Loading the player...

What is a 'Mean'

A mean is the simple mathematical average of a set of two or more numbers. The mean for a given set of numbers can be computed in more than one way, including the arithmetic mean method, which uses the sum of the numbers in the series, and the geometric mean method. However, all of the primary methods for computing a simple average of a normal number series produce the same approximate result most of the time.


The mean is a statistical indicator that can be used to gauge the performance of: a company’s stock price over a period of days, months, or years; a company through its earnings over a number of years; a firm by assessing its fundamentals such as P/E ratio, FCF, liabilities on the balance sheet, etc.; and a portfolio by estimating its average returns over a certain period.

An analyst who wants to measure the trajectory of a company’s stock value in the last, say 10 days, would sum up the closing price of the stock in each of the 10 days. The sum total would then be divided by the number of days to get the arithmetic mean. The geometric mean will be calculated by multiplying all the values together. The nth root of product total is then taken, in this case the 10th root, to get the mean.

Arithmetic vs. Geometric Mean

Let’s put this into practice by examining the stock price of Nvidia Corp. (NVDA) over the last ten days. An investor that purchased NVDA on June 5th for $148.01 wants to know how well his investment has fared after 10 days. The table below shows the price and returns from June 6th to June 19th, 2017.

Table of Nvidia's mean of returns calculated with the arithmetic and geometric methods

The arithmetic mean is 0.67%, and is simply the sum total of the returns divided by 10. However, the arithmetic mean of returns is only accurate when there is no volatility which is nearly impossible with the stock market.

The geometric mean factors in compounding and volatility, which makes it a better metric of average returns. Since it is impossible to take the root of a negative value, add 1 to all the percentage returns so that the product total yields a positive number. Take the 10th root of this number and remember to subtract from 1 to get the percentage figure. The geometric mean of returns for the investor in the last five days is 0.61%. As a mathematical rule, the geometric mean will always be equal to or less than the arithmetic mean.

The arithmetic and geometric methods for calculating the mean of a set of number

Proof that the geometric mean provides a better value is given in the table. When the arithmetic mean of 0.67% is applied to each of the stock prices, the end value is $152.63. But clearly, NVDA traded for $157.32 on the last day – this means that the arithmetic mean of returns is overstated. On the other hand, when each of the closing prices is raised by the geometric average return of 0.61%, the exact price of $157.32 is calculated. This is an example of why the geometric mean is an accurate reflection of the true return of a portfolio.

While the mean is a good tool to evaluate the performance of a company or portfolio, it should also be used with other fundamentals and statistical tools to get a better and broader picture of the investment's historical and future prospects.

  1. Arithmetic Mean

    A mathematical representation of the typical value of a series ...
  2. Arithmetic Index

    An index of securities that uses an arithmetic sum to determine ...
  3. Time-Weighted Rate of Return

    The time-weighted rate of return is a measure of the compounded ...
  4. Value Line Index

    A stock index containing approximately 1,675 companies from the ...
  5. Annual Return

    Annual return is the compound average rate of return for a stock, ...
  6. Trimmed Mean

    A method of averaging that removes a small percentage of the ...
Related Articles
  1. 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 ...
  2. Investing

    How to Calculate Your Investment Return

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

    Gauge Portfolio Performance By Measuring Returns

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

    The Uses And Limits Of Volatility

    Check out how the assumptions of theoretical risk models compare to actual market performance.
  5. Managing Wealth

    3 Steps to Assess Your Portfolio's Annual Performance

    Learn about three simple steps you can use to evaluate the annual performance of your investment portfolio, and why rate of return isn't enough.
  6. 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.
  7. Investing

    Overcoming Compounding's Dark Side

    Understanding how money is made and lost over time can help you improve your returns.
  8. 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.
  9. Investing

    The Equity-Risk Premium: More Risk For Higher Returns

    Learn how the expected extra return on stocks is measured and why academic studies usually estimate a low premium.
  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. 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 >>
  3. 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 >>
  4. 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 >>
  5. I keep hearing about the 50-day, 100-day and 200-day moving averages. What do they ...

    Whether you are using the 50-day, 100-day or 200-day moving average, the method of calculation and how the moving average ... 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. Liquidity

    Liquidity is the degree to which an asset or security can be quickly bought or sold in the market without affecting the asset's ...
  3. Federal Funds Rate

    The federal funds rate is the interest rate at which a depository institution lends funds maintained at the Federal Reserve ...
  4. Call Option

    An agreement that gives an investor the right (but not the obligation) to buy a stock, bond, commodity, or other instrument ...
  5. Standard Deviation

    A measure of the dispersion of a set of data from its mean, calculated as the square root of the variance. The more spread ...
  6. Entrepreneur

    An entrepreneur is an individual who founds and runs a small business and assumes all the risk and reward of the venture.
Trading Center