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Geometric Averages
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RCourtemanche
Member
posted
Does anyone have any code around calculating a geometric average? I can't seem to find any and there is no prefix operator for this type of calculation.

Please help.

Thanks!
 
Posts: 19 | Location: Springfield, MA | Registered: May 04, 2004Report This Post
Noreen Redden
Gold member
posted Hide Post
I'm sorry. this is definitely a flaw in my math education, but could you explain what a Geometric average is as opposed to a regular average?
 
Posts: 60 | Location: 2 penn | Registered: May 22, 2003Report This Post
Leah
Virtuoso
posted Hide Post
Noreen,

Me also, so I did a web search. Geometric mean in simple terms, if I interpret correctly. Say you have N values. Get the Product of the values and then take the Nth root of the values.

Say N {1,2,3} product is 1*2*3 = 6 so then you'd have to find what number 'cubed' would give 6.
 
Posts: 1317 | Location: Council Bluffs, IA | Registered: May 24, 2004Report This Post
susannah
Expert
posted Hide Post
The harmonic mean is always less than the geometric mean, which is always less than the arithmetic mean.
geometric mean
= (x1 * x2 * x3 * x4 * ...)**(1/n)
harmonic mean
= 1/ [((1/x1)+(1/x2)+(1/x3)+(1/x4)...)/n]
you can use Geometric Mean to calculate average growth rate given compound interest with variable rates.
The harmonic mean is the reciprocal of the arithmetic mean of reciprocals.
ps: you know that taking a root is the same as exponentiating to its reciprocal, yes?
square root of x = x**(1/2)
so that's how you do it in focus.
where there's a will,....there's a way!
 
Posts: 3811 | Location: Manhattan | Registered: October 28, 2003Report This Post
k.lane
Platinum Member
posted Hide Post
I too Googled 'geometric average' (not mean) and found the following definition:

The Geometric Average is the time weighted average compound rate of return. Geometric average is the most common method used to measure and compare investment manager performance for periods over one year.

Ken
 
Posts: 177 | Location: Calgary, Alberta, Canada | Registered: April 25, 2005Report This Post
RCourtemanche
Member
posted Hide Post
Thanks everyone for your ideas. I know the formula for the calculations but am having a hard time coming up with how to implement it with a data set of performance results for an investment portfolio.

Thoughts or examples??
 
Posts: 19 | Location: Springfield, MA | Registered: May 04, 2004Report This Post
Leah
Virtuoso
posted Hide Post
http://www.facstaff.bucknell.edu/djensen/mgmt377/fall%2...c%20mean.pdf#search='geometric%20average'

This had a discussion and a short cut at the end which might help. ROOTS in FOCUS I'm not to familiar with.

Sounds like we need a reverse EXP and LOG functions to do the job.
 
Posts: 1317 | Location: Council Bluffs, IA | Registered: May 24, 2004Report This Post
RCourtemanche
Member
posted Hide Post
Thanks Leah. The PRODUCT() function in excel is essentially what I'm trying to reproduce using WebFOCUS and am coming up empty handed.
 
Posts: 19 | Location: Springfield, MA | Registered: May 04, 2004Report This Post
Leah
Virtuoso
posted Hide Post
Maybe we should have asked just what are you trying to calculate and what type of data, maybe we're making it harder than it is meant to be?
 
Posts: 1317 | Location: Council Bluffs, IA | Registered: May 24, 2004Report This Post
Tony A
Expert
posted Hide Post
PRODUCT in Excel? Are you sure? It's nowhere near geometric averages (or any other average for that matter Frowner ).


From Excel -

If cells A2:C2 contain 5, 15, and 30:
PRODUCT(A2:C2) equals 2,250

e.g. 5 * 15 * 30
If this is what you really want then I would probably use FML (SRL, FRL, EMR or whatever it's called nowadays), using a RECAP in the required column / row, as it can be easier to manipulate the cell data than using straight forward reporting.

If this is really what you want then try and build an example using the GGSALES file to show us your report structure and advise where and how your product column should be.

e.g.
TABLE FILE GGSALES
SUM CNT.ST AS 'Num of,States'
-* Could have used AVE.DOLLARS but it only gives an integer
    COMPUTE AVG_DOLLARS/D20.2 = SUM.DOLLARS / CNT.ST; AS 'Avg,Dollars'
    COMPUTE AVG_BUDDOLL/D20.2 = SUM.BUDDOLLARS / CNT.ST; AS 'Avg,Budget,Dollars'
    COMPUTE PRODUCT/D20.2 = AVG_DOLLARS * AVG_BUDDOLL;
FOR REGION
'Midwest' OVER
'Southeast' OVER
'Northeast' OVER
'West' OVER
""
END

This message has been edited. Last edited by: <Maryellen>,


In FOCUS
since 1986		WebFOCUS Server 8.2.01M, thru 8.2.07 on Windows Svr 2008 R2  
WebFOCUS App Studio 8.2.06 standalone on Windows 10 
 
Posts: 5694 | Location: United Kingdom | Registered: April 08, 2004Report This Post
RCourtemanche
Member
posted Hide Post
Sorry, I've probably posed the question incorrectly. Here's an example.

1) If you have 3 times periods where you earn 5%, 6%, 7% respectively, what is your return over the entire time period (geometrically linked returns)?

To solve this in excel you do the following:
=PRODUCT((1 + 0.05)*(1 + 0.06)*(1 + 0.07))-1 for a result of 19.09%
 
Posts: 19 | Location: Springfield, MA | Registered: May 04, 2004Report This Post
susannah
Expert
posted Hide Post
in focus (1.05+1.06+1.05)**(1/3) is the geometric mean of these return rates.
19% is not, repeat NOT the geometric mean. Its just compounded.
Lets make it more interesting
1.05, 1.09, 1.07
The geometric mean is 1.069875 or 6.9875%
the aggregate return is 22.4615%
the annual average of the aggregate return is
((1.05*1.09*1.07)-1)/3 or 7.4872%
There is nothing about the word geometric that applies to your revised question.
 
Posts: 3811 | Location: Manhattan | Registered: October 28, 2003Report This Post
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