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#1 2013-11-19 09:05:57

kloser123
Member
Registered: 2013-11-19
Posts: 5

geomean

Hi there,

Given N sets of values, I'm trying to figure out why averaging the returns per period across sets of values always produces a higher geomean than

first averaging the values per period across tests, then calculating period-to-period returns, and then taking the geomean of those returns.

I used the RAND function for each value as to quickly iterate different "tests".

Thank you

Last edited by kloser123 (2013-11-19 09:42:57)

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#2 2013-11-19 09:29:33

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,164

Re: geomean

Hi kloser123;

Welcome to the forum. I do not see the spreadsheet.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#3 2013-11-20 01:29:10

kloser123
Member
Registered: 2013-11-19
Posts: 5

Re: geomean

obviously, monthly return and avg geomeans differ in some months.
But I don't know why the final geomean for the whole period is always higher.
Can you help please?
Thank you

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#4 2013-11-20 01:45:45

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,164

Re: geomean

Hi;

Please provide the spreadsheet or an example.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#5 2013-11-20 02:02:16

kloser123
Member
Registered: 2013-11-19
Posts: 5

Re: geomean

how can I attach it?

    1 year    Jan      Feb               Mar    Apr        May    Jun     Jul            Aug    Sep    Oct            Nov    Dec          Jan          Geomean       
             $1.000     $1.285    $1.153    $815    $1.362    $905     $1.041    $859    $931    $1.027    $878    $860       $1.038            
                       29%    -10%           -29%    67%           -34%    15%          -17%    8%    10%           -15%    -2%        21%           
            $1.000    $985             $1.195    $1.251 $929    $830    $1.049 $1.295    $963    $1.139 $1.173    $1.057  $1.231            
                     -2%             21%            5%       -26%    -11%     26%           23%      -26%     18%      3%         -10%    16%           
        $1.000    $1.153    $910         $1.187   $802  $1.235    $923       $1.308 $1.205    $806      $949    $992      $919            
                     15%           -21%          30%    -32%           54%    -25%           42%    -8%    -33%      18%         5%    -7%           
                                                                   
                                                                   
1)    Avg values    $1.000    $1.141    $1.086    $1.084    $1.031    $990    $1.004    $1.154    $1.033    $991    $1.000    $970    $1.063           
    Monthly return        1,14    0,95    1,00    0,95    0,96    1,01    1,15    0,90    0,96    1,01    0,97    1,10    0,508%    =    0,508%
                                                                    CAGR formula matches averaging values perfectly
2)    Avg geomeans        1,14    0,97    1,02    1,03    1,03    1,05    1,16    0,92    0,98    1,02    0,98    1,10    3,097%       
                                                                   
                        Geomean of averaged monthly geomeans - geomean of averaged monthly values                                    2,589%

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#6 2013-11-20 02:27:57

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,164

Re: geomean

Hi;

I am sorry I cannot read that, can you take a screenshot?

This is what your post looks like on my browser.

View Image: 2013-11-20_062447.gif

In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#7 2013-11-20 13:30:18

kloser123
Member
Registered: 2013-11-19
Posts: 5

Re: geomean

how can I paste it?

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#8 2013-11-20 13:48:01

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,164

Re: geomean

You would need a screen capture. or you can post it in small pieces.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#9 2013-11-20 14:22:03

kloser123
Member
Registered: 2013-11-19
Posts: 5

Re: geomean

1 year    Jan       Feb     Mar       Apr    May    Geomean       
         $1.000     $1.144    $1.074    $994    $962            
                  14%    -6%            -7%    -3%           
    $1.000    $1.159    $1.158    $944    $1.036            
                 16%              0%           -18%    10%           
    $1.000    $1.112    $914         $1.217    $1.214            
                  11%    -18%          33%    0%           
                               
                               
Avg values    $1.000 $1.138    $1.049 $1.052    $1.071           
Monthly return        1,14    0,92    1,00    1,02    1,722%    =    1,722%
                                CAGR formula matches averaging values perfectly
Avg geomeans        1,14    0,92    1,02    1,02    2,292%       
                               
                    Geomean of averaged monthly geomeans - geomean of averaged monthly values    0,570%

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#10 2013-11-20 14:38:05

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,164

Re: geomean

Hi;

The picture below is what I am seeing. I can not make any sense out of it. Maybe someone else can, sorry for the bother.

View Image: 2013-11-20_183326.gif

In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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