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# Expected geometric return?

#### sparty

##### New Member
Hi David, Nicole,

I was looking for a spreadsheet which demonstrated estimating future n-period geometric return, given E(r) and sd. I'm fairly certain I've seen this. It calculated geometric mean for n-periods with the specification:
((1+g)^2)^(n/2) = (E(r)^2 - sd^2)^(n/2)

PS: As a follow-up question, if given a time-series of observed returns, what should E(r) be? Simple arithmetic mean?

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @sparty I wonder if you refer to the sheet below (see snapshot)?
I broke off the sheet for you here https://www.dropbox.com/s/6cl645mg6ekz611/051319-realized-return.xlsx?dl=0
... located in this learning XLS at https://www.bionicturtle.com/topic/hull-chapters-13-15-19/
... please note that I'm referring to how the geometric average is lower than the arithmetic average by approximately σ^2/2, which is different than what you are showing above. I hope this is helpful! 