risks associated with their investments.
How Do You Calculate the Mean Value of a Stock?
The mean value of a stock is its average value. You can calculate the mean or average value of a stock by multiplying the number of shares by the purchase price. If there are multiple prices, multiply the total number of shares purchased at each price and add them up. Divide this figure by the total number of shares to get the mean or average value.
The Bottom Line
Investors are almost always chasing positive returns. But there’s never any guarantee that you’ll come out on top. There are ways, though, that can limit the potential for loss while preserving your capital. Consider using some simple statistical tools like the geometric mean as part of your research and due diligence. This, combined with other tools, can help you calculate potential returns for your investments and portfolio before you invest and as your nest egg grows to help keep you on track.