## 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.

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## BREAKING DOWN 'Mean'

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.

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.

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.

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