Geometric Average
- Thread starter fashepard
- Start date
Frank,
If you take a series of returns, say: +10%, -10%, +20%, -20%
The arithmetic average is 0%
As you say, the geometric average = [(1.1)(0.9)(1.2)(0.8)]^(1/4) - 1< 0
I like to say "the volatility erodes (geometric) return"
This geometric return will be approximated by: arithmetic average - (1/2) variance
(not 1/2 standard deviation), so in this case:
[(1.1)(0.9)(1.2)(0.8)]^(1/4) - 1 ~ 0% - S.D.^2/2
David
If you take a series of returns, say: +10%, -10%, +20%, -20%
The arithmetic average is 0%
As you say, the geometric average = [(1.1)(0.9)(1.2)(0.8)]^(1/4) - 1< 0
I like to say "the volatility erodes (geometric) return"
This geometric return will be approximated by: arithmetic average - (1/2) variance
(not 1/2 standard deviation), so in this case:
[(1.1)(0.9)(1.2)(0.8)]^(1/4) - 1 ~ 0% - S.D.^2/2
David
emilioalzamora1
Well-Known Member
Hi David,I
I remember most probably from Part I that there is practice question asking something about the relationship between Rgeometric = ln ( 1 + Rarithmetic). If I remember it correclty, it is given in an equation form ................... but I simply do not remember where in the question set it is. Do you remember this one? Thought I note it down in my notes but now after searching for it like hell I can't find it anymore. I do need this practice question following the excellent link provided by you in the forum about the 'Misuse of expected returns'.
Can you please re-post the practice question again, David! This would be very much appreciated.
http://leeds-faculty.colorado.edu/stutzer/Papers/MisuseOfExpectedReturnsInFAJ.pdf
Many thanks!
I remember most probably from Part I that there is practice question asking something about the relationship between Rgeometric = ln ( 1 + Rarithmetic). If I remember it correclty, it is given in an equation form ................... but I simply do not remember where in the question set it is. Do you remember this one? Thought I note it down in my notes but now after searching for it like hell I can't find it anymore. I do need this practice question following the excellent link provided by you in the forum about the 'Misuse of expected returns'.
Can you please re-post the practice question again, David! This would be very much appreciated.
http://leeds-faculty.colorado.edu/stutzer/Papers/MisuseOfExpectedReturnsInFAJ.pdf
Many thanks!
Last edited:
Hi @emilioalzamora1 we're looking ... yes, the question is familiar to me, but i can't quite exactly remember it ....
berrymucho
Member
For what it's worth, I keep this paper handy when I need a quick reference on the (distributional) assumptions and approximations related to arithmetic vs geometric returns:
http://www.cdiadvisors.com/papers/CDIArithmeticVsGeometric.pdf
emilioalzamora1
Well-Known Member
Thanks for sharing @berrymucho!
If someone can still help with the practice question about geometric/arithmetic average, it would be perfect.
If someone can still help with the practice question about geometric/arithmetic average, it would be perfect.
Last edited:
@emilioalzamora1 I think maybe I found it (because in the thread i reference the paper "On the Relationship between Arithmetic and Geometric Returns"), see: https://forum.bionicturtle.com/threads/p2-t8-15-time-weighted-versus-dollar-weighted-returns.5529/
... another possibility is https://forum.bionicturtle.com/thre...sus-dollar-weighted-returns-topic-review.7731
... another possibility is https://forum.bionicturtle.com/thre...sus-dollar-weighted-returns-topic-review.7731
emilioalzamora1
Well-Known Member
Excellent! It is the first link I was looking for, David. Thank you for your help with this!
Awesome!
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