The geometric average return, which is commonly called the geometric mean return, is the rate at which a person must invest money to get the same return on his investment. The underlying concept is that you can invest the same amount of money in an account that accrues compound interest. Investors use geometric average returns to compare the profitability of different investments. To calculate the geometric mean return, you only need to know the initial investment, the final return and the number of years until the payoff.
Denote the initial amount of the investment by P, the final return by F and the number of years by N. For example, you invest $1,000 in a project, and five years later you earn a return of $2,000. Then P = 1,000, F = 2,000 and N = 5.
Compute (F / P)^(1 / N) - 1. Using the sample numbers above, (2,000 / 1,000)^(1 / 5) - 1 = (2)^(0.2) - 1, and so 1.1487 - 1 = 0.1487.
Move the decimal point 2 units to the right to obtain the geometric average return as a percentage. The example scenario has a geometric average return of 14.87 percent. This means that if you had invested $1,000 in an account that earned 14.87 percent interest annually, you would have $2,000 at the end of five years.
Compare the profitability of different investments. For example, suppose you also invest $500 in a project that pays you $2,000 after 7 years. Then P = 500, F = 2,000 and N = 7. Since (2,000 / 500)^(1 / 7) - 1 = 0.219, this investment has a geometric average return of 21.9 percent, so it is more profitable than the first investment.