Mean Return

• The arithmetic mean is what statisticians call the average. If you add ten numbers together and divide by ten, the result is the arithmetic mean.
• The arithmetic mean is the proper measure of the average return achieved by an investment manager.
• Unless otherwise stated, the mean usually refers to the arithmetic mean.
• The geometric mean is the rate of return that when compounded over a number of periods equates the beginning and ending values of an investment.
• The geometric mean is the proper measure of return realized by an investor.
• Many third party publishers of mutual fund data are now publishing the geometric mean.
• Third party publishers usually compute the mean from NAVs, which is the correct way to do it, as it results in returns that are net of expenses other than loads and commissions.
• The geometric mean will always be less than the arithmetic mean except in the case where the returns for each period are exactly the same.
• The geometric mean is calculated from the compound return over the period of interest. If the annual returns for three years were 12%, -9% and 15%, the geometric mean would be: [(1 + 0.12) (1 - 0.09) (1 + 0.15)]^(1/3) - 1 = 0.0544 = 5.44%.
• Excess return is actual return minus the risk-free T-Bill rate. Excess return is the basis from which all risky assets are measured, as it is presumed that the risk-free rate is embedded in the long-term average return of all risky assets.

• Mutual Fund Returns - Calculating the Arithmetic and Geometric Means