What is the 'Geometric Mean'
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 'n'th root product of 'n' numbers." The geometric mean must be used when working with percentages, which are derived from values, while the standard arithmetic mean works with the values themselves.
The geometric formula is: [(1+Return1) x (1+Return2) x (1+Return3)...)]^{1/n}  1
BREAKING DOWN 'Geometric Mean'
The main benefit to 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 "applestoapples" comparison when looking at two investment options over more than one time period.
Geometric Mean
If you have $10,000 and get paid 10% interest on that $10,000 every year for 25 years, the amount of interest is $1,000 every year for 25 years, or $25,000. However, this does not take the interest into consideration. That is, the calculation assumes you only get paid interest on the original $10,000, not the $1,000 added to it every year. 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 geometric mean return is specifically used for investments that offer a compounding return. Going back to the example above, instead of only making $25,000 on a simple interest investment, the investor makes $108,347.06 on a compounding interest investment. Simple interest or return is represented by the arithmetic mean, while compounding interest or return is represented by the geometric mean.
Geometric Mean Calculation
To calculate compounding interest using the geometric mean, the investor needs to first calculate the interest in year one, which is $10,000 multiplied by 10%, or $1,000. In year two, the new principal amount is $11,000, and 10% of $11,000 is $1,100. The new principal amount is now $11,000 plus $1,100, or $12,100. In year three, the new principal amount is $12,100, and 10% of $12,100 is $1,210. At the end of 25 years, the $10,000 turns into $108,347.06, which is $98,347.05 more than the original investment. 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. The calculation is $10,000 Ã— (1+0.1) 25 = $108,347.06.

Mean
The simple mathematical average of a set of two or more numbers. ... 
Value Line Index
The value line index is a stock index containing approximately ... 
Compound Interest
Compound Interest is interest calculated on the initial principal ... 
Interest Rate
Interest rate is the amount charged, expressed as a percentage ... 
Compound Return
The compound return is the rate of return that represents the ... 
Periodic Interest Rate
The periodic interest rate is the interest rate charged on a ...

Investing
How to Calculate Your Investment Return
How much are your investments actually returning? The method of calculation can make a significant difference in your true rate of return. 
Tech
How Uber Is Betting on AI (FB, INTC)
Uber has placed a wager on artificial intelligence by purchasing Geometric Intelligence in an effort to create an inhouse research lab. 
Investing
The Effective Annual Interest Rate
The effective annual interest rate is a way of restating the annual interest rate so that it takes into account the effects of compounding. 
Investing
Continuous compound interest
Different frequency in compound interest results in different returns. Check out how continuous compounding accelerates your return. 
Investing
The Uses And Limits Of Volatility
Check out how the assumptions of theoretical risk models compare to actual market performance. 
Investing
Look Smart: Financial Calculations You Can Do In Your Head
Ditch your financial calculator and use these handy tips for estimating complex financial calculations on the fly. 
Retirement
Present and Future Value of Annuities
Do you want to invest in annuities that get you a series of payments over a period of time. Here's everything you need to account for when calculating the present and future value of annuities. 
Investing
Understanding the Time Value of Money
Find out why time really is money by learning to calculate present and future value. 
Investing
Why Your Investment Growth Calculator May Be Wrong
Many simple investment growth calculators fall short, so here's one you should use instead. 
Investing
Investors Need A Good WACC
Weighted average cost of capital may be hard to calculate, but it's a solid way to measure investment quality.

What is the difference between arithmetic and geometric averages?
An arithmetic average is the sum of a series of numbers divided by how many numbers being averaged.Â However, geometric average ... Read Answer >> 
What formula calculates interest on interest?
Find out about compounding interest, what it measures, and how to calculate the amount of compound interest accrued using ... Read Answer >> 
How to calculate compound loan interest in Excel?
Find out about compound interest and how to use the compounding interest formula in Microsoft Excel to calculate the compound ... Read Answer >> 
Compound interest versus simple interest
Simple interest is only based on the principal amount of a loan, while compound interest is based on the principal amount ... Read Answer >> 
Simple versus compound interest
Different methods in interest calculation can end up different interest payment. Learn the differences between simple and ... Read Answer >> 
What is the historical market risk premium?
Learn what the historical market risk premium is and the different figures that result from an analyst's choice of calculations ... Read Answer >>