# Calculating a Geometric Mean with some negative values

#### Marcus from Belmont

##### New Member
I am trying to work out how to calculate the geometric mean of a series of values, some of which are negative, ie. investment returns over a series of years with some negatives.

The Geomean function doesn't work because it only uses positive numbers.

Any help would be greatly appreciated.

### Excel Facts

Can a formula spear through sheets?
Use =SUM(January:December!E7) to sum E7 on all of the sheets from January through December

#### thazan

##### Board Regular
Can you just use the average function?

I don't think that any negative values can ever be used with the geometric mean.

I think this formula calculates the geometric mean.

=PRODUCT(A1:A6)^(1/COUNT(A1:A6))

I hope that helps.

#### pgc01

##### MrExcel MVP
Hi Marcus
Welcome to the board

I never saw applications with geometric mean with negatives (doesn't mean it doesn't exist, of course).

Usually when you calculate the geometric mean of the returns of an investment over the years with positive and negative returns you are trying to find an equivalent average compounded return for the period.

The returns you usually use are not the percentages you add or subtract but the values you multiply to get the final amount.

Example
You invest 100
Year 1: return 20% (total: 120)
Year 2: return -5% (total: 114)

The geometric mean is calculated relative to the total (100%)

=((1+.2)*(1-.05))^(1/2)-1= 6.77%

This means that an investment with a constant return of 6.77% each period is equivalent to your investment.

You invest 100
Year 1: return 6.77% (total: 106.77)
Year 2: return 6.77% (total: 114)

Is this not your case? Please elaborate and post a sample with inputs, the logic and the expected results.

Kind regards
PGC

#### facethegod

##### Well-known Member
Try this

Code:
``=PRODUCT(1+A1:A3)^(1/COUNT(A1:A3))-1``

Confirm with Ctrl + Shift + Enter

#### pgc01

##### MrExcel MVP
P. S.
If you agree with my post you can use the Geomean as you originally wanted:

=Geomean(1+a1:a3)-1

Confirmed with Ctrl + Shift + Enter

#### Marcus from Belmont

##### New Member
Thanks to you all - have solved the problem which was a lack of thinking on behalf of the user. Was using negative percentages - what I should have been doing was using 100%=1 and -6%= 0.94.

Then I can use the simple GEOmean function as is.

Thank you all

#### kennyw

##### New Member
P. S.
If you agree with my post you can use the Geomean as you originally wanted:

=Geomean(1+a1:a3)-1

Confirmed with Ctrl + Shift + Enter

Another happy customer served! I vaguely remember some of this math from freshman college. But, its a stretch. And, that was all well before spreadsheets!

#### Mukundane

##### New Member
Re: Calculating a Geometric Mean with some negative values of Bank Investments

 Geometric mean of negative and positive returns. 23.5,33.6,-18.8,14.4,-14.9,-1,3,96.2,3.4,0 Calculating your bank returns for 10 years using Excel Spreadsheet. % Add 1 23.5 0.235 1.235 1.104352 =GEOMEAN(D3,D4,D5,D6,D7,D8,D9,D10,D11,D12) 33.6 0.336 1.336 using excel D3=1.235 D12=1 -18.8 -0.188 0.812 B3=23.5 C3=0.235 14.4 0.144 1.144 -14.9 -0.149 0.851 -1 -0.01 0.99 3 0.03 1.03 Note: Add one to remove negative and subtract 1 from answer. 96.2 0.962 1.962 3.4 0.034 1.034 0 0 1 Geometric mean = 10.4% is the answer =10.4%

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Last edited:

#### Gregorio

##### New Member
Can you just use the average function?

I don't think that any negative values can ever be used with the geometric mean.

I think this formula calculates the geometric mean.

=PRODUCT(A1:A6)^(1/COUNT(A1:A6))

I hope that helps.

great help! =GEOMEAN(1+A1:A6)-1 is also working, thank you both

#### Haigts

##### New Member
Hi Marcus
Welcome to the board

I never saw applications with geometric mean with negatives (doesn't mean it doesn't exist, of course).

Usually when you calculate the geometric mean of the returns of an investment over the years with positive and negative returns you are trying to find an equivalent average compounded return for the period.

The returns you usually use are not the percentages you add or subtract but the values you multiply to get the final amount.

Example
You invest 100
Year 1: return 20% (total: 120)
Year 2: return -5% (total: 114)

The geometric mean is calculated relative to the total (100%)

=((1+.2)*(1-.05))^(1/2)-1= 6.77%

This means that an investment with a constant return of 6.77% each period is equivalent to your investment.

You invest 100
Year 1: return 6.77% (total: 106.77)
Year 2: return 6.77% (total: 114)

Is this not your case? Please elaborate and post a sample with inputs, the logic and the expected results.

Kind regard
Re: Calculating a Geometric Mean with some negative values of Bank Investments

 Geometric mean of negative and positive returns. 23.5,33.6,-18.8,14.4,-14.9,-1,3,96.2,3.4,0 Calculating your bank returns for 10 years using Excel Spreadsheet. % Add 1 23.5 0.235 1.235 1.104352 =GEOMEAN(D3,D4,D5,D6,D7,D8,D9,D10,D11,D12) 33.6 0.336 1.336 using excel D3=1.235 D12=1 -18.8 -0.188 0.812 B3=23.5 C3=0.235 14.4 0.144 1.144 -14.9 -0.149 0.851 -1 -0.01 0.99 3 0.03 1.03 Note: Add one to remove negative and subtract 1 from answer. 96.2 0.962 1.962 3.4 0.034 1.034 0 0 1 Geometric mean = 10.4% is the answer =10.4%

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</tbody>
Hi if my growth value return is not less than 0 but it is1.65827674. Do i have to 1+ too?

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