Average percentage return and CAGR Average

a type of average used in finance average percentage return. example of geometric mean. when returns annual, called compound annual growth rate (cagr). example, if considering period of 2 years, , investment return in first year −10% , return in second year +60%, average percentage return or cagr, r, can obtained solving equation: (1 − 10%) × (1 + 60%) = (1 − 0.1) × (1 + 0.6) = (1 + r) × (1 + r). value of r makes equation true 0.2, or 20%. means total return on 2-year period same if there had been 20% growth each year. note order of years makes no difference – average percentage returns of +60% , −10% same result −10% , +60%.

this method can generalized examples in periods not equal. example, consider period of half of year return −23% , period of 2 , half years return +13%. average percentage return combined period single year return, r, solution of following equation: (1 − 0.23) × (1 + 0.13) = (1 + r), giving average percentage return r of 0.0600 or 6.00%.