I'm not sure if I have a math error, or a comprehension error.
I have a series of ROIs over different periods (
5 years, etc)
roi = (value-cost)/cost
I also annualized all of these ROIs using this formula:
aroi = (value/cost)**(365/days) - 1
These return identical values for a period of
365 days as expected.
Now, here is where I get confused. I will use a period of
2 years as example.
If I take my mean of ROIs over this two year period, I get
23.6% which annualizes to
But if I take these same ROI's, annualize all of them, and take the mean of that, I get
Do I have a math error? Do we expect these numbers to be the same? And if not, which is the better estimate?