Why is geometric mean important

Select personalised ads. Apply market research to generate audience insights. Measure content performance. Develop and improve products. List of Partners vendors. The geometric mean is the average of a set of products, the calculation of which is commonly used to determine the performance results of an investment or portfolio.

It is technically defined as "the nth root product of n numbers. The geometric mean is an important tool for calculating portfolio performance for many reasons, but one of the most significant is it takes into account the effects of compounding. The geometric mean, sometimes referred to as compounded annual growth rate or time-weighted rate of return , is the average rate of return of a set of values calculated using the products of the terms.

What does that mean? For example, the geometric mean calculation can be easily understood with simple numbers, such as 2 and 8. However, when there are many numbers, it is more difficult to calculate unless a calculator or computer program is used. The longer the time horizon, the more critical compounding becomes, and the more appropriate the use of geometric mean.

The main benefit of using the geometric mean is the actual amounts invested do not need to be known; the calculation focuses entirely on the return figures themselves and presents an "apples-to-apples" comparison when looking at two investment options over more than one time period. Geometric means will always be slightly smaller than the arithmetic mean, which is a simple average. The shortcut is to multiply the current principal by one plus the interest rate, and then raise the factor to the number of years compounded.

However, this does not take the interest into consideration. If the investor gets paid interest on the interest, it is referred to as compounding interest, which is calculated using the geometric mean. Using the geometric mean allows analysts to calculate the return on an investment that gets paid interest on interest.

This is one reason portfolio managers advise clients to reinvest dividends and earnings. The geometric mean is also used for present value and future value cash flow formulas. The investment position after two years is as below:. Therefore, the Geometric mean shows the true picture of investment that there is a loss in investment with an annualized negative return of Since the return in each year impacts the absolute return in the next year, a geometric mean is a better way to calculate the annualized return on investment.

When one needs to calculate the average of variables that are not dependent on each other, Arithmetic means a suitable tool to calculate the average.

The average of marks of a student for 5 subjects can be calculated by the arithmetic mean as scores of the student in different subjects are independent of each other. Such as calculating the average score of a student in all the subjects. Geometric mean shall be used to calculate the mean where the variables are dependent on each other.

Such as calculating the annualized return on investment over a period of time. Effect of Compounding The arithmetic mean does not take into account the impact of compounding, and therefore, it is not best suited to calculate the portfolio returns. The geometric mean takes into account the effect of compounding, therefore, better suited for calculating the returns. Accuracy The use of Arithmetic means to provide more accurate results when the data sets are not skewed and not dependent on each other.

Where there is a lot of volatility in the data set, a geometric mean is more effective and more accurate. Application The arithmetic mean is widely used in day to day simple calculations with a more uniform data set. It is used in economics and statistics very frequently. The geometric mean is widely used in the world of finance, specifically in calculating portfolio returns. Ease of Use The arithmetic mean is relatively easy to use in comparison to the Geometric mean.

The geometric mean is relatively complex to use in comparison to the Arithmetic mean. Mean for the same set of numbers The arithmetic mean for two positive numbers is always higher than the Geometric mean.

Develop and improve products. List of Partners vendors. In statistics, 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.

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 on a portfolio of securities. It is also used in certain financial and stock market indexes, such as the Financial Times' Value Line Geometric index. The geometric mean is used in finance to calculate average growth rates and is referred to as the compounded annual growth rate.

The geometric mean of the growth rate is calculated as follows:. The geometric mean is commonly used to calculate the annual return on portfolio of securities. The geometric mean is also occasionally used in constructing stock indexes.

Many of the Value Line indexes maintained by the Financial Times employ the geometric mean. The index is calculated by taking the geometric mean of the proportional change in price of each of the stocks within the index. 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.

The geometric mean is also used for sets of numbers, where the values that are multiplied together are exponential. Examples of this phenomena include the interest rates that may be attached to any financial investments, or the statistical rates if human population growth.

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