Loading the player...

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 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.

Example of 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 × (1+0.1) 25 = $108,347.06.

RELATED TERMS
  1. Mean

    The simple mathematical average of a set of two or more numbers. ...
  2. Value Line Composite Index

    The Value Line Composite Index is a stock gauge containing approximately ...
  3. Compound Interest

    Compound Interest is interest calculated on the initial principal ...
  4. Annualized Total Return

    Annualized total return gives the yearly return of a fund calculated ...
  5. Compounding

    Compounding is the process in which an asset's earnings, from ...
  6. Effective Annual Interest Rate

    The effective annual interest rate is an investment's annual ...
Related Articles
  1. 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.
  2. Investing

    Understanding the Power of Compound Interest

    Understanding compound interest is important for both investing and borrowing money.
  3. Trading

    Analyzing Chart Patterns

    Learn how to evaluate a stock with a few easy-to-identify chart patterns.
  4. IPF - Banking

    How Interest Rates Work on Savings Accounts

    Here's what you need to know to grow your rainy-day fund.
  5. Investing

    The Uses And Limits Of Volatility

    Check out how the assumptions of theoretical risk models compare to actual market performance.
  6. Investing

    How to use Monte Carlo simulation with GBM

    Learn how to estimate risk with the use of a Monte Carlo simulation to predict future events through a series of random trials.
  7. Investing

    Time Value Of Money: Determining Your Future Worth

    Determining monthly contributions to college funds, retirement plans or savings is easy with this calculation.
  8. Investing

    Understanding the Time Value of Money

    Find out why time really is money by learning to calculate present and future value.
RELATED FAQS
  1. 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 >>
  2. 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 >>
  3. 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 >>
Hot Definitions
  1. Diversification

    Diversification is the strategy of investing in a variety of securities in order to lower the risk involved with putting ...
  2. Intrinsic Value

    Intrinsic value is the perceived or calculated value of a company, including tangible and intangible factors, and may differ ...
  3. Current Assets

    Current assets is a balance sheet item that represents the value of all assets that can reasonably expected to be converted ...
  4. Volatility

    Volatility measures how much the price of a security, derivative, or index fluctuates.
  5. Money Market

    The money market is a segment of the financial market in which financial instruments with high liquidity and very short maturities ...
  6. Cost of Debt

    Cost of debt is the effective rate that a company pays on its current debt as part of its capital structure.
Trading Center