Average of a financial ratio: which average A financial ratio, like e.g., return on equity (ROE) is a division of two numbers ROE=return/equity.
If I analyse a whole sector then one can compute the ROE for each company in that sector and thus the distribution of ROE for that sector.
If I want to 'summarise' the distribution then I have the choice (ao) to (1) take the average of all ROE or (2) take (sum of all returns) / (sum of all equities).
Which one is preferable?
 A: It depends on what you are interested in. Assume that only two companies are in your sample and the ROE is defined as
$ROE  = \frac{Icome}{Equity}$
Company 1 has an ROE of 10 and company 2 has an ROE of 0.0001: 
$ROE_1 = \frac{1}{0.1} = 10$
$ROE_2 = \frac{1}{10000} = 0.0001$
Your second suggestion implies that the mean ROE is 
$\overline{ROE} = \frac{2}{10000.1} = 0.0002$
This would be the appropriate number if you needed to calculate the return on equity of a whole sector and you want to compare it to another sector. But the statistic would hide the fact that there are very profitable companies in your sector and maybe one badly managed company with huge equity dominates the mean. Or put differently, there would be no variance within a sector. If you have several sectors and each sector contains several companies I would actually use both statistics that you suggested. 
A: @HOSS_JFL, thanks a lot, this makes things clearer to me, do I get it right if I say that $\overline{ROE}$ as you defined it above is more like a ratio at an aggregated (sectoral) level ?
If this is the case than could I not have 'trouble' with some ratios like e.g. profit margin = $\frac{profit}{turnover}$, because in that case, summing all the turnovers of the companies in one sector may have ''double countings'': if a company sells to another company in the same sector, then the sales of the first one are counted in the turnover of the first company, but also in the turnover of the second company ?
