is geometric mean and compounded annual growth rate are the same?
Yes, CAGR is a use case of geometric mean. As such, it is the geometric progression ratio that provides a constant rate of return over the time period.
I wouldn't say they are the "same". I mean they are distinct concepts, but yes, the geometric mean can be used to calculate the compounded annual growth rate.
The following uses R to calculate the CAGR, using Example 1 at the following link as an example. Note that using log is a little simpler than their method.
Note one distinction is that the rates need to be adjusted so that 1.00 indicates a return of 0%, so 1 is added to the returns. In turn, 1 is subtracted at the end of the calculation.
https://www.investopedia.com/articles/investing/071113/breaking-down-geometric-mean.asp
Return = c(0.03, 0.05, 0.08, -0.01, 0.10)
geomean = function(x){GM = exp(mean(log(x))); return(GM)}
geomean(Return + 1) - 1
### 0.04929024
Geometric Mean(GM) is used to compute CAGR. GM is a better predictor of growth rate than Arithmetic Mean or Harmonic Mean.
Geometric mean and compounded annual growth rate are not same but are two different concepts.
Geometric mean is a measure of average in general while compounded annual growth rate is rate of growth. Compounded annual growth rate i(or equivalently coefficient of growth) is a coefficient in the mathematical / statistical model describing growth of the associated variable.
Of course Geometric Mean can be used to compute compounded annual growth rate in some situations.
Geometric mean and compounded annual growth rate are different. The formula of the compounded annual growth rate uses the geometric mean inside it.
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