The Arithmetic mean and Geometric mean are the tools widely used to calculate the returns on investment for investment portfolios. Since the return on investment for a portfolio over years is dependent on returns in previous years, geometric mean is the more accurate way to calculate the return on investment for a specific time period. Arithmetic mean is better suited in the situation wherein variables being used for calculation of average are not dependent on each other.
Geometric means takes into account the compounding effects during the calculation period. When there is volatility in the data set, geometric mean is a more accurate calculation than arithmetic mean. The geometric mean is smaller by an amount equal to about one half of the variance of returns, so it is always smaller than the arithmetic mean given any variability in returns (the geometric mean is equal to the arithmetic mean when the returns for all periods are equal).
If there are two numbers X and Y in the series:
Geometric mean = (XY)^(1/2)
