I am trying to calculate the mean annualised return for a fund using historical monthly returns but I am having difficulty in finding an appropriate method to do so. Many studies have used mean annualised returns but none seem to explain the calculation. Based on my research, I think there should be a geometric mean function involved but I am not too sure.
You can use either method, as long as you are consistent for comparisons of, say, fund A vs fund B. Average monthly return * 12 is simple and basic. Geometric mean compounded to an annual figure is more accurate and rigorous.
For example 4 monthly returns: 0.032, -0.053, 0.052, 0.014
Mean annual return
(0.032 - 0.053 + 0.052 + 0.014)/4*12 = 13.5 %
Mean cumulative return
(1.032*0.947*1.0511*1.014)^(12/4) - 1 = 13.0147 %