A percentage rate of return measures the percentage of an investment that it generates as profit over a certain time period. If you know an investment’s percentage rate of return for any period of time other than one year, you can annualize the return using the geometric average formula. This converts the rate of return to an annual return, which is equivalent to the return the investment would earn on a yearly basis. This can make it easier to compare investments that you hold for different time periods.
Determine an investment’s known percentage rate of return and the time period for which the return was measured. For example, assume an investment generated a 12 percent rate of return over 18 months.
Divide the number of months by 12 to convert the rate of return’s time period to number of years. If the rate of return’s time period is in days, divide the number of days by 365. In this example, divide 18 months by 12 to get 1.5 years.
Substitute the percentage rate of return and the time period in years into the geometric average formula: (1 + r)^(1/n) - 1. In the formula, “r” represents the percentage rate of return and “n” represents the time period in years. In this example, substitute the values to get the following formula: (1 + 0.12)^(1/1.5) - 1.
Calculate the numbers inside each set of parentheses. In this example, add 1 and 0.12 to get 1.12. Divide 1 by 1.5 to get 0.67. This leaves 1.12^0.67 - 1.
Raise the number to the power of the exponent. Then subtract 1 from your result. In this example, raise 1.12 to the 0.67 power to get 1.079. Then subtract 1 from 1.079 to get 0.079.
Multiply your result by 100 to calculate the annualized percentage rate of return. In this example, multiply 0.079 by 100 to get a 7.9 percent annualized rate of return for the investment.
Compare the annualized returns of different investments to measure and rank their performance.