A type of average used in finance is the average percentage return. It is an example of a geometric mean. When the returns are annual, it is called the Compound Annual Growth Rate (CAGR). For example, if we are considering a period of two years, and the investment return in the first year is −10% and the return in the second year is +60%, then the average percentage return or CAGR, "R", can be obtained by solving the equation: . The value of "R" that makes this equation true is 0.2, or 20%. This means that the total return over the 2-year period is the same as if there had been 20% growth each year. Note that the order of the years makes no difference – the average percentage returns of +60% and −10% is the same result as that for −10% and +60%. 

This method can be generalized to examples in which the periods are not equal. For example, consider a period of a half of a year for which the return is −23% and a period of two and a half years for which the return is +13%. The average percentage return for the combined period is the single year return, "R", that is the solution of the following equation: , giving an average percentage return "R" of 0.0600 or 6.00%.

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Average percentage return and CAGR
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