1. ## Average of averages?

Hello, I need some help with calculating average returns.

I have a set of 3 portfolios, and they have their own average annual returns. Now how do I calculate the average return for all the portfolios combined?

I have both arithmetic return and geometric return for the portfolios, can I for example take the arithmetic average of the geometric returns?

2. ## Re: Average of averages?

Hello, actionman777!

I have a set of 3 portfolios, and they have their own average annual returns.
Now how do I calculate the average return for all the portfolios combined?

In general, we must not take the average of a set of averages.

We have three portfolios, $A,B,C.$ and their average returns: . $\bar a,\:\bar b,\:\bar c$

$\text{The average }\bar a\text{ comes from:}$

. . $\text{the sum of the }a\text{'s, }\sum a_i\:\text{ divided by the number of }a\text{-scores, }n_a$

$\text{The average }\bar b\text{ comes from:}$

. . $\text{the sum of the }b\text{'s, }\sum b_i\:\text{ divided by the number of }b\text{-scores, }n_b$

$\text{The average }\bar c\text{ comes from:}$

. . $\text{the sum of the }c\text{'s, }\sum c_i\:\text{ divided by the number of }c\text{-scores, }n_c$

We must know all six of these values.

The overall average is: . $\frac{\sum a_i + \sum b_i + \sum c_i}{n_a+n_b+n_c}$