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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
From: Bumpkinland
Registered: 2009-04-12
Posts: 104,717

### 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.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

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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.
Thank you

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

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 104,717

### Re: geomean

Hi;

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

Online

## #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
From: Bumpkinland
Registered: 2009-04-12
Posts: 104,717

### 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.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

Online

## #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
From: Bumpkinland
Registered: 2009-04-12
Posts: 104,717

### 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.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

Online

## #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
From: Bumpkinland
Registered: 2009-04-12
Posts: 104,717

### 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.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

Online