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.

Geometric Mean

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 "apples-to-apples" 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 × (1+0.1) 25 = $108,347.06.

  1. Mean

    The simple mathematical average of a set of two or more numbers. ...
  2. Unweighted Index

    A simple arithmetic or geometric average used to calculate stock ...
  3. Time-Weighted Rate of Return

    A measure of the compound rate of growth in a portfolio. Because ...
  4. Compound Interest

    Compound Interest is interest calculated on the initial principal ...
  5. Discrete Compounding

    Discrete compounding refers to the method by which interest is ...
  6. Annual Return

    The return an investment provides over a period of time, expressed ...
Related Articles
  1. Investing

    Explaining the Geometric Mean

    The average of a set of products, the calculation of which is commonly used to determine the performance results of an investment or portfolio.
  2. Investing

    Breaking Down The Geometric Mean

    Understanding portfolio performance, whether for a self-managed, discretionary portfolio or a non-discretionary portfolio, is vital to determining whether the portfolio strategy is working or ...
  3. Investing

    How To Calculate Your Investment Return

    How much are your investments actually returning? Find out why the method of calculation matters.
  4. Investing

    Learn Simple And Compound Interest

    Interest is defined as the cost of borrowing money, and depending on how it is calculated, can be classified as simple interest or compound interest.
  5. Investing

    The Most Accurate Way To Gauge Returns: The Compound Annual Growth Rate

    The compound annual growth rate, or CAGR for short, represents one of the most accurate ways to calculate and determine returns for individual assets, investment portfolios and anything that ...
  6. Investing

    Explaining Interest

    Interest is the price charged to borrow money, and is typically expressed as a percentage of the principal, or the amount loaned.
  7. Managing Wealth

    Dissecting the Simple Interest Formula

    Simple interest ignores the effect of compounding: it's only calculated on the principal amount. This makes it easier to calculate than compound interest.
  8. Investing

    The Difference Between Compounding Interest and Simple Interest

    Interest is the cost a borrower pays to use someone else’s money. Interest can be either simple or compounded.
  9. Investing

    Gauge Portfolio Performance By Measuring Returns

    Calculate returns frequently and accurately to ensure that you're meeting your investing goals.
  10. Investing

    How does Compound Interest Work?

    A quick way to understand the impact of compound interest is to ask yourself if you’d rather receive $100,000 a day for a month, or start with a penny on day one and double it every day for those ...
  1. How can investors benefit by understanding geometric means?

    Discover why investors should know the difference between geometric and arithmetic means, and why the geometric mean is more ... Read Answer >>
  2. What are some examples of applications of the geometric mean?

    Learn about applications of the geometric mean based on examples such as calculations of portfolio return, growth rates and ... Read Answer >>
  3. What is a geometric mean in statistics?

    Learn what the geometric mean is in statistics and how it is used to calculate various growth rates and returns by financial ... Read Answer >>
  4. How do you calculate the geometric mean to assess portfolio performance?

    Learn how to calculate the geometric mean. Understand when the geometric mean should be used and how it differs from the ... Read Answer >>
  5. Can two numbers have the same arithmetic and geometric means?

    Learn about the often complicated relationship between the geometric mean and arithmetic mean for a set of numbers, and which ... Read Answer >>
  6. What is the difference between arithmetic and geometric averages?

    An arithmetic average is the sum of a series of numbers divided by the count of that series of numbers. If you were asked ... Read Answer >>
Hot Definitions
  1. Cash Flow

    The net amount of cash and cash-equivalents moving into and out of a business. Positive cash flow indicates that a company's ...
  2. PLUS Loan

    A low-cost student loan offered to parents of students currently enrolled in post-secondary education. With a PLUS Loan, ...
  3. Graduate Record Examination - GRE

    A standardized exam used to measure one's aptitude for abstract thinking in the areas of analytical writing, mathematics ...
  4. Graduate Management Admission Test - GMAT

    A standardized test intended to measure a test taker's aptitude in mathematics and the English language. The GMAT is most ...
  5. Magna Cum Laude

    An academic level of distinction used by educational institutions to signify an academic degree which was received "with ...
  6. Cover Letter

    A written document submitted with a job application explaining the applicant's credentials and interest in the open position. ...
Trading Center